We use **dimensional analysis **as a fail proof process to convert from one unit to another.

Concept #1: Understanding Unit Conversions

**Unit conversions** deal with three basic areas of measurement: l**ength, volume** and **mass**.

Example #1: Every Saturday morning Gregor has to travel from Main Campus to his parents’ home. If his car gets 58.5 km/L how many L will his car need to travel the 19.3 miles?

Set up the problem to begin with your given information and to end with your unknown information.

Example #2: A backyard swimming pool holds 315 cubic yards (yd** ^{3}**) of water. What is the mass of the water in pounds?

Practice: An intravenous bag delivers medication to a patient at a rate of 2.75 drops a second. If a drop weighs 42 mg, how many grams of solution are delivered in 7.0 hours?

Concept #2: Examining Dimensional Analysis

**Dimensional Analysis** is simply a word problem dealing with unit conversions. It is design to begin with your given value and to end with the unknown value we need to find.

Example #3: Natty Light contains 4.2% alcohol. Steve from Kappa Epsilon Gamma, KEG for short, wants to get tanked tonight, and he is aiming to down at least 175 ml of alcohol in one night. If each can of Natty light contains 355 mL of beer, how many cans of Natty Light must Steve consume at minimum to reach his goal?

Example #4: A Volkswagen diesel engine consumes diesel at a rate of 25.83 L per hour. If the density of the diesel is 0.850 g/mL, what is the mass (in mg) of diesel needed to drive for a continuous 8.5 hours?

Practice: An acetaminophen suspension for toddlers contains 95 mg/0.85 mL suspension. The recommended dose is 22 mg/kg body weight. How many liters of this suspension should be given to a toddler weighing 30.5 lbs?

A penny has a thickness of approximately 1.0 mm. If you stacked Avogadro's number of pennies one on top of the other on Earth's surface, how far would the stack extend (in km)? [For comparison, the sun is about 150 million km from Earth and the nearest star (Proxima Centauri) is about 40 trillion km from Earth.]

Consider the stack of pennies in the previous problem. How much money (in dollars) would this represent? If this money were equally distributed among the world's population of 6.5 billion people, how much would each person receive? Would each person be a millionaire? Billionaire? Trillionaire?

What is dimensional analysis?

In Section 2.9, it was stated that 1 mol of sand grains would cover the state of Texas to several feet. Estimate how many feet by assuming that the sand grains are roughly cube-shaped, each one with an edge length of 0.10 mm. Texas has a land area of 268,601 square miles.

The diameter of the nucleus of an atom is approximately 1 × 10 -15 m. If 1 nm is equal to 10 Ångstroms, what is the diameter of the nucleus in Ångstroms?
A) 1 × 10 -5 Å
B) 1 × 10 -7 Å
C) 1 × 10 -23 Å
D) 1 × 10 -8 Å

A pascal is a newton per square meter and a newton is a kilogram-meter per second squared, while a joule is a newton-meter. What is a pascal-meter cubed?
A. newton
B. atmosphere
C. joule
D. Watt
E. volt

The density of iron is 7.86 g/cm3. What is its density in pounds per cubic inch (lb/in3)?

Distances over land are measured in statute miles (5280 ft), but distances over water are measured in nautical miles, where 1 nautical mile was originally defined as 1 minute of arc along an Earth meridian, or 1/21600 of the Earths circumference through the poles. A ships speed through the water is measured in knots, where 1 knot = 1 nautical mile per hour. Historically, the unit knot derived from the practice of measuring a ships speed by throwing a log tied to a knotted line over the side. The line had a knot tied in it at intervals of 47 ft. 3 in., and the number of knots run out in 28 seconds was counted to determine speed.How many feet are in a nautical mile?

Distances over land are measured in statute miles (5280 ft), but distances over water are measured in nautical miles, where 1 nautical mile was originally defined as 1 minute of arc along an Earth meridian, or 1/21600 of the Earths circumference through the poles. A ships speed through the water is measured in knots, where 1 knot = 1 nautical mile per hour. Historically, the unit knot derived from the practice of measuring a ships speed by throwing a log tied to a knotted line over the side. The line had a knot tied in it at intervals of 47 ft. 3 in., and the number of knots run out in 28 seconds was counted to determine speed.A league is defined as 3 nautical miles. The Mariana Trench, with a depth of 35798 feet, is the deepest point in the ocean. How many leagues deep is this?

Distances over land are measured in statute miles (5280 ft), but distances over water are measured in nautical miles, where 1 nautical mile was originally defined as 1 minute of arc along an Earth meridian, or 1/21600 of the Earths circumference through the poles. A ships speed through the water is measured in knots, where 1 knot = 1 nautical mile per hour. Historically, the unit knot derived from the practice of measuring a ships speed by throwing a log tied to a knotted line over the side. The line had a knot tied in it at intervals of 47 ft. 3 in., and the number of knots run out in 28 seconds was counted to determine speed.By international agreement, the nautical mile is now defined as exactly 1852 meters. By what percentage does this current definition differ from the original definition?

The Statue of Liberty is 151 ft tall. Calculate its height in meters.

Which is larger, a mile or a kilometer?

Which is larger, a centimeter or an inch?

A table is given below listing the heights of each member in a group. Using the table, perform the following calculations. Use appropriate rules for significant figures at each step.
Group Member
Height
Student 1
4 ft
6.0 in
Student 2
5 ft
6.0 in
Student 3
5 ft
6.0 in
Convert the height of Student 1 from feet and inches to meters.

A table is given below listing the heights of each member in a group. Using the table, perform the following calculations. Use appropriate rules for significant figures at each step.
Group Member
Height
Student 1
4 ft
6.0 in
Student 2
5 ft
6.0 in
Student 3
5 ft
6.0 in
Convert the height of Student 2 from feet and inches to meters.

A table is given below listing the heights of each member in a group. Using the table, perform the following calculations. Use appropriate rules for significant figures at each step.
Group Member
Height
Student 1
4 ft
6.0 in
Student 2
5 ft
6.0 in
Student 3
5 ft
6.0 in
Convert the height of Student 3 from feet and inches to meters.

Carry out the following conversions.How tall in meters is the Sears Tower in Chicago (1454 ft)?

The height of a horse is usually measured in hands instead of in feet, where 1 hand equals 1/3 ft (exactly).How tall (in centimeters) is a horse of 18.1 hands ?

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convertkm to ft

Perform the following conversions.0.0550 mi to m,

Perform each of the following conversions.153 cm to in

Perform each of the following conversions.111 mm to in

The Toyota Prius, a hybrid electric vehicle, has an EPA gas mileage rating of 52 mi/gal in the city.How many kilometers can the Prius travel on 16 liters of gasoline?

The diameter of a hydrogen atom is 212 pm. Find the length in kilometers of a row of 6.02 1023 hydrogen atoms.

The diameter of a ping pong ball is 4.0cm. Find the length in kilometers of a row of 6.02 1023 ping pong balls.

A length of #8 copper wire (radius = 1.63 mm) has a mass of 24.1 kg and a resistance of 2.061 ohm per km (Ω/km). What is the overall resistance of the wire?
(d (copper) = 8.96 g/cm3)

The distance from Earth to the Moon is approximately 240,000 mi.What is the distance from Earth to the Moon in meters?

The radius of an atom of gold (Au) is about 1.35 Å.Express this distance in nanometers (nm).

The radius of an atom of gold (Au) is about 1.35 Å.Express this distance in picometers (pm).

A 12-oz vanilla milkshake at a fast-food restaurant contains 551 Calories. What quantity of energy is this in joules?

What is a derived unit?

On a new Jekyll temperature scale, water freezes at 17 oJ and boils at 97 oJ. On another new temperature scale, the Hyde scale, water freezes at 0 oH and boils at 120 oH.If methyl alcohol boils at 84 oH, what is its boiling point on the Jekyll scale?

Force is defined as mass times acceleration. Starting with SI base units, derive a unit for force. Using SI prefixes suggest a convenient unit for the force resulting from a collision with a 10-ton trailer truck moving at 55 miles per hour. (Assume 1 second deceleration time)

A force of 2.26×104 N is applied to a divers face mask that has an area of 125 cm2 .Find the pressure in atm on the face mask. (1 atm = 101,325 Pa)

The SI unit of force is the Newton, derived from the base units by using the definition of force, F = ma. The dyne is a non-SI unit of force in which mass is measured in grams and time is measured in seconds. The relationship between the two units is 1 dyne = 10-5N.Find the unit of length used to define the dyne.

Use of the British thermal unit (Btu) is common in some
types of engineering work. A Btu is the amount of heat
required to raise the temperature of 1 lb of water by 1 oF.Calculate the number of joules in a Btu.

Convert this energy, 2.04×105 J to calories.

The total power used by humans worldwide is approximately 15 TW (terawatts). Sunlight striking Earth provides 1.336 kW per square meter (assuming no clouds). The surface area of Earth is approximately 197,000,000 square miles.What percentage of the Earths surface would we need to cover with solar energy collectors to power the planet for use by all humans? Assume that the solar energy collectors can only convert 10 % of the available sunlight into useful power.

A 1.0 ounce piece of chocolate contains 15 mg of caffeine, and a 6.0 ounce cup of regular coffee contains 105 mg of caffeine.How much chocolate would you have to consume to get as much caffeine as you would from 4.0 cups of coffee?

A bag of Hersheys Kisses contains the following information:
Serving size: 9pieces= 41grams
Calories per serving: 230.
Total fat per serving: 13 gThe bag contains 3.5 lb of Hersheys Kisses. How many Kisses are in the bag?

Volume relationships. The volume occupied by a cube 1 m on each edge is one cubic meter, 1 m3. Each cubic meter contains 1000 dm3. One liter is the same volume as one cubic decimeter, 1 L = 1 dm3. Each cubic decimeter contains 1000 cubic centimeters, 1 dm3 = 1000 cm3. One cubic centimeter equals one milliliter, 1 cm3 = 1 mL.How many 1-L bottles are required to contain 1 m3 of liquid?

Consider the jar of jelly beans in the photo. To get an estimate of the number of beans in the jar you weigh six beans and obtain masses of 3.15, 3.12, 2.98, 3.14, 3.02, and 3.09 g . Then you weigh the jar with all the beans in it, and obtain a mass of 2086 g . The empty jar has a mass of 655 g . Based on these data estimate the number of beans in the jar.

The diameter of a rubidium atom is 4.95 Å. We will consider two different ways of placing the atoms on a surface. In arrangement (a), all the atoms are lined up with one another. Arrangement (b) is called a close-packed arrangement because the atoms sit in the "depressions" formed by the previous row of atoms: Using arrangement (a), how many Rb atoms could be placed on a square surface that is 5.5 cm on a side?

The diameter of a rubidium atom is 4.95 Å. We will consider two different ways of placing the atoms on a surface. In arrangement (a), all the atoms are lined up with one another. Arrangement (b) is called a close-packed arrangement because the atoms sit in the "depressions" formed by the previous row of atoms: How many Rb atoms could be placed on a square surface that is 5.5 cm on a side, using arrangement (b)?

Nanotechnology, the field of trying to build ultrasmall structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would probably mimic red blood cells, the bodys oxygen transporters. For example, nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a persons bloodstream. If the person needed additional oxygen-due to a heart attack perhaps, or for the purpose of space travel-these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had an edge length of 24 nanometers.What is the minimum number of nanocontainers that a person would need in their bloodstream to provide 1 hours worth of oxygen?

A 40-lb container of peat moss measures 14in 20lb 30 gal. A 40-lb container of topsoil has a volume of 1.9 {
m gal}.How many bags of the peat moss are needed to cover an area measuring 13 ft by 21 ft to a depth of 2.1 in .?

How many 1-cm squares would it take to construct a square that is 3 m on each side?

The radius of an atom of gold (Au) is about 1.35 Å.How many gold atoms would have to be lined up to span 5.5 mm ?

A 1/12 inch thick lead sheet is used for protection from medical X-rays. If a single lead atom has a diameter 350 pm, how many atoms thick is the lead sheet?

A period at the end of sentence written with a graphite pencil has a diameter of 1.6 mm. How many carbon atoms would it take to line up across the period, if a single carbon atom has a diameter of 150 pm?

A cube has an edge length of
8
cm.If it is divided into 1-cm cubes, how many 1-cm cubes are there?

Consider an Avogadro’s number of pennies stacked one on top of the other.How much money (in dollars) would this represent?

Consider an Avogadro’s number of pennies stacked one on top of the other.If this money were equally distributed among the worlds population of 7.0 billion people, how much would each person receive?

Consider an Avogadro’s number of pennies stacked one on top of the other.Would each person be a millionaire? A billionaire? A trillionaire?

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly 1 ft. An acre is 4840 yd2. An acre-foot is enough water to supply two typical households for 1.00 yr.If desalinated water costs $
2100 per acre-foot, how much does desalinated water cost per liter?

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly 1 ft. An acre is 4840 yd2. An acre-foot is enough water to supply two typical households for 1.00 yr.How much would it cost one household per day if it were the only source of water?

A large tanker truck for carrying gasoline has a capacity of 3.6×104 L .If the retail price of gasoline is $3.00 per gallon, what is the value of the trucks full load of gasoline?

The value of the Euro is currently $1.36 U.S. and the price of 1 liter of gasoline in France is 1.43 Euro.What is the price of 1 gallon of gasoline in U.S. dollars in France?

The average U.S. farm occupies 435 acres.How many square miles is this? (1 acre = 43,560 ft2, 1 mile = 5280 ft).

Total U.S. farmland occupies 954 million acres.How many square miles is this? (1 acre = 43,560 ft2, 1 mile = 5280 ft).

Total U.S. farmland occupies 954 million acres.Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is farmland?

A 12-inch pizza has an area of 113.097 square inches (in2). What is the area in units of cm2? (1 inch = 2.54 cm, exactly)

In 2009, a team from Northwestern University and Western Washington University reported the preparation of a new "spongy" material composed of nickel, molybdenum, and sulfur that excels at removing mercury from water. The density of this new material is 0.20 g/cm3, and its surface area is 1242 m2 per gram of material.Calculate the surface area for a 35.0 -mg sample of this material.

The physical fitness of athletes is measured by "VO2 max," which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a VO2 max of 45 mL
O2/kg body mass/min, but a world-class male athlete can have a VO2 max reading of 88.0 mL
O2/kg body mass/min.Calculate the volume of oxygen, in mL, consumed in 1 hr by an average man who weighs 186 lbs and has a VO2 max reading of 47.6 mL
O2/kg body mass/min.

The lung capacity of the blue whale is 5100 L . Convert this volume into gallons.

Which is larger, a liter or a quart?

One inch is equal to 2.54 cm. The below image shows a line that is 1 in
long with centimeter segments drawn on the line. A cube that is 1 in
on each side with lines on each face of the cube that are 1 cm
apart is also shown.
How many cubic centimeters are there in 1 in3?

The volume of water used for crop irrigation is measured in acre-feet, where 1 acre-foot is the amount of water needed to cover 1 acre of land to a depth of 1 ft.If there are 640 acres per square mile, how many cubic feet of water are in 4.0 acre-feet ?

The volume of water used for crop irrigation is measured in acre-feet, where 1 acre-foot is the amount of water needed to cover 1 acre of land to a depth of 1 ft.How many acre-feet are in Lake Erie (total volume=116mi3)?

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convertin.3 to cm3

Perform the following conversions.1.90 $/gal
to dollars per liter,

Perform each of the following conversions.3.6 L to qt

How many liters of wine can be held in a wine barrel whose capacity is 33 gal ?

An infant acetaminophen suspension contains 80 mg/0.80 mL
suspension. The recommended dose is 15 mg/kg body weight.How many mL of this suspension should be given to an infant weighing 16 lb ? (Assume two significant figures.)

A large tanker truck for carrying gasoline has a capacity of 3.6×104 L .What is the tankers capacity in gallons?

Assuming the diameters of the nucleus and atom are 10-4
Å and 1 - 5 Å correspondingly, what fraction of the volume of the atom is taken up by the nucleus?

Nanotechnology, the field of trying to build ultrasmall structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would probably mimic red blood cells, the bodys oxygen transporters. For example, nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a persons bloodstream. If the person needed additional oxygen-due to a heart attack perhaps, or for the purpose of space travel-these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had an edge length of 24 nanometers.What is the minimum volume occupied by the number of nanocontainers computed in part D?

A can of soda has a volume of 355
mL. What is the volume expressed in SI units of m3?

The radius of an atom of gold (Au) is about 1.35 Å.If the atom is assumed to be a sphere, what is the volume in cm3
of a single Au atom?

A sample of gaseous neon atoms at atmospheric pressure and 0 oC contains 2.691022 atoms per liter. The atomic radius of neon is 69 pm.What fraction of the space is occupied by the atoms themselves?

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, which are principally N2 (~79%) and O2 (~20%). In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas.Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "NOx" gases. In 2004, the United States emitted an estimated 20 million short tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? Note that one short ton equals 2,000 lb.

Which is larger, a gram or an ounce?

Carry out the following conversions.How many grams of meat are in a quarter-pound hamburger (0.25 lb)?

Administration of digitalis, a drug used to control atrial fibrillation in heart patients, must be carefully controlled because even a modest overdosage can be fatal. To take differences between patients into account, drug dosages are prescribed in terms of mg/kg body weight. Thus, a child and an adult differ greatly in weight, but both receive the same dosage per kilogram of body weight.At a dosage of 21 g/kg body weight, how many milligrams of digitalis should a 170 lb patient receive?

The concentration of carbon monoxide in an urban apartment is 48 g/m3. What mass of carbon monoxide in grams is present in a room measuring 12.0
imes ;
12.5
imes ;
21.5
ft?

By using estimation techniques, determine which of the following is the heaviest and which is the lightest: a 5-lb bag of potatoes, a 5-kg bag of sugar, or 1 gal of water (density = 1.0 g/mL).

The recommended adult dose of Elixophyllin, a drug used to treat asthma, is 6 mg/kg of body mass. Calculate the dose in milligrams for a 180 lb person.

When
the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee (4 cups = 1 qt). How many kg
of coffee are required to produce 250 cups of coffee?

A backyard swimming pool holds 180 cubic yards (yd3 ) of water.What is the weight of the water in pounds?

An iceberg has a volume of 7655 cubic feet.What is the mass of the ice (in kg) composing the iceberg?

Gemstones are weighed in carats, with 1 carat = 200 mg (exactly).What is the mass in grams of the Hope Diamond, the worlds largest blue diamond at 44.4 carats?

Gemstones are weighed in carats, with 1 carat = 200 mg (exactly).What is this mass in ounces?

Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food and Drug Administration (FDA) recommends that adults consume less than 2.40 g of sodium per day. A particular snack mix contains 1.21 g of salt per 100 g of the mix.What mass of the snack mix can you consume and still be within the FDA limit?

Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% galena by mass.If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 6.00 cm radius?

At 20 oC (approximately room temperature) the average velocity of N2 molecules in air is 1050 mph.What is the average speed in m/s?

Perform the following conversions.5.50 days to s,

There are exactly 60 seconds in a minute, exactly 60 minutes in an hour, exactly 24 hours in a mean solar day, and 365.24 solar days in a solar year.How many seconds are in a solar year? Give your answer with the correct number of significant figures.

A 130 mL sample of water at 290.2 K was heated for 9 min , 31 s so as to give a constant temperature increase of 3.0 oF/min.What is the final temperature of the water in degrees Celsius?

Ocean currents are measured in Sverdrups (sv) where 1 sv=109 m3/s. The Gulf Stream off the tip of Florida, for instance, has a flow of 35 sv.What is the flow of the Gulf Stream in milliliters per minute?

Ocean currents are measured in Sverdrups (sv) where 1 sv=109 m3/s. The Gulf Stream off the tip of Florida, for instance, has a flow of 35 sv.How much time is required for 1 petaliter (PL, 1PL=1015L) of seawater to flow past a given point?

The world record for the womens outdoor 20,000 meter run, set in 2000 by Tegla Loroupe, is 1:05:26.6 (seconds are given to the nearest tenth).What was her average speed, expressed in miles per hour with the correct number of significant figures? (Assume that the race distance is accurate to 5 significant figures.)

A Big Mac hamburger from McDonalds contains 540 Calories.For how many hours could the amount of energy in a Big Mac light a 100 watt lightbulb? (1 watt = 1 J/s)

In August 2011, the Juno spacecraft was launched from Earth
with the mission of orbiting Jupiter in 2016. The closest distance
between Jupiter and Earth is 391 million miles.If it
takes 5.0 years for Juno to reach Jupiter, what is its average
speed in mi/hr over this period?

The worlds record in the 100m dash is 9.69s and in the 100 yard dash is 9.21s.Find the speed in mi/h of the runner who set first record (9.69s).

The worlds record in the 100m dash is 9.69s and in the 100 yard dash is 9.21s.Find the speed in mi/h of the runner who set second record (9.21s).

The distance from Earth to the Moon is approximately 240,000 mi.The peregrine falcon has been measured as traveling up to 350 km/hr in a dive. If this falcon could fly to the Moon at this speed, how many seconds would it take?

The distance from Earth to the Moon is approximately 240,000 mi.The speed of light is 3.00 108m/s. How long does it take for light to travel from Earth to the Moon and back again?

A runner wants to run
11.1
km. Her running pace is
7.6
miperhour.How many minutes must she run?

Distances over land are measured in statute miles (5280 ft), but distances over water are measured in nautical miles, where 1 nautical mile was originally defined as 1 minute of arc along an Earth meridian, or 1/21600 of the Earths circumference through the poles. A ships speed through the water is measured in knots, where 1 knot = 1 nautical mile per hour. Historically, the unit knot derived from the practice of measuring a ships speed by throwing a log tied to a knotted line over the side. The line had a knot tied in it at intervals of 47 ft. 3 in., and the number of knots run out in 28 seconds was counted to determine speed.The northern bluefin tuna can weigh up to 1500 pounds and can swim at speeds up to 48 miles per hour. How fast is this in knots?

A bumblebee flies with a ground speed of 15.1 m/s . Calculate its speed in km/h.

Bamboo can grow up to 60.0 cm/day. Convert this growth rate into inches per hour.

In the U.S., the emissions limit for carbon monoxide in motorcycle engine exhaust is 12.0 g of carbon monoxide per kilometer driven.
What is this limit expressed in mg per mile with the correct number of significant figures?

Perform the following conversions.0.510 in/ms
to km/hr,

Perform the following conversions.23.50 gal/min
to L/s,

If an automobile is able to travel 400 km on 47.5 L of gasoline, what is the gas mileage in miles per gallon?

The density of ethanol is 0.789 g/cm3 .What is its density in pounds per cubic inch (lb/in3)?

The density of polystyrene, a plastic commonly used to make CD cases and transparent cups is 0.037
lbs/in3.Calculate the density in units of g/cm3.

The density of polypropylene, a plastic commonly used to make bottle caps, yogurt containers, and carpeting, is 0.55
oz/in3.Calculate the density in units of g/cm3.

The distance from Earth to the Moon is approximately 240,000 mi.Earth travels around the Sun at an average speed of 29.783 km/s. Convert this speed to miles per hour.

A certain European automobile has a gas mileage of
16 km/L.What is the gas mileage in miles per gallon?

The Honda Insight, a hybrid electric vehicle, has an EPA gas mileage rating of 57 mi/gal in the city. How many kilometers can the Insight travel on the amount of gasoline that would fit in a soda pop can? The volume of a soda pop can is 355 mL.

a. Calculate the mass of ethanol in 1.50 qt of ethanol. (See Table 1.5.)

b. Calculate the mass of mercury in 3.5 in3 of mercury. (See Table 1.5.)

Assume the ideal gas constant, R, has a value of .08206 (L * atm)/(mol * K). Convert this value into expressions for R in terms of J/(mol* K), (cubic meters * Pa)/(mol * K), (L * bar)/(mol * K), and J/(molecule * K).

The diameter of a hydrogen atom is 212 pm. Find the length in kilometers of a row of 6.02 X 1023 hydrogen atoms. The diameter of a ping pong ball is 4.0 cm. Find the length in kilometers of a row of 6.02 X 1023 ping pong balls.

Table salt contains 39.33 g of sodium per 100 g of sail. The U.S. Food and Drug Administration (FDA) recommends that adults consume less than 2.40 g of sodium per day. A particular snack mix contains 1.25 g of salt per 100 g of the mix. What mass of the snack mix can you consume and still be within the FDA limit? (Assume three significant figures for 100 g.)

In the year 1900, the total area of the mountain covered by glaciers was 1.60 km 2. What is this surface area with units cm2?A) 1.60 x 1010 cm2B) 1.60 x 105 cm2C) 1.60 x 10-10 cm2D) 1.60 x 10-5 cm2

The recommended adult dose of a drug used to treat asthma is 10.0 mg/kg of body mass. Calculate the dose in mg for a 200-lb person . (1 kg = 2.205 lb)A. 0.110 mgB. 907 mgC. 4.41 mgD. 2.00 x 103 mg

The ebola virus is structured like a long filament that ranges from 974 to 1086 nm in length. If length of a virus filament is found to be 1046 nm, what would the the length be in cm?a. 1.046 x 1010 cmb. 1.046 x 10 -4 cmc. 1.046 x 1014 cmd. 1.046 x 10 -8 cme. 1.046 x 10-3 cm

The man in the wilderness said to me, How many buckets could empty the sea? Who-who’s that crying in the cold night air? Who-who? Who-who? Who-who goes there? How many buckets could empty the sea? Three times ten to the power of twenty Is the number of gallons in all the oceans. According to the best of the mathematicians. Now if each bucket is of good parameters, say five hundred cubic centimeters, how many moles of these do we need to completely empty the sea. And where will we put all that water? Never mind that, my little daughter. Just tell me how many moles please of buckets to buy, to empty the seas. (1 gal=3.78 L) a) 4 x 10-3b) 1 x 1045c) 2 x 1015d) 2 x 1021e) none of the given answers is even within an order of magnitude

In ancient times, the closest thing to a formal unit area was the yoke (Hebrew semed) which referred to the amount of land that a pair of yoked oxen could plough in a single day. The standard estimate of this was usually taken as equal to 6480 square cubits. How many acres is this? (1 cubit = 18 units, 12 inches = 1 foot, 1 acre = 43,560 square feet)a) 7.9b) 0.25c) 0.33d) 10e) none of the given answers is close.

Imagine that you took a road trip. Based on the information in the table, what was the average speed of your car?Express your answer to three significant figures and include the appropriate units. Use mi as an abbreviation for miles, and h for hours, or mph can be used to indicate miles per hour.

If you had a mol of U.S. dollar bills and equally distributed the money to all of the people of the world, how rich would every person be? Assume a world population of 6 billion.

If you had a mole of U.S. dollar bills and equally distributed the money to all of the people of the world, how rich would every person be? Assume a world population of 7 billion.

Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a 100 ft by 86 ft ceiling with gold leaf that is five-millionths of an inch thick. The density of gold is 19.32 g/cm3, and gold costs $ 953 per troy ounce (1 troy ounce = 31.1034768 g{
m g}). How much will it cost the architect to buy the necessary gold?

The density of methanol is 0.7918 g/mL. Calculate the mass of 89.9 mL of liquid in milligrams.

A student in their chemistry lab is asked to measure out the area of the classroom and report the answer in m2. Using a measuring tape, the student found that the room is 18.8 by 15.5 ft in area, What should the student report for the area in m2? ( 1 in. = 2.54 cm )a. 27.1 m2b. 291 m2c. 88.8 m2d. 5.20 m2e. 17.1 m2

How many liters of air are in a room that measures 10.0 ft x 11.0 ft and has an 8.00 ft ceiling?

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (c) km to ft

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (d) in.3 to cm3

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (c) mi to km

a. There are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour. Use these data to determine how many minutes are in a month.

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (d) ft3 to L.

b. Now use the following data to calculate the number of minutes in a month: 24 hours per day, 60 minutes per hour, 7 days per week, and 4 weeks per month.

Perform the following conversions: (a) 0.076 L to mL, (b) 5.0 x 10 -8 m to nm, (c) 6.88 x 105 ns to s, (d) 0.50 lb to g, (e) 1.55 kg/m 3 to g/L, (f) 5.850 gal/hr to L/s.

Why are these answers different? Which (if any) is more correct? Why?

(a) A bumblebee flies with a ground speed of 15.2 m/s. Calculate its speed in km/hr.

(b) The lung capacity of the blue whale is 5.0 x 10 3 L. Convert this volume into gallons.

(c) The Statue of Liberty is 151 ft tall. Calculate its height in meters.

(d) Bamboo can grow up to 60.0 cm/day. Convert this growth rate into inches per hour.

(a) The speed of light in a vacuum is 2.998 x 10 8 m/s. Calculate its speed in miles per hour.

(b) The Sears Tower in Chicago is 1454 ft tall. Calculate its height in meters.

(c) The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of 3,666,500 m3. Convert this volume to liters and express the result in standard exponential notation.

The iodide ion is a dietary mineral essential to good nutrition. In countries where potassium iodide is added to salt, iodine deficiency (or goiter) has been almost completely eliminated. The recommended daily allowance (RDA) for iodine is 150 µg/day. How much potassium iodide (76.45% I) should you consume if you want to meet the RDA?

(d) An individual suffering from a high cholesterol level in her blood has 242 mg of cholesterol per 100 mL of blood. If the total blood volume of the individual is 5.2 L, how many grams of total blood cholesterol does the individual’s body contain?

The American Dental Association recommends that an adult female should consume 3.0 mg of fluoride (F–) per day to prevent tooth decay. If the fluoride is consumed in the form of sodium fluoride (45.24% F), what amount of sodium fluoride contains the recommended amount of fluoride?

Perform the following conversion: (a) 5.00 days to s

Perform the following conversion: (b) 0.0550 mi to m,

Perform the following conversion: (c) $1.89/gal to dollars per liter

Perform the following conversion: (d) 0.510 in./ms to km/hr

Perform the following conversion: (e) 22.50 gal/min to L/s

Perform the following conversion: (f) 0.02500 ft3 to cm3.

Carry out the following conversion: (a) 0.105 in. to mm

Carry out the following conversion: (b) 0.650 qt to mL

Carry out the following conversion: (c) 8.75 μm/s to km/hr

A planet is travelling around the sun at 68.2 miles/hour. What will be the speed of the planet in m/s?a. 30.5 m/sb. 3.05 x 10-5 m/sc. 11.8 m/sd. 3.95 x 108 m/se. 1.52 x 108 m/s

How many milliseconds are there in 2.50 minutes?a. 150 msb. 9.0 x 103 msc. 1.5 x 105 msd. 2.5 x 103 mse. 41.7 ms

Carry out the following conversion: (d) 1.955 m3 to yd3

An olympic runner training for the marathon ran 9.308 miles in one hour. What was his speed in meters per second? (1 mile = 1.609 km)a. 15.0 m/sb. 4.16 m/sc. 1.61 m/sd. 2.59 m/se. 53.9 m/s

Carry out the following conversion: (e) $3.99/lb to dollars per kg

Carry out the following conversion: (f) 8.75 lb/ft3 to g/mL

(a) How many liters of wine can be held in a wine barrel whose capacity is 31 gal?

(b) The recommended adult dose of Elixophyllin®, a drug used to treat asthma, is 6 mg/kg of body mass. Calculate the dose in milligrams for a 150-lb person.

(b) The recommended adult dose of Elixophyllin®, a drug used to treat asthma, is 6 mg/kg of body mass. Calculate the dose in milligrams for a 185-lb person.

(c) If an automobile is able to travel 254 mi on 11.2 gal of gasoline, what is the gas mileage in km/L?

You are driving 65 mi/h and take your eyes off the road for “just a second.” What distance (in feet) do you travel in this time?

(c) If an automobile is able to travel 400 km on 47.3 L of gasoline, what is the gas mileage in miles per gallon?

(d) A pound of coffee beans yields 50 cups of coffee (4 cups = 1 qt). How many milliliters of coffee can be obtained from 1 g of coffee beans?

(d) When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee (4 cups = 1 qt). How many kg of coffee are required to produce 200 cups of coffee?

If an object has a density of 8.65 g/cm3, what is its density in units of kg/m3?a. 8.65 x 10-3 kg/m3b. 8.65 x 10-7 kg/m3c. 8.65 x 103 kg/m3d. 8.65 x 101 kg/m3e. 8.65 x 10-1 kg/m3

(a) If an electric car is capable of going 225 km on a single charge, how many charges will it need to travel from Boston, Massachusetts, to Miami, Florida, a distance of 1486 mi, assuming that the trip begins with a full charge?

(a) If an electric car is capable of going 225 km on a single charge, how many charges will it need to travel from Seattle, Washington, to San Diego, California, a distance of 1257 mi, assuming that the trip begins with a full charge?

(b) If a migrating loon flies at an average speed of 14 m/s, what is its average speed in mi/hr?

(c) What is the engine piston displacement in liters of an engine whose displacement is listed as 450 in.3?

The painting American Gothic, by Grant Wood, is a rectanglar shaped canvas with a length of 29 inches and width of 24 inches. What is the area of the painting in cm? Recal 1 inch = 2.54 cmA. 1.3 X 102 cm2B. 4.5 X 103 cm2C. 2.7 X 102 cm2D. 1.1 X 102 cm2E. 1.8 X 103 cm2

(d) In March 1989 the Exxon Valdez ran aground and spilled 240,000 barrels of crude petroleum off the coast of Alaska. One barrel of petroleum is equal to 42 gal. How many liters of petroleum were spilled?

The concentration of carbon monoxide in an urban apartment is 48 μg/m 3. What mass of carbon monoxide in grams is present in a room measuring 9.0 x 14.5 x 18.8 ft?

The concentration of carbon monoxide in an urban apartment is 48 μg/m 3. What mass of carbon monoxide in grams is present in a room measuring 11.0 ft x 11.5 ft x 20.5 ft?

The concentration of carbon monoxide in an urban apartment is 48 mg/m 3. What mass of carbon monoxide in grams is present in a room measuring 10.6 ft x 14.8 ft x 20.5 ft?

If the walls in a room are 955 square feet in area, and a gallon of paint covers 15 square yards, how many gallons of paint are needed for the room? (3 ft = 1 yd)A) 7.0 gallonsB) 2.3 gallonsC) 21 gallonsD) 47 gallonsE) 24 gallons

Your infant child weighs 13lbs and has a fever. You want to give the baby a dose of Tylenol that contains 160mg acetaminophen/5 mL, but administering too much could cause damage to the child's liver. Your doctor says you can give your child 14 mg acetaminophen/kg. What volume (mL) of Tylenol should you give your baby? Note: 1kg =2.2 lbsA. 2.6 mLB. 13 mLC. 0.013 mLD. 1.0 mL

If an object has a density of 8.65 g/cm3 what is its density in units of kg/m3?

Convert $2.99/kg to dollars per Ib.

The distance from Earth to the Moon is approximately 240,000 mi. (b) The peregrine falcon has been measured as traveling up to 350 km/hr in a dive. If this falcon could fly to the Moon at this speed, how many seconds would it take?

A mass of mercury occupies 0.750 L. What volume would an equal mass of ethanol occupy? The density of mercury is 13.546 g/mL and the density of ethanol is 0.789 g/mL.A) 0.0437 LB) 22.9 LC) 12.9 LD) 0.0777 L

Convert:a. 154 cm to in

Convert:c. 3.5 L to qt

Because of the high heat and low humidity in the summer in Death Valley, California, a visitor requires about one quart of water for every two miles traveled on foot. If the density of water is 0.990 g/mL at 45°C, how many kilograms of water are required for a person to walk 30 kilometers in Death Valley?A) 8.7 kgB) 70 kgC) 7.0 × 10 2 kgD) 3.5 × 10 2 kg

Convert:d. 109 mm to in

Convert:a. 1.4 in to mm

Convert:b. 116 ft to cm

Convert:c. 1845 kg to lb

Convert:d. 815 yd to km

A runner wants to run 100.0 km. She knows that her running pace is 7.5 miles per hour. How many minutes must she run?

A European automobile has a gas mileage of 17 km/L. What is the gas mileage in miles per gallon?

Perform each unit conversion.27.8 L to cm3

A cyclist rides at an average speed of 18 miles per hour. If she wants to bike 212 km, how long (in hours) must she ride?

A gas can holds 5.0 gallons of gasoline. What is this quantity in cm 3?

What amount of energy is required to change a spherical drop of water with a diameter of 2.20 mm to three smaller spherical drops of equal size? The surface tension, γ, of water at room temperature is 72.0 mJ/m2.

The density of vegetable oil is 0.92 g/mL. There are 3.8 L in a gallon. There are 2.2 pounds (lb) in a kilogram (kg). How much in pounds does a gallon of vegetable oil weigh?A) Less than 7.5B) 7.5 to 7.6C) 7.6 to 7.7D) 7.7 to 7.8E) More than 7.8

The diameter of a hydrogen atom is 212 pm. Find the length in km of a row of 6.02 x 1023 hydrogen atoms. 1 pm = 10 -12 m.A. 2.41 x 1019 kmB. 1.28 x 1011 kmC. 3.60 x 1012 kmD. 5.59 x 1023 km

The average U.S. farm occupies 435 acres. How many square miles is this? (1 acre = 43,560 ft2, 1 mile = 5280 ft)

Total U.S. farmland occupies 954 million acres. How many square miles is this? (1 acre= 43,560ft2, 1 mile= 5280ft). Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is farmland?

An acetaminophen suspension for infants contains 80 mg/0.80 mL suspension. The recommended dose is 15 mg/ kg body weight. How many mL of this suspension should be given to an infant weighing 14 lb? (Assume two significant figures.)

How many inches per minute (in./min) are in 4.65 x 107 Ångstrom per millisecond (Å/ms)?A. 1.10 x 106 in./minB. 1.10 x 104 in./minC. 11.0 in./minD. 1.10 x 10-2 in./minE. None of these choices are correct.

Perform the following unit conversions.a. 908 oz to kilograms

Perform the following unit conversions.b. 12.8 L to gallons

Perform the following unit conversions.c. 125 mL to quarts

How many minutes are in 2.5 hours?

Perform the following unit conversions.d. 2.89 gal to milliliters

The average person breathes 14 times per minute. Each breath is about 350 mL. The exhaled air is about 5.3% carbon dioxide. In all about 5,300 moles (44 g in a mole) of carbon dioxide are exhaled per person per year. If the human population of the earth is 7.2 x 109, how many kilograms of carbon dioxide are released into the atmosphere by all people in a year?

Perform the following unit conversions.e. 4.48 lb to grams

Perform the following unit conversions.f. 550 mL to quarts

An ibuprofen (C13H18O2) suspension for infants contains 100 mg/5.0 mL suspension. The recommended dose is 10 mg/kg body weight. How many mL of this suspension should be given to an infant weighing 18 lb??

Use the following exact conversion factors to perform the stated calculations:5 1/2 yards = 1 rod40 rods = 1 furlong8 furlongs = 1 milea. The Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers?

Use the following exact conversion factors to perform the stated calculations:5 1/2 yards = 1 rod40 rods = 1 furlong8 furlongs = 1 mileb. A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to 10,000 m2. In the English system, land is often measured in acres (1 acre = 160 rod2). Use the exact conversions and those given in Exercise 39 to calculate the following.a. 1 ha = ________ km2.

In the television series, The Office, Dwight K. Schrute, acting as Regional Manager of Dunder Mifflin Paper Company, awards Stanley Hudson 1 Schrute buck for answering a question correctly. 3.35 Schrute bucks is equivalent to 80.103 unicorns and 84.2 leprechauns is equivalent to 4.10 unicorns. How many Schrute bucks would Stanley have if he was awarded 1.98 leprechauns?

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to 10,000 m2. In the English system, land is often measured in acres (1 acre = 160 rod2). Use the exact conversions and those given in Exercise 39 to calculate the following.b. The area of a 5.5-acre plot of land in hectares, square meters, and square kilometers.

There are exactly 60 seconds in a minute. there are exactly 60 minutes in an hour, there are exactly 24 hours in a mean solar day, and there are 365.24 solar days in a solar year. Find the number of seconds in a solar year. Be sure to give your answer with the correct number of significant figures.

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to 10,000 m2. In the English system, land is often measured in acres (1 acre = 160 rod2). Use the exact conversions and those given in Exercise 39 to calculate the following.c. A lot with dimensions 120 ft by 75 ft is to be sold for $6500. What is the price per acre? What is the price per hectare?

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to 10,000 m2. In the English system, land is often measured in acres (1 acre = 160 rod2). Use the exact conversions and those given in Exercise 43 to calculate the following.a. 1 ha = ________ km 2.

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to 10,000 m2. In the English system, land is often measured in acres (1 acre = 160 rod2). Use the exact conversions and those given in Exercise 43 to calculate the following.b. The area of a 5.5-acre plot of land in hectares, square meters, and square kilometers.

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to 10,000 m2. In the English system, land is often measured in acres (1 acre = 160 rod2). Use the exact conversions and those given in Exercise 43 to calculate the following.c. A lot with dimensions 120 ft by 75 ft is to be sold for $6500. What is the price per acre? What is the price per hectare?

Precious metals and gems are measured in troy weights in the English system:24 grains = 1 pennyweight (exact)20 pennyweight = 1 troy ounce (exact)12 troy ounces = 1 troy pound (exact)1 grain = 0.0648 gram1 carat = 0.200 gram a. The most common English unit of mass is the pound avoirdupois. What is one troy pound in kilograms and in pounds?

The speed of light is 3.0 x 108 m/s. How many milliseconds does it take for a light signal from earth to reach and return from a satellite that is in orbit 30 miles above the earth?A) 320 msec B) 16 msec C) 32 msec D) 0.32 msec E) 0.16 msec

Precious metals and gems are measured in troy weights in the English system:24 grains = 1 pennyweight (exact)20 pennyweight = 1 troy ounce (exact)12 troy ounces = 1 troy pound (exact)1 grain = 0.0648 gram1 carat = 0.200 gram b. What is the mass of a troy ounce of gold in grams and in carats?

On the planet Tatooine, the unit of length is the zither which is defined by the relationship 7.50 cm = 1 zither. A distance of 100 meters would be _________ zithers.a. 133b. 266c. 750d. 1.33 X 103e. 7.5 X 104

A car averages 35 miles per gallon. How many liters of gasoline will be needed for a trip of 450 kilometers? Some Conversion factors which may be helpful are: 1 qt = 946 mL; 4qts = 1 gallon; 1 mile = 1.609 km;a. 8 Lb. 25 Lc. 30 Ld. 34 Le. 40 L

For a pharmacist dispensing pills or capsules, it is often easier to weigh the medication to be dispensed rather than to count the individual pills. If a single antibiotic capsule weighs 0.65 g, and a pharmacist weighs out 15.6 g of capsules, how many capsules have been dispensed?

A children’s pain relief elixir contains 80. mg acetaminophen per 0.50 teaspoon. The dosage recommended for a child who weighs between 24 and 35 lb is 1.5 teaspoons. What is the range of acetaminophen dosages, expressed in mg acetaminophen/kg body weight, for children who weigh between 24 and 35 lb?

If an object has a density of 8.65 g/cm3, what is its density in units of kg/m3?A) 8.65 × 10-3 kg/m3B) 8.65 × 10-7 kg/m3C) 8.65 × 103 kg/m3D) 8.65 × 101 kg/m3E) 8.65 × 10-1 kg/m3

Science fiction often uses nautical analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor 1.71, what is its speed in knots and in miles per hour? (Warp 1.71= 5.00 times the speed of light; speed of light = 3.00 x 108 m/s; 1 knot = 2000 yd/h, exactly.)

The world record for the hundred meter dash is 9.77 s. What is the corresponding average speed in units of m/s, km/h, ft/s, and mi/h? At this speed, how long would it take to run 1.00 x 102 yards?

The world record for the hundred meter dash is 9.74 s. What is the corresponding average speed in units of m/s, km/h, ft/s, and mi/h? At this speed, how long would it take to run 1.00 x 102 yards?

Which of the following represents the LARGEST mass?a) 1.20 x 107 mgb) 120 kgc) 12.0 tond) 1200 lbe) 1.20 metric ton

The world record for the hundred meter dash is 9.58 s. What is the corresponding average speed in units of m/s, km/h, ft/s, and mi/h? At this speed, how long would it take to run 1.00 x 102 yards?

Would a car traveling at a constant speed of 65 km/h violate a 40. mi/h speed limit?

You pass a road sign saying “New York 112 km.” If you drive at a constant speed of 65 mi/h, how long should it take you to reach New York? If your car gets 28 miles to the gallon, how many liters of gasoline are necessary to travel 112 km?

If you put 8.21 gallons of gas in your car and it cost you a total of $17.25, what is the cost of gas per liter in Canadian dollars? Assume 0.82 dollar U.S. = 1.00 dollar Canadian.

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost 2.45 euros per kilogram. Given that 1 euro is equivalent to approximately $1.46, calculate what a pound of peaches will cost in dollars.

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost 2.45 euros per kilogram. Given that 1 euro is equivalent to approximately $1.32, calculate what a pound of peaches will cost in dollars.

The human nose is so sensitive to vanillin (used to flavor vanilla ice cream) that it can detect it at a concentration of 200 picograms/L of air. The current market price for 50.0 grams of vanillin is $148. Determine the cost to supply enough vanillin so that the aroma could be detected in a large aircraft hanger with a volume of 6.40 x 109 ft3.a. $ 107b. $ 124c. $ 1.07 x 108d. $ 0.115e. $ 35.9

There are currently 7.37 billion people in the world. If we distributed 1 mole of pennies to everyone evenly, how many dollars would each person get?a). 8.17 Trillion Dollarsb). 817 Billion Dollarsc). 81.7 Thousand Dollarsd). 817 Million Dollarse). 81.7 Trillion Dollars

The value of the Euro is currently $1.35 U.S. and the price of 1 liter of gasoline in France is 0.97 Euro. What is the price of 1 gallon of gasoline in U.S. dollars in France?

Diamonds are measured in carats, and 1 carat = 0.200 g. The density of diamond is 3.51 g/cm3. What is the volume of a 5.0-carat diamond?

Diamonds are measured in carats, and 1 carat = 0.200 g. The density of diamond is 3.51 g/cm3.b. What is the mass in carats of a diamond measuring 2.8 mL?

The volume of a diamond is found to be 2.8 mL. What is the mass of the diamond in carats?

Ethanol and benzene dissolve in each other. When 100. mL of ethanol is dissolved in 1.00 L of benzene, what is the mass of the mixture? (See Table 1.5.)

The mountain is 19, 341 feet tall. Convert this height to the SI unit for length. To get you started, 1km = 3280.84 ft.A) 5.8951 kmB) 6.3455 x 107 kmC) 5895.1 mD) 6.3455 x 108 m

An iceberg has a volume of 7655 cubic feet. What is the mass of the ice (in kg) composing the iceberg?

A small speck of carbon the size of a pinhead contains about 4×1019 atoms, the diameter of a carbon atom is 1.5 10-10 m, and the circumference of the earth at the equator is 40,075 km.How many times around the earth would the atoms from this speck of carbon extend if they were laid side by side?

Make the conversion indicated in each of the following: (a) the men’s world record long jump, 29 ft 4¼ in., to meters

Make the conversion indicated in each of the following:(b) the greatest depth of the ocean, about 6.5 mi, to kilometers

Perform each of the following conversions.1.6 in to mm

Perform each of the following conversions.117. ft to cm

Make the conversion indicated in each of the following:(a) the length of a soccer field, 120 m (three significant figures), to feet

Use the following exact conversion factors to perform the stated calculations:51/2 yards = 1 rod40 rods = 1 furlong8 furlongs = 1 milea. The Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers?

Perform each of the following conversions.825 yd to km

A penny has a thickness of approximately 1.0 mm.If you stacked Avogadros number of pennies one on top of the other on Earths surface, how far would the stack extend (in kilometers)? [For comparison, the sun is about 150 million km from Earth and the nearest star (Proxima Centauri) is about 40 trillion km from Earth.]

Make the conversion indicated in each of the following:(b) the height of Mt. Kilimanjaro, at 19,565 ft the highest mountain in Africa, to kilometers

Use the following exact conversion factors to perform the stated calculations:51/2 yards = 1 rod40 rods = 1 furlong8 furlongs = 1 mileb. A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?

Many chemistry conferences have held a 50-Trillion Angstrom Run (two significant figures). How long is this run in kilometers and in miles? (1 Å = 1 × 10−10 m)

Would a car traveling at a constant speed of 65 km/h violate a 40 mi/h speed limit?

Convert 268 cm to yards.

The distance between two adjacent peaks on a wave is called the wavelength. The wavelength of a beam of red light is 6760 pm. What is its wavelength in angstroms (Å)?

Solve these problems about lumber dimensions. (a) To describe to a European how houses are constructed in the US, the dimensions of “two-by-four” lumber must be converted into metric units. The thickness × width × length dimensions are 1.50 in. × 3.50 in. × 8.00 ft in the US. What are the dimensions in cm × cm × m?

Solve these problems about lumber dimensions.(b) This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimeters?

At a particular instant in time the Earth is judged to be 92,955,000 miles from the sun. What is the distance in kilometers to four significant figures? (See back inside cover
for conversion factor).

Convert the following quantities into SI units with the correct number of significant figures.5.6 in .

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to make the following conversions.mi to km

Carry out the following conversions.0.150 in. to mm

Perform the following unit conversions.b. The circumference of the earth is 25,000 mi at the equator. What is the circumference in kilometers? in meters?

The Sears Tower in Chicago is 1454 ft tall. Calculate its height in meters.

Write conversion factors (as ratios) for the number of:(a) yards in 1 meter

The radius of a barium atom is 2.22 × 10−10 m. What is its radius in angstroms (Å)?

What is the length in inches (in) of a 100 m soccer field?

Write conversion factors (as ratios) for the number of: (a) kilometers in 1 mile

The center on your school’s basketball team is 6 ft 10 in tall. How tall is the player in millimeters (mm)?

Is a meter about an inch, a foot, a yard, or a mile?

Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?

A woman's basketball has a circumference between 28.5 and 29.0 inches and a maximum weight of 20 ounces (two significant figures). What are these specifications in units of centimeters and grams?

The diameter of a red blood cell is about 3 × 10−4 in. What is its diameter in centimeters?

The distance between the centers of the two oxygen atoms in an oxygen molecule is 1.21 × 10−8 cm. What is this distance in inches?

Express the quantity 33.2m10-4 mm in {
m mm}.

A hybrid electric vehicle has an EPA gas mileage rating of 56 mi/gal in the city.How many kilometers can the car travel on the amount of gasoline that would fit in a soda can? The volume of a soda can is 355 mL.

The longest river in the world is the Nile River with a length of 4145 mi. How long is the Nile in cable lengths, meters, and nautical miles?Use these exact conversions to help solve the problem:6 ft = 1 fathom100 fathoms = 1 cable length10 cable lengths = 1 nautical mile3 nautical miles = 1 league

Using SI prefixes suggest a convenient unit for the force resulting from the collision of a molecule of mass around 10–20 kg moving almost at the speed of light (3 x 108 m/s) with the wall of its container.

A watt is a measure of power (the rate of energy change) equal to 1 J/s.Calculate the number of joules in a kilowatt-hour.

A watt is a measure of power (the rate of energy change) equal to 1 J/s.An adult person radiates heat to the surroundings at
about the same rate as a 100-watt electric incandescent light
bulb. What is the total amount of energy in kcal radiated to
the surroundings by an adult over a 25
h period?

Very small semiconductor crystals composed of approximately 1000 to 100,000 atoms, are called quantum dots. Quantum dots made of the semiconductor CdSe are now being used in electronic reader and tablet displays because they emit light efficiently and in multiple colors depending on dot size. The density of CdSe is 5.82 g/cm3.(E) If you wanted to make one 6.5-nm dot from multiple 2.5-nm dots, how many 2.5-nm dots would you need,How many CdSe formula units in part E would be left over, if any?

For a pharmacist dispensing pills or capsules, it is often easier to weigh the medication to be dispensed than to count the individual pills. If a single antibiotic capsule weighs 0.65 g, and a pharmacist weighs out 15.6 g of capsules, how many capsules have been dispensed?

An electric car is capable of going 225 km on a single charge. With a full charge to start, how many additional charges will it need to travel from Seattle, Washington, to San Diego, California, a distance of 1257 mi?

The data density of a Blu-ray disk using a 405-nm laser is 1.5 × 10 7 bits mm−2. Disks have an outside diameter of 120 mm and a hole of 15-mm diameter. How many data bits can be contained on the disk? If a Blu-ray disk can hold 9,400,000 pages of text, how many data bits are needed for a typed page? (Hint: Determine the area of the disk that is available to hold data. The area inside a circle is given by A = πr2, where the radius r is one-half of the diameter.)

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick.How many quarters would have to be stacked to reach 575 ft, the height of the Washington Monument?

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick.How many quarters would have to be stacked to reach 575 ft, the height of the Washington Monument?How much would this stack weigh?

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick.How many quarters would have to be stacked to reach 575 ft, the height of the Washington Monument?How much money would this stack contain?

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick.The U.S. National Debt Clock showed the outstanding public debt
to be $16,213,166,914,811 on October 28, 2012. How many
stacks like the one described would be necessary to pay off
this debt?

How many 1-cm cubes would it take to construct a cube that is 4 cm on edge?

A small hole in the wing of a space shuttle requires a 20.7 cm 2 patch. If the patching material costs NASA $3.25/in 2, what is the cost of the patch?

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to 10,000 m2. In the English system, land is often measured in acres (1 acre = 160 rod2). Use the exact conversions and those given in Exercise 31 to calculate the following.c. A lot with dimensions 120 ft by 75 ft is to be sold for $6500. What is the price per acre? What is the price per hectare?

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost 2.45 euros per kilogram. Given that 1 euro is equivalent to approximately $1.32, calculate what a pound of peaches will cost in dollars.

In recent years, there has been a large push for an increase in the use of renewable resources to produce the energy we need to power our vehicles. One of the newer fuels that has become more widely available is E85, a mixture of 85% ethanol and 15% gasoline. Despite being more environmentally friendly, one of the potential drawbacks of E85 fuel is that it produces less energy than conventional gasoline. Assume a car gets 28.0 mi/gal using gasoline at $3.50/gal and 22.5 mi/gal using E85 at $2.85/gal. How much will it cost to drive 500. miles using each fuel?

A barrel of oil as measured on the oil market is equal to 1.333 U.S. barrels. A U.S. barrel is equal to 31.5 gal. If oil is on the market at $94.00 per barrel, what is the price in dollars per gallon?

Gasoline is a mixture of hydrocarbons, but the heat released when it burns is close to that of octane, C8H18(l) (ΔH°f = −250.1 kJ/mol). Research is underway to use H 2 from the electrolysis of water in fuel cells to power cars instead of gasoline.(a) Calculate ΔH° when 1.00 gal of gasoline (d = 0.7028 g/mL) burns to produce carbon dioxide gas and water vapor.(b) How many liters of H2 at 25°C and 1.00 atm must burn to produce this quantity of energy?(c) How long would it take to produce this amount of H 2 by electrolysis with a current of 1.00 × 10 3 A at 6.00 V?(d) How much power in kilowatt-hours (kW·h) is required to generate this amount of H 2 (1 W = 1 J/s, 1 J = 1 C·V, and 1 kW·h = 3.6 × 106 J)?(e) If the cell is 88.0% efficient and electricity costs $0.123 per kW·h, what is the cost of producing the amount of H2 equivalent to 1.00 gal of gasoline?

Electrodes used in electrocardiography are disposable, and many of them incorporate silver. The metal is deposited in a thin layer on a small plastic “button,” and then some is converted to AgCl:Ag(s) + Cl−(aq) ⇌ AgCl(s) + e −(a) If the surface area of the button is 2.0 cm2 and the thickness of the silver layer is 7.5×10−6 m, calculate the volume (in cm3) of Ag used in one electrode.(b) The density of silver metal is 10.5 g/cm3. How many grams of silver are used per electrode?(c) If Ag is plated on the button from an Ag+ solution with a current of 12.0 mA, how many minutes does the plating take?(d) If bulk silver costs $28.93 per troy ounce (31.10 g), what is the cost (in cents) of the silver in one disposable electrode?

The automobile fuel called E85 consists of 85% ethanol and 15% gasoline. E85 can be used in so-called flex-fuel vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of C8H18), that the average heat of combustion of C8H18(l) is 5400 kJ/mol, and that gasoline has an average density of 0.70 g/mL. The density of ethanol is 0.79 g/mL.(a) By using the information given as well as data in Appendix C, compare the energy produced by combustion of 1.0 L of gasoline and of 1.0 L of ethanol. (b) Assume that the density and heat of combustion of E85 can be obtained by using 85% of the values for ethanol and 15% of the values for gasoline. How much energy could be released by the combustion of 1.0 L of E85?(c) How many gallons of E85 would be needed to provide the same energy as 40 gal of gasoline?(d) If gasoline costs $3.88 per gallon in the United States, what is the break-even price per gallon of E85 if the same amount of energy is to be delivered?

Asbestos is a fibrous silicate mineral with remarkably high tensile strength. But it is no longer used because airborne asbestos particles can cause lung cancer. Grunerite, a type of asbestos, has a tensile strength of 3.5 x 102 kg/mm2 (thus, a strand of grunerite with a 1-mm 2 cross-sectional area can hold up to 3.5 x 102 kg). The tensile strengths of aluminum and Steel No. 5137 are 2.5 x 104 lb/in2 and 5.0 x 104 lb/in2, respectively. Calculate the cross-sectionalareas (in mm2) of wires of aluminum and of Steel No. 5137 that have the same tensile strength as a fiber of grunerite with a crosssectional area of 1.0 μm2.

In a sunny location, sunlight has a power density of about 1 kW/m2. Photovoltaic solar cells can convert this power into electricity with 16% efficiency. If a typical home uses 390 kWh of electricity per month, how many square meters of solar cells would be required to meet its energy requirements? Assume that electricity can be generated from the sunlight for 8 h/day.

Make the conversion indicated in each of the following:(c) the area of the state of Oregon, 96,981 mi2 , to square kilometers

Make the conversion indicated in each of the following:(c) the area of an 8.5 × 11-inch sheet of paper in cm2

Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to 10,000 m2. In the English system, land is often measured in acres (1 acre = 160 rod2). Use the exact conversions and those given in Exercise 31 to calculate the following.b. The area of a 5.5-acre plot of land in hectares, square meters, and square kilometers.

Convert the following quantities into SI units with the correct number of significant figures.2.390 mi2 .

Write the conversion factor(s) for • in2 to m2

A small hole in the wing of a space shuttle requires a 20.7 cm 2 patch. What is the patch’s area in square kilometers (km 2)?

The area of a telescope lens is 7903 mm 2. What is the area in square feet (ft 2)?

Gasoline is sold by the liter in many countries. How many liters are required to fill a 12.0-gal gas tank?

Milk is sold by the liter in many countries. What is the volume of exactly 1/2 gal of milk in liters?

Make the conversion indicated in each of the following:(d) the volume of 1 gill (exactly 4 oz) to milliliters

Make the conversion indicated in each of the following:(e) the estimated volume of the oceans, 330,000,000 mi3 , to cubic kilometers.

Perform the following unit conversions.b. 12.8 L to gallons

Perform the following unit conversions.c. 125 mL to quarts

Perform the following unit conversions.d. 2.89 gal to milliliters

Perform each unit conversion.1432
cm3 to L

The physical fitness of athletes is measured by "VO2 max," which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a VO2 max of 45 mL O2/kg body mass/min, but a world-class male athlete can have a VO2 max reading of 88.0 mL O2/kg body mass/min.(a) Calculate the volume of oxygen, in mL, consumed in 1 hr by an average man who weighs 185 lbs and has a VO2 max reading of 47.5 mL O2/kg body mass/min. (b) If this man lost 21 lbs , exercised, and increased his VO2 max to 65.1 mL O2/kg body mass/min, how many mL of oxygen would he consume in 1 hr?

Write the conversion factor(s) for • m3 to in3

Perform the following unit conversions.f. 550 mL to quarts

A gas can holds 5.2 gallons of gasoline.What is this quantity in cm3?

An infant ibuprofen suspension contains 100 mg/5.0mL suspension. The recommended dose is 10 mg/kg body weight.How many milliliters of this suspension should be given to an infant weighing 21 lb ? (Assume two significant figures.)

Make the conversion indicated in each of the following:(d) the displacement volume of an automobile engine, 161 in.3 , to liters

The volume of a certain bacterial cell is 2.56 μm 3. What is the volume of 10 5 cells in liters (L)?

How many cubic centimeters are there in 2.11
yd3

How many liters of milk are in 835 gal (1 gal = 4 qt)?

Convert 6635 cm3 to gallons.

Convert the following quantities into SI units with the correct number of significant figures.0.5600 gal .

Helium is the lightest noble gas and the second most abundant element (after hydrogen) in the universe.(a) The radius of a helium atom is 3.1×10−11 m; the radius of its nucleus is 2.5×10−15 m. What fraction of the spherical atomic volume is occupied by the nucleus (V of a sphere = 4πr3/3)?

Convert the following quantities into SI units with the correct number of significant figures.975.1 yd3 .

d. How many liters are in 8.0 cubic decimeters?

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to make the following conversions.ft3 to L

Carry out the following conversions.0.880 qt to mL

Perform the following unit conversions.c. A rectangular solid measures 1.0 m by 5.6 cm by 2.1 dm. Express its volume in cubic meters, liters, cubic inches, and cubic feet.

What is the engine piston displacement in liters of an engine whose displacement is listed as 460 in3?

In March 1989 the Exxon Valdez ran aground and spilled 240,000 barrels of crude petroleum off the coast of Alaska. One barrel of petroleum is equal to 42 gal. How many liters of petroleum were spilled?

Write conversion factors (as ratios) for the number of:(b) liters in 1 liquid quart

The contents of one 40-lb bag of topsoil will cover 10. square feet of ground to a depth of 1.0 inch. How many bags areneeded to cover a plot that measures 200. by 300. m to a depth of 4.0 cm?

Write conversion factors (as ratios) for the number of:(b) liters in 1 cubic foot

Is one liter about an ounce, a pint, a quart, or a gallon?

The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

The volume of a certain bacterial cell is 2.56 μm 3. What is its volume in cubic millimeters (mm3)?

How many cubic meters of milk are in 1 qt (946.4 mL)?

How many milliliters of a soft drink are contained in a 12.0-oz can?

A barrel of oil is exactly 42 gal. How many liters of oil are in a barrel?

How large is the volume of a red blood cell (in cm3) if the cell has a cylindrical shape with a diameter of 7 x 10-6 m and a height of 2 x 10-6 m?

A wooden block has a volume of 18.6 in3. Express the volume of the cube in cm3.

A long ton is defined as exactly 2240 lb. What is this mass in kilograms?

Make the conversion indicated in each of the following:(f) the mass of a 3525-lb car to kilograms

Make the conversion indicated in each of the following:(g) the mass of a 2.3-oz egg to grams

Perform the following unit conversions.a. 908 oz to kilograms

Perform the following unit conversions.e. 4.48 lb to grams

Perform each of the following conversions.1830. kg to lb

Make the conversion indicated in each of the following:(e) the estimated mass of the atmosphere, 5.6 × 1015 tons, to kilograms

Make the conversion indicated in each of the following:(f) the mass of a bushel of rye, 32.0 lb, to kilograms

Precious metals and gems are measured in troy weights in the English system:24 grains = 1 pennyweight (exact)20 pennyweight = 1 troy ounce (exact)12 troy ounces = 1 troy pound (exact)1 grain = 0.0648 gram1 carat = 0.200 grama. The most common English unit of mass is the pound avoirdupois. What is one troy pound in kilograms and in pounds?

Fluoride ion is poisonous in relatively low amounts: 0.2 g of F − per 70 kg of body weight can cause death. Nevertheless, in order to prevent tooth decay, F− ions are added to drinking water at a concentration of 1 mg of F− ion per L of water. How many liters of fluoridated drinking water would a 70-kg person have to consume in one day to reach this toxic level? How many kilograms of sodium fluoride would be needed to treat an 8.50×107-gal reservoir?

Make the conversion indicated in each of the following:(g) the mass of a 5.00-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)

Precious metals and gems are measured in troy weights in the English system:24 grains = 1 pennyweight (exact)20 pennyweight = 1 troy ounce (exact)12 troy ounces = 1 troy pound (exact)1 grain = 0.0648 gram1 carat = 0.200 gramb. What is the mass of a troy ounce of gold in grams and in carats?

Apothecaries (druggists) use the following set of measures in the English system:20 grains ap = 1 scruple (exact)3 scruples = 1 dram ap (exact)8 dram ap = 1 oz ap (exact)1 dram ap = 3.888 g24 grains = 1 pennyweight (exact)20 pennyweight = 1 troy ounce (exact)12 troy ounces = 1 troy pound (exact)1 grain = 0.0648 gram1 carat = 0.200 grama. Is an apothecary grain the same as a troy grain?

Apothecaries (druggists) use the following set of measures in the English system:20 grains ap = 1 scruple (exact)3 scruples = 1 dram ap (exact)8 dram ap = 1 oz ap (exact)1 dram ap = 3.888 g24 grains = 1 pennyweight (exact)20 pennyweight = 1 troy ounce (exact)12 troy ounces = 1 troy pound (exact)1 grain = 0.0648 gram1 carat = 0.200 gramb. 1 oz ap = ________ oz troy.

Apothecaries (druggists) use the following set of measures in the English system:20 grains ap = 1 scruple (exact)3 scruples = 1 dram ap (exact)8 dram ap = 1 oz ap (exact)1 dram ap = 3.888 gc. An aspirin tablet contains 5.00 x 102 mg of active ingredient. What mass in grains ap of active ingredient does it contain? What mass in scruples?

Apothecaries (druggists) use the following set of measures in the English system:20 grains ap = 1 scruple (exact)3 scruples = 1 dram ap (exact)8 dram ap = 1 oz ap (exact)1 dram ap = 3.888 gd. What is the mass of 1 scruple in grams?

A children’s pain relief elixir contains 80. mg acetaminophen per 0.50 teaspoon. The dosage recommended for a child who weighs between 24 and 35 lb is 1.5 teaspoons. What is the range of acetaminophen dosages, expressed in mg acetaminophen/kg body weight, for children who weigh between 24 and 35 lb?

To prepare for a laboratory period, a student lab assistant needs 125 g of a compound. A bottle containing 1/4 lb is available. Did the student have enough of the compound?

A chemistry student is 159 cm tall and weighs 45.8 kg. What is her height in inches and weight in pounds?

A vineyard has 165 acres of Chardonnay grapes. A particular soil supplement requires 5.50 grams for every square meter of vineyard. How many kilograms of the soil supplement are required for the entire vineyard? (Recall that 1 km2 = 247 acres)

Convert the following quantities into SI units with the correct number of significant figures.66.54 lb .

Helium is the lightest noble gas and the second most abundant element (after hydrogen) in the universe.(b) The mass of a helium-4 atom is 6.64648×10−24 g, and each of its two electrons has a mass of 9.10939×10−28 g. What fraction of this atom’s mass is contributed by its nucleus?

Perform the following unit conversions.a. Congratulations! You and your spouse are the proud parents of a new baby, born while you are studying in a country that uses the metric system. The nurse has informed you that the baby weighs 3.91 kg and measures 51.4 cm. Convert your baby’s weight to pounds and ounces and her length to inches (rounded to the nearest quarter inch).

Carry out the following conversions.4.00 $/lb to dollars per kg

Lipitor, a pharmaceutical drug that has been shown to lower “bad” cholesterol while raising “good” cholesterol levels inpatients taking the drug, had over $11 billion in sales in 2006. Assuming one 2.5-g pill contains 4.0% of the active ingredient by mass, what mass in kg of active ingredient is present in one bottle of 100 pills?

The anticancer drug Platinol (cisplatin), Pt(NH3)2Cl2, reacts with a cancer cell’s DNA and interferes with its growth. (b) If Pt costs $51/g, how many grams of Platinol can be made for $1.00 million (assume that the cost of Pt determines the cost of the drug)?

Write conversion factors (as ratios) for the number of:(c) pounds in 1 kilogram

During a recent winter month in Sheboygan, Wisconsin, it was necessary to obtain 3500 kWh of heat provided by a natural gas furnace with 89% efficiency to keep a small house warm (the efficiency of a gas furnace is the percent of the heat produced by combustion that is transferred into the house).Although electricity is 100% efficient in producing heat inside a house, production and distribution of electricity is not 100% efficient. The efficiency of production and distribution of electricity produced in a coal-fired power plant is about 40%. A certain type of coal provides 2.26 kWh per pound upon combustion. What mass of this coal in kilograms will be required to produce the electrical energy necessary to heat the house if the efficiency of generation and distribution is 40%?

Express your body weight in kilograms (kg).

Write conversion factors (as ratios) for the number of:(c) grams in 1 ounce

There are 2.60 x 1015 short tons of oxygen in the atmosphere (1 short ton = 2000 lb). How many metric tons of oxygen are present in the atmosphere (1 metric ton = 1000 kg)?

The label on a box of cereal gives the mass of cereal in two units: 978 grams and 34.5 oz. Use this information to find a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

Consider the two spheres shown here, one made of silver and
the other of aluminum.What is the mass of the silver sphere
in kg?

Solar winds composed of free protons, electrons, and α particles bombard Earth constantly, knocking gas molecules out of the atmosphere. In this way, Earth loses about 3.0 kg of matter per second. It is estimated that the atmosphere will be gone in about 50 billion years. Use this estimate to calculate the mass (kg) of Earth’s atmosphere.

Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?

A very good 197-lb weight lifter lifted 192 kg in a move called the clean and jerk. What was the mass of the weight lifted in pounds?

A jogger runs at an average speed of 5.9 mi/h. How many kilometers does she run in 98 min?

A jogger runs at an average speed of 5.9 mi/h. If she starts a run at 11:15 am, what time is it after she covers 4.75 x 104 ft?

The area of a telescope lens is 7903 mm 2. If it takes a technician 45 s to polish 135 mm 2, how long does it take her to polish the entire lens?

Science fiction often uses nautical analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor 1.71, what is its speed in knots and in miles per hour? (Warp 1.71 = 5.00 times the speed of light; speed of light = 3.00 x 108 m/s; 1 knot = 2000 yd/h, exactly.)

The world record for the hundred meter dash is 9.58 s. What is the corresponding average speed in units of m/s, km/h, ft/s, and mi/h? At this speed, how long would it take to run 1.00 x 102 yards?

You pass a road sign saying “New York 112 km.” If you drive at a constant speed of 65 mi/h, how long should it take you to reach New York? If your car gets 28 miles to the gallon, how many liters of gasoline are necessary to travel 112 km?

A cyclist rides at an average speed of 25 miles per hour.If she wants to bike 200 km, how long (in hours) must she ride?

A parsec is an astronomical unit of distance where 1 parsec = 3.26 light years (1 light year equals the distance traveled by light in one year). If the speed of light is 186,000 mi/s, calculate the distance in meters of an object that travels 9.6 parsecs.

You are driving 65 mi/h and take your eyes off the road for “just a second.” What distance (in feet) do you travel in thistime?

The world burns the fossil fuel equivalent of 6x1012 kg of petroleum per year. Assume that all of this petroleum is in the form of octane (C8H18). If the atmosphere currently contains approximately 3x1015 kg of CO2, how long will it take for the worlds fossil fuel combustion to double the amount of atmospheric carbon dioxide?

Secretariat is known as the horse with the fastest run in the Kentucky Derby. If Secretariat’s record 1.25-mi run lasted 1 minute 59.2 seconds, what was his average speed in m/s?

Complete the following conversions.626 mK/s = ________ µK/ms

Complete the following conversions.3.056 mg/mL = ________ µg/mL

A jogger runs at an average speed of 5.9 mi/h. How fast is she running in m/s?

Write the conversion factor(s) for • mi/h to m/s

Write the conversion factor(s) for • lb/ft3 to g/cm3

Write the conversion factor(s) for • m/s2 to km/h2

Write the conversion factor(s) for • gal/h to L/min

The average density of Earth is 5.52 g/cm3. What is its density in lb/ft 3.

The speed of light in a vacuum is 2.998 x 10 8 m/s. What is its speed in mi/min.

In a recent Grand Prix, the winner completed the race with an average speed of 229.8 km/h. What was his speed in miles per hour, meters per second, and feet per second?

Convert the following quantities into SI units with the correct number of significant figures.61 mi/h .

Among many alternative units that might be considered as a measure of time is the shake rather than the second. Based on the expression "faster than a shake of a lambs tail," well define 1 shake as equal to 2.5 x 10-4 s. If a car is traveling at 56 mi/h , what is its speed in cm/shake?

Carry out the following conversions.8.80 m/s to km/hr

Carry out the following conversions.8.80
lb/ft3 to g/mL

The speed of light in a vacuum is 2.998 108 m/s. Calculate its speed in miles per hour (miles/h).

If a migrating loon flies at an average speed of 16 m/s, what is its average speed in mi/hr?

Write the conversion factor(s) for • cm/min to in/s

The average density of Earth is 5.52 g/cm3. What is its density in kg/m3.

The speed of light in a vacuum is 2.998 x 10 8 m/s. What is its speed in km/h.

A German automobile gets a gas mileage of 23 km/L. Convert this quantity to miles per gallon.

Jewelers measure masses of precious metals in troy ounces. If a jeweler has an ingot of silver that weighs 6.44 troy oz, what is the volume of the ingot? 1 troy oz = 31.103 g

The density of iron is 7.874 g/cm^3. Assuming there is no space between the atoms in an iron sample, estimate the volume occupied by an atom of iron.

Convert 2538 kg to ton, using the fact that there are 2.2 pounds in one kilogram and 2000 pounds in a ton.

There are 18 cans of soda in a case. Each can contain 15 ounces of soda. Every 45 ounces of soda contains 1 cup of sugar. How many cups of sugar are in 5 cases of soda?

A children's liquid medicine contains 100 mg of the active ingredient in 5 mL. If a child should receive 250 mg of the active ingredient, how many milliliters of the medicine should the child be given? For the purposes of this question, assume that these numbers are exact. The package states that one teaspoon (tsp) is approximately equal to five milliliter. Calculate the number of teaspoons that the child should receive. Use the approximation as your conversion factor.

If a bullet travels at 437.0 m/s, what is its speed in miles per hour?

If the heat of combustion for a specific compound is -1110.0 kJ/mol and its molar mass is 36.79 g/mol, how many grams of this compound must you burn to release 997.70 kJ of heat?

You collected a personal air sample for 84 minutes at an actual flow rate of 2 liters per minute. You submitted the sample to the lab and requested an analysis for total particulate (total dust). The lab reported back to you that the sample result was 3 milligrams (mg). What is the worker's exposure to total particulate? Select one:

Calculate the mass of water that would be released if the water of hydration were completely driven off 2.6 mol of the following substances: a. plaster of Paris (CaSO4 • H2O) b. gypsum (CaSO4 • 2H2O)

A metallurgist wants to gold-plate a surface with the following dimensions: 2.5 in times 6.5 in. The gold plating must be 0.0010 in thick. How many grams of gold (d = 19.3 g/cm^3) are required?

How many liters of wine can be held in a wine barrel whose capacity is 26.0 gal? 1 gal = 4 qt = 3.7854 L. (i) 6.87 (ii) 0.146 (iii) 6.87 x 103 (iv) 98.4 (v) 1.46 x 104

377 km/s = _____ m/ms Express your answer using three significant figures.

The speed of sound at one atmosphere of pressure is 4.06 x 108 feet per hour. What is the speed of sound in units of meters per second, m/s? These equalities should be helpful: 1 km = 0.621 miles, 1 mile = 5280 feet.

Norgestrel and ethinyl estradiol tablets are available containing 0.5 mg of norgestrel and 50 ug of ethinyl estradiol. How many grams of each ingredient would be used in making 10,000 tablets? For norgestrel round to the nearest whole number. For ethinyl estradiol to round the tenths place.

1294 g/L = ________ g/mL Express your answer using four significant figures. 1294 g/L = _______ kg/mL Express your answer using four significant figures.

Use the conversion factor from Step 2 and dimensional analysis to convert the volume of the cell from the given units to the desired units. Express the result with the proper number of significant figures. The volume of the cell in cubic meters is: Determine the number of significant figures for a calculation. Use dimensional analysis to set up and solve for a desired calculated outcome.

604 mK/s = _____ K/s Express your answer using three significant figures. 604 mK/s = _____ μK/ms Express your answer using three significant figures.

Part AThree gases (8.00 g of methane, CH4, 18.0 g of ethane, C2H4, and an unknown amount of propane, C3H8) were added to the same 10.0-L container. At 23.0°C, the total pressure in the container is 4.10 atm. Calculate the partial pressure of each gas in the container.Express the pressure values numerically in atmospheres, separated by commas. Enter the partial pressure of methane first, then ethane, then propane. Part B A gaseous mixture of O2 and N2 contains 34.8% nitrogen by mass. What is the partial pressure of oxygen in the mixture if the total pressure is 665 mmHg?Express you answer numerically in millimeters of mercury.

Part AThe equation for density, d is d = m/Vwhere m is mass and V is volume. What is the density, d, of a substance with a volume of V = 16.4 cm3 and a mass of m = 45.2 g? Express your answer numerically in grams per cubic centimeter.Part B The equation for molarity, M, is M = n/V where V is volume and n is the number of moles of solute.A certain solution has a molarity of M = 5.19 mol/L and has a volume of V = 0.590 L. What is the value of n? Express your answer numerically in moles. Part CThe equation for photon energy, E, is E = hc/λ where h = 6.626 x 10-34 J•s (Planck's constant) and c = 299 x 108 m/s (the speed of light).What is the wavelength, λ, of a photon that has an energy of E = 4.77 x 10-19 J? Express your answer numerically in meters.

If 500 mL of liquid mercury weighs 6.53 x 103 g, what is the mass in kg? If the radius of a potassium (K) atom is 2.27 x 10-7 mm, what is the radius in um?

A titanium bicycle frame displaces 0.314 L of water and has a mass of 1.41 kg. What is the density of the titanium in g/cm3?

The men's world record for swimming 1500.0 m in a long course pool (as of 2007) is 14 min 34.56 s. At this rate, how many seconds would it take to swim 0.250 miles? (1 mi = 1609 m.)

The area of a 15-inch pizza is 176.7 in2. Express this area in square centimeters. 1) 1140. cm2 2) 448.8 cm2 3) 96.8 cm2 4) 69.57 cm2 5) 27.39 cm2

If an object has a density of 8.65 g/cm3, what is its density in units of kg/m3? (i) 8.65 x 103 kg/m3 (ii) 8.65 x 10-3 kg/m3 (iii) 8.65 x 101 kg/m3 (iv) 8.65 x 10-1 kg/m3 (v) 8.65 x 10-7 kg/m3 If the walls in a room are 955 square feet in area, and a gallon of paint covers 15 square yards, how many gallons of paint are needed for the room? (3 ft = 1 yd) (i) 2.3 gallons (ii) 47 gallons (iii) 24 gallons (iv) 21 gallons (v) 7.1 gallons

A student sets up and solves the following equation to solve a problem in solution stoichiometry. Fill in the missing part of the student's equation.

Hydrogen cyanide, HCN, is a poisonous gas. The ethal dose is approximately 300 mg HCN per kilogram of air when inhaled. The density of air at 26°C is 0.00118 g/cm3. Calculate the amount of HCN that gives the lethal dose in a small laboratory room measuring 12.0 ft x 15.0 ft × 960 ft. Express your answer to three significant figures and include the appropriate units.

The density of titanium metal is 4.51 g/cm3. A cube of titanium has a mass of 62.00 kilograms. Calculate the length of each side of the cube in inches. 1 inch = 2.54 cm exactly.

A technical machinist is asked to build a cubical steel tank that will hold 565 L of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.01 m.

Earth's oceans contain 3.50 x 108 m3 of water and cover an area of 1.40 x 108 mi3.What is the volume of ocean water in cubic kilometers?

The density of titanium is 4.51 g/cm3. What is the volume (in cubic inches) of 3.0 lb of titanium?

If the caffeine concentration in a particular brand of soda is 2.11 mg/oz, drinking how many cans of soda would be lethal? Assume 10.0 grams of caffein e is a lethal dose, and there are 12 oz in a can

A doctor has ordered that a patient be given 25 g of glucose, which is available in a concentration of 35.00 g glucose/1000.0 mL of solution. What volume of solution should be given to the patient?

Your favorite FM radio station has a wavelength of 2.827 meters. Convert that length to feet using the centimeter to inch conversion factor. How many significant figures should there be in your answer?

Part A A package of aluminum foil contains 50, ft2 of foil, which weighs approximately 8.5 oz. Aluminum has a density of 2.70 g/cm3. What is the approximate thickness of the fol in millmeters?Express your answer to two significant figures and include the appropriate units.

4.934 mg/mL = _____ g/L Express your answer using four significant figures. 4.934 mg/mL = ________ μg/mL Express your answer using four significant figures.

A chemist adds 210.0 mL of a 0.00468 mM calcium sulfate (CaSO4) solution to a reaction flask. Calculate the mass in milligrams of calcium sulfate the chemist has added to the flask. Be sure your answer has the correct number of significant digits.

If the caffeine concentration in a particular brand of soda is 2.15 mg/oz, drinking how many cans of soda would be lethal? Assume 10.0 grams of caffeine is a lethal dose, and there are 12 oz in a can.

3.90 x 105 gallons of tar (SG = 1.20) is stored in a 23.0-ft tall storage tank. What is the total mass of the liquid in the tank? What is the pressure at the bottom of the tank?

A 170-lb adult has approximately 10 pt of blood. If a drop of blood has a volume of 0.07 mL, how many drops of blood are in the adult? Enter your answer in scientific notation. Be sure to answer all parts.

Radio communications travel at the speed of light (2.9979 x 108 meters/sec). How long will it take for a radio transmission to reach a space probe located 4.980 x 108 miles from earth?

The speed of light in a vacuum is 2.998 x 10 8 m/s. (a) What is its speed in kilometers per hour (km/h)? (b) What is its speed in miles per minute (mi/min)?

9.7 x 10-5 g/cm3 = ________ kg/m3

Given that 1 inch = 2.54 cm, 1 cm3 is equal to 1) 16.4 in32) 6.45 in3 3) 0.394 in3 4) 0.155 in3 5) 0.0610 in3

A student sets up the following equation to convert a measurement. (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation. Note: your answer should be in the form of one or more fractions multiplied together.

The density of water at 3.98°C is 1.00000 g/mL. What is the mass in pounds of 17.736 L of water?

The men's world record for swimming 1500.0 m. In a long course pool (as of 2007) is 14 min 34.56 s. At this rate, how many seconds would it take to swim 0.400 miles? (1 mi = 1609 m.)

A certain ore is 30.3% nickel by mass. How many kilograms of this ore would you need to dig up to have 60.0 g of nickel?

Determine the number of atoms in 1.80 mL of mercury. (The density of mercury is 135 g/mL.) (i) 246 x 1027 atoms (ii) 4.07 x 1020 atoms (iii) 7.29 x 1022 atoms (iv) 1.40 x 1025 atoms

A box of paper clips contains 1465 paper clips. How many reams of paper clips does the box contain? 1 ream = 500 objects

At the end of 2012, global population was about 7.0 billion people. What mass of glucose in kg would be needed to provide 1600 cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to CO2 (g) and H2O(l) according to the following thermochemical equation: C6H12O6(s)+ 6O2(g) → 6CO2(g) + 6H2O(l) ΔH° = 2803 kJ Express your answer to two significant figures and include the appropriate units.

If the caffeine concentration in a particular brand of soda is 2.87 mg/oz, drinking how many cans of soda would be lethal? Assume 10.0 grams of caffeine is a lethal dose, and there are 12 oz in a can.

1 mole of Si atoms contains 6.02 x 1023 atoms. 6.02 x 1023 atoms of Si have a mass of 28.1 g. How many atoms of Si are contained in a computer chip that masses 38.0 mg? (6.02 x 1023 atoms 28.1 g)

If 5 kg of water has a volume of 5.0 x 103 mL, what is the volume in quarts? (1L = 1.06 qt)

Estimate the volume, V, of one sodium atom (Na) using its metallic radius of 186 pm. Express your answer with the appropriate units.