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?

What is dimensional analysis?

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 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.

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.

A copper wire (density = 8.96 g/cm3) has a diameter of 0.25 mm. If a sample of this copper wire has a mass of 22 g, how long is the wire?

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.)

A sheet of copper is 18.0 in x 7.00 in and a mass of 0.0318 g. Given that the density of copper is 8.96 g/cm3. What is the thickness of the copper sheet?a. 282 nmb. 4.4 x 10-6 nmc. 0.044 nmd. 43.7 nme. 3.51 x 103 nm

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

Indicate which of the following are exact numbers:(a) the mass of a paper clip(b) the surface area of a dime(c) the number of inches in a mile(d) the number of ounces in a pound, (e) the number of microseconds in a week (f) the number of pages in this book

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

Indicate which of the following are exact numbers:(a) the mass of a 32-oz can of coffee(b) the number of students in your chemistry class(c) the temperature of the surface of the sun(d) the mass of a postage stamp(e) the number of milliliters in a cubic meter of water(f) the average height of students in your school

A cube of aluminum metal contains 3.35 x 1023 atoms. The density of aluminum is 2.70 g/cm3. What is the length of the edge of the cube? Recall, volume = length 3 (for a cube).A) 1.77 cmB) 5.56 cmC) 2.70 cmD) 15.0 cm

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.

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

Titanium metal, density of 4.54 g/cm3, is used to make golf clubs. A rectangular bar of titanium which weighs 45.7 g measures 1.84 cm in length and 2.24 cm in width. What is the height of the bar?A) 50.3 cmB) 2.44 cmC) 252 cmD) 12.3 cmE) 4.09 cm

The density of aluminum is 2.70 ×10 3 kg/m3. Calculate the volume (in m3) occupied per atom of aluminum.

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

A sample has a density of 1.05 g/mL. What is the volume in mL (written in scientific notation) that 2.9 kg of the sample would occupy? You must use dimensional analysis

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?

The density of cobalt (II) oxide is 6.45 g/cm3. What is the volume occupied by a 5.57 kg sample of cobalt (II) oxide?a. 3.40 x 103 cm3b. 817 cm3c. 122 cm3d. 34.0 cm3e. 864 cm3

(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

Convert $2.99/kg to dollars per Ib.

A gold ingot weighs 5.50 lbs. If the density of gold is 19.31 g/cm 3, and the length and width of the ingot are 12.0 cm and 3.00 cm respectively, what is the height of the ingot?A) 10.2 cm B) 1.34 × 103 cm C) 3.59 cm D) 6.50 × 10-3 cm

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

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

Osmium is the densest known element, with density 22.59 g/cm3. The tip of a fountain pen contains 152 mg of Osmium. What is the volume of Osmium in the pen in units of microliters, μL?a. 0.152 μLb. 6.73 μLc. 0.149 μLd. 149 μL

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 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?

Osmium is the densest known element, with density 22.59 g/cm 3 . The tip of a fountain pen contains 152 mg osmium. What is the volume of osmium in the pen in units of microliters, µL? A. 0.152 µLB. 6.73 µLC. 0.149 µLD. 149 µL

The density of gold is 19.31 g/cm 3. A rectangular bar of gold has a mass of 66.75 g and measures 3.04 cm width and 25.5 cm in height. What is the length of the gold bar?a) 0.0446 cm b) 0.0550 cm c) 0.0189 cm d) 0.0592 cm

What mass of silver is required for an object that is to be coated in a uniform 0.32 mm thick layer of silver that has surface area of 162 cm 2? The density of silver is 10.49 g/cm 3.

What is the mass (in grams) of 4 L of gasoline if the density of gasoline is 0.79 g/ml?a. 2.2e3b. 3.2e3c. 4.3e3d. 5.4e3e. 6.5e3

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 daily dietary energy requirement for an adult is 2.00 x 10 3 kcal (1 ca = 4.184 J). This is equivalent to a. 47.8 x 104 kJb. 8.37 x 103 kJ c. 8.37 x 103 Jd. 2.00 x 103 kJe. 478 kJ

The Earth’s oceans have an average depth of 3.6 x 10 8 cm, a total area of 3.6 x 10 8 km 2, and an average density of 5.8 x 10 -9 g/L of dissolved gold. How many grams of gold are in the oceans?

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

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?

The density of lead is 11.4 g/cm3 at 25oC. The volume occupied by 25.0 g of lead isa. 2.19 cm3b. 1.24 cm3c. 0.456 cm3d. 285 cm3e. 6.05 cm3

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?

The density of magnesium is 1.7 g/cm3, while that of iron is 7.9 g/cm3. A block of iron has a mass of 819 g. What is the mass of a block of magnesium that has the same volume as the block of iron?A) 4.7 gB) 1.8 x 102 g C) 3.8 x 102 g D) 4.8 x 103 gE) 8 x 103 g

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 c. The density of gold is 19.3 g/cm3. What is the volume of a troy pound of gold?

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.

Ethylene glycol (antifreeze) has a density of 1.11 g/ cm 3. What is the volume in L of 4.1 kg of this liquid?

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

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.a. 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.)

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

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

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

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

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 to five milliliter. Calculate the number of that the child should receive. Use the approximation as your conversion factor.

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.

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 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.

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.

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?

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?

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.

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 108 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 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

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.