Dimensional Analysis

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

Unit Conversions

Concept: Understanding Unit Conversions

Video Transcript

When it comes to conversions we belong in three different categories. We are going to say we are in length, volume, and mass. What we're going to say here, we're just going to take a look at some of the most basic and most common types of conversions that you're going to be expected to know.
If you look at length, we have conversions to go from kilometers to miles, between meters and yards, inches and centimeters, miles and feet.
For volume, we have gallons to liters. One liter is equal to one decimeter cubed. We're going to say that one milliliter is equal to one centimeter cubed. That one's especially important to remember. We have one liter equals that many quarts.
For mass, we're going to say one kilogram is equal to this many pounds. One pound is equal to 454 grams. And then finally, one ounce is equal to 28.35 grams.
Now, it may seem like a lot, but a majority of these calculations you'll be dealing with on a daily basis when it comes to chem one. Some of them will naturally become a part of your memory, so you will remember how to use them and when to use them through practice. 

Unit conversions deal with three basic areas of measurement: length, volume and mass

Example: 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: A backyard swimming pool holds 315 cubic yards (yd3) of water. What is the mass of the water in pounds?


Problem: 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?


Understanding Dimensional Analysis

Concept: Examining Dimensional Analysis

Video Transcript

We use dimensional analysis as a way of helping us figure out how to convert from one unit to another. We're going to say we design the problems to begin with your known, which is known values, and to end with the units of your unknown. That's the strategy we always take. What did they give me? What am I looking for? We're going to say be sure all of your units cancel out and that's the way we ensure we're using dimensional analysis correctly. 

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: 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: 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? 


Problem: 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?


Dimensional Analysis Additional Practice Problems

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?

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

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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: 

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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 kJ

b. 8.37 x 103 kJ 

c. 8.37 x 103 J

d. 2.00 x 103 kJ

e. 478 kJ

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The molecular weight of ethanol (C2H5OH) is 46.1 and the density of absolute (100%) ethanol = 0.79 g/mL.

During a romantic candlelight dinner a 75 kg person drinks a bottle (750 mL) of wine in the space of 3 hours. Ethanol is metabolized at a constant rate of 120 mg per hour per kg body weight, regardless of its concentration. A 75 kg person contains about 40 L of ‘water’. Ignore the metabolism, and assume the water content of the person remains constant.

a)What is their blood alcohol content (mg/100 mL blood) at the end of the dinner?




b)How long will it take for their blood alcohol level to fall below the legal limit of 50mg of ethanol per 100mL of blood (0.05%)?

Watch Solution

The molecular weight of ethanol (C2H5OH) is 46.1 and the density of absolute (100%) ethanol = 0.79 g/mL. The legal limit for a driver’s blood alcohol is 50 mg of ethanol per 100 mL of blood (referred to as a blood alcohol content (BAC) of 0.05%). And a bottle of wine is 14% ethanol by volume. 

How much wine (standard serving size = 100 mL) could a 75 kg person drink and remain under the legal limit? The blood alcohol content will be equivalent to the alcohol content in the total ‘water’ component of the human body. A 75 kg person contains about 40 L of ‘water’. Ignore the metabolism, and assume the water content of the person remains constant.

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A certain cylinder has a diameter of 5.0 in and a height of 5 in. Calculate the volume (in cubic centimeters) of the cylinder. (Vcylinder = π r 2h)

If the density of the cylinder is 25 g/mL, what is its mass (in kg)? 

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Precious metals are sometimes weighed in old-timey units like “troy ounces”, where 1 troy ounce = 31.1035 grams.  A platinum coin is made that weighs 0.5003 troy ounces.  The coin has a radius of 13.5 mm and a thickness of 1.28 mm.  (Useful information: volume of a cylinder = (π r2)h  where r is radius, and h is height or thickness)

a) What is its density, in g/cm3?  





b) How many atoms of platinum are in the coin?

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Dimensional Analysis

How many milligrams in 125.0 gram   ____________________

The boiling point of H2 is -253°C, what is the boiling point in Kelvin. ________________

Oil has a density of 0.916 g/ml. What is the mass of 225 mL of the oil? ________________

What is the formula and charge of the phosphate ion? ___________________


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The atmospheric pressure is 700 mm Hg. What is the pressure in inches of Hg?

A) 16.0 in Hg

B) 0.921 in Hg

C) 13.5 in Hg

D) 27.6 in Hg

E) 32.5 in Hg

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What is dimensional analysis? 

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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

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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 10-3

b) 1 x 1045

c) 2 x 1015

d) 2 x 1021

e) none of the given answers is even within an order of magnitude

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