Dimensional Analysis

The secret to making chemistry easy.Or, at least a lot easier!

INPUT

Many people are afraid of chemistry. Usually, they say it is because of the math involved.

2

22

1

11

T

VP

T

VP

SgCuxSmolCu

SCu

molCu

SmolCu

g

molCUgCu 2

2

2

22 1000.11

1.159

2

1

5.63

180

2

1

4

3

3

2x

x

x

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Most of the math skill you need to succeed in chemistry, you learned by 5th grade. In fact, three of the four equations on the previous slide use this simple type of math. (The fourth only requires addition.)Here’s an example of the math skill you will need:

1

2

1

1

frogdog

cat

frogskunk

catdog

dog

skunkcat

2

2

INPUT

This same method works with anything!

dog x dog

1

1

1

dog

Remember, also, that anything not canceled must be included in your answer.

INPUT

In chemistry, it is always important to keep track of the units so that you can use this trick to solve problems. You will solve long conversions that look scary, but really just use this simple method of cross canceling (also known as dimensional analysis).

2

22

O mol

O g 23

C mol 1

O mol 1

C g 12.0

C molC g 0.02

This problem may look complicated, but uses the same trick. It is set up so that things you want to get rid of cancel.

Remember, canceling works with anything, so you can use it to simplify the numbers, too.

8

3

160 g O2

353.3 g O2

$1.70

gal 1or

gal

$1.70

mol

C g 12or

C g 12

mol 1

DIMENSIONAL ANALYSIS

Both in chemistry and in real life, you can use dimensional analysis. The trick is to find two ways to describe the same thing.

Like 1 mole of carbon = 12 g or $1.70 = 1 gallon of gas

If you turn them into fractions, they become the nearly magical conversion factors.

The trick is to have one unit on the top of the fraction and another on the bottom. Then you can use the fraction to convert from one of the units to the other!

DIMENSIONAL ANALYSIS

Here’s an example of how to use conversion factors. How far can you get on just $5.00 of gas? You have $5.001 gallon = $1.70, or Gas costs ($1.70/gal)Your car gets 25 miles to the gallon.

25 miles = gallon25 miles/gal

Solving problems involves just three steps.1. List the given information. (done)2. Decide what you want to end up with.3. Arrange the conversion factors to cancel

what you don’t want and leave what you do want.

miles 73.5 galmiles 25

$1.70

gal 1 $5.00

Now the only units left are what we wanted. Multiply by numbers on the top and divide by numbers on the bottom.

Next, get rid of the gallons.

We don’t want $ in the answer, souse a conversion factor to get rid of the $.

Start with thegiven value.

DIMENSIONAL ANALYSIS

Here’s an example of how to use conversion factors. How far can you get on just $5.00 of gas? You have $5.001 gallon = $1.70, or Gas costs ($1.70/gal)Your car gets 25 miles/gal.

We’re solving for a distance.

This unit measures distance, so we’ll solve for miles.

DIMENSIONAL ANALYSIS

Now it’s your turn to try some dimensional analysis problems on your own!

Keep track of those units!