High School Science - Dimensional Analysis

Dimensiona l 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.  1molCU 80 gCu   63.5 g

 1molCu 2 S  159.1Cu 2 S   = 1.00 x10 2 gCu 2 S    2molCu  1molCu 2 S 

P1V1 P2V2 = T1 T2

INPUT • 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: x 1 1

2 3 1 x = 3 4 2 x 1 2

INPUT This same method works with anything! 1

1

 cat × skunk   dog × cat  cat 2    × = 2     dog    skunk × frog  dog × frog dog x dog

1

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 asalso, dimensional analysis) . anything, This known problem canceling maythat lookanything works complicated, with but uses so Remember, not canceled you the same can trick. it toItsimplify is your set up the sonumbers, that things too. you must be use included in answer. want to get rid of cancel. 8

 mol C  1 mol O 2  32 g O 2  160 g O2  = 53.3 g O2  20.0 g C ×   3  12.0 g C  1 mol C  mol O 2  3

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.

1 mol 12 g C or 12 g C mol

$1.70 1 gal or gal $1.70

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 $5.00 • 1 gallon = $1.70, or Gas costs ($1.70/gal) 25 miles = gallon miles/gal • Your car gets 25 miles to the gallon. 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.

DIMENSIONAL ANALYSIS • Here’s an example of how to use conversion factors. How far can you get on just $5.00 of gas? We’re solving for a • You have $5.00 distance. • 1 gallon = $1.70, or Gas costs ($1.70/gal) • Your car gets 25 miles/gal. This unit Now the only units We don’t want $ measures left are what we inthe answer, so 1 with gal the  25miles wanted. distance, so Start Multiply by gallons.  get rid of =the $5.00×use 73.5 miles  a conversion  ×Next, given value. numbers on the top we’ll solve factor to get rid $1.70 gal     and divide by of the $. for miles. numbers on the bottom.

DIMENSIONAL ANALYSIS

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

Keep track of those units!