Using Dimensional Analysis

• What happens when you divide a number by itself?

• What happens when you divide a unit by itself?

• In both cases, you get the number 1

Using Dimensional Analysis to solve problems in chemistry

Always focus on the

UNITS

Conversion Factors

• Conversion factors are used in dimensional analysis to convert one unit to another.

• Conversion factors take a definition and turn it into a fraction equal to one

• For example:The molar mass of Neon is 20.18

g/mol. So…

1 mole of Ne = 20.18 grams

1 mole Ne = 20.18 grams

• Can be written as a fraction equal to one in two different ways:

or

We can use the conversion factor to convert between grams and moles of neon.

Using dimensional analysis to solve mole calculations.

• Question:

How many grams are in 2 moles of Neon?

• Step 1: Read the question determine the starting point (given) and ending point (desired)

In this case the start is moles of Neon and the end point is grams of Neon.

Step 2: Create a fraction by placing your starting point over 1

Step 3: Use a conversion factor to convert from moles to grams. Write in the bottom unit of the new fraction .

x

You know that 1 mole Neon = 20.18 grams. Choose the conversion factor that has moles on the bottom

or

• x =

• Cancel all possible units. This should leave only the units that represent the ending point.

x = grams

Step Four: Do the Math:• Multiply the numbers on top (2)(20.18)=40.36

x = 40.36 grams

Let’s try grams to moles

• How many moles are in 30 grams of carbon?

• Step One: Start point (given): grams End point (desired): moles.

• Step Two : place given over one

Step Three: Use a conversion factor to convert from grams to moles. Write in the bottom unit of the new fraction.

x

Choose the conversion factor that has grams on the bottom. (12.01 g C = 1 mole C)

or

x = 2.5 mole• Cancel out all possible units.

• Step Four – Do the math– Multiply the numbers on top (30)(1).– Divide by the product of the numbers on

the bottom (1)(12.01).– 30/12.01 = 2.5

Let’s try moles to atoms.

• How many atoms are in 20 moles of carbon?

• Step One: Start point (given): moles End point (desired): atoms.

• Step Two: Place given over one

Step Three: Use a conversion factor to convert from moles to atoms. Write in the bottom unit of the new fraction.

x

Choose the conversion factor that has moles on the bottom. 1 mole = 6.022 x 1023 atoms

or

• x = 1.2 x 1025 atoms• Cancel out all possible units.• Step Four – do the math:

Multiply the numbers on top20 x (6.022 x 1023) = 1.2 x 1025

x = 1.2 x 1025 atoms