This worked example problem shows how to convert the number grams of a molecule to the number of moles of the molecule. Why would you need to do this? Mainly this type of conversion problem arises when you are given (or measure) the mass of a sample in grams and then need to work a ratio or balanced equation problem that requires moles.

### Grams To Moles Conversion Problem

Determine the number of moles of CO_{2} in 454 grams of CO_{2}.

**Solution**

First, look up the atomic masses for carbon and oxygen from the Periodic Table. The atomic mass of C is 12.01 and the atomic mass of O is 16.00. The formula mass of CO_{2} is:

12.01 + 2(16.00) = 44.01

Thus, one mole of CO_{2} weighs 44.01 grams. This relation provides a conversion factor to go from grams to moles. Using the factor 1 mol/44.01 g:

moles CO_{2} = 454 g x 1 mol/44.01 g = 10.3 moles

**Answer**

There are 10.3 moles CO_{2} in 454 grams of CO_{2}

### Moles to Grams Example Problem

On the other hand, sometimes you're given a value in moles and need to convert it to grams. To do this, first calculate the molar mass of a sample. Then, multiply it by the number of moles to get an answer in grams:

grams of sample = (molar mass) x (moles)

For example, find the number of grams in 0.700 moles of hydrogen peroxide, H_{2}O_{2}.

Calculate the molar mass by multiplying the number of atoms of each element in the compound (its subscript) times the atomic mass of the element from the periodic table.

Molar mass = (2 x 1.008) + (2 x 15.999) - note the use of more significant figures for oxygen

Molar mass = 34.016 grams/mol

Multiply the molar mass by the number of moles to get the grams:

grams of hydrogen peroxide = (34.016 grams/mol) x (0.700 mol)

grams of hydrogen peroxide = 23.811 grams

### Tips Performing Grams and Moles Conversions

- The two problems most commonly encountered are setting up the problem incorrectly, so the units don't cancel out and give the correct result. It helps to write out the conversion and make sure units cancel. You may want to draw a line through them in complex calculations to keep track of active units.
- Watch your significant figures. Chemistry professors are unforgiving when it comes to reporting an answer, even if you set up the problem correctly!

This worked example problem shows you how to convert moles to grams.

**Problem**

Determine the mass in grams of 3.60 mol of H2SO4.

**Solution**

First, look up the atomic masses for hydrogen, sulfur, and oxygen from the Periodic Table. The atomic mass is 1.008 for H; 32.06 for S; 16.00 for O. The formula mass of H2SO4 is:

2(1.008) + 32.06 + 4(16.00) = 98.08

Thus, one mole of H2SO4 weights 98.08 grams. This relation provides a conversion factor to go from grams to moles. Using the factor 98.08 g / 1 mol:

grams H2SO4 = 3.60 mol x 98.08 g / 1 mol = 353 g H2SO4

**Answer**

353 g H2SO4