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

### Converting Moles to Grams (and Vice Versa)

- Grams and moles are two units that express the amount of matter in a sample. There is no "conversion formula" between the two units. Instead, you must use atomic mass values and the chemical formula to do the conversion.
- To do this, look up atomic masses on the periodic table and use the formula mass to know how many atoms of each element are in a compound.
- Remember, subscripts in a formula indicate number of atoms. If there is no subscript, it means there is only one atom of that element in the formula.
- Multiply the number of atoms of an element by its atomic mass. Do this for all the atoms and add the values to get the number of grams per mole. This is your conversion factor.

## Grams to Moles Conversion Problem

**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 of CO_{2} in 454 grams of CO_{2.}

### Moles to Grams Example Problem

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)

**Problem**

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

**Solution**

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)

Molar mass = 34.014 grams/mol

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

grams of hydrogen peroxide = (34.014 grams/mol) x (0.700 mol) = 23.810 grams

**Answer**

There are 23.810 grams of hydrogen peroxide in 0.700 moles of hydrogen peroxide.

## Moles to Grams Conversion Problem

Here is another example showing how to convert moles to grams.

**Problem**

Determine the mass in grams of 3.60 mol of H_{2}SO_{4}.

**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, and 16.00 for O. The formula mass of H_{2}SO_{4} is:

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

Thus, one mole of H_{2}SO_{4} weighs 98.08 grams. This relation provides a conversion factor to go from grams to moles. Using the factor 98.08 g / 1 mol:

grams H_{2}SO_{4} = 3.60 mol x 98.08 g / 1 mol = 353 g H_{2}SO_{4}

**Answer**

There are 353 grams of H_{2}SO_{4} in 3.60 moles of H_{2}SO_{4}.

## Performing Grams and Moles Conversions

Here are some tips for performing these conversions. The two problems most commonly encountered are not cancelling the units correctly and using the incorrect number of significant figures.

- It helps to write out the conversion and make sure units cancel. You might 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.

## Sources

- Andreas, Birk; et al. (2011). "Determination of the Avogadro Constant by Counting the Atoms in a 28Si Crystal".
*Physical Review Letters*. 106 (3): 30801. doi:10.1103/PhysRevLett.106.030801 - Cooper, G.; Humphry, S. (2010). "The ontological distinction between units and entities".
*Synthese*. 187 (2): 393–401. doi:10.1007/s11229-010-9832-1 - "Weights and Measures Act 1985 (c. 72)". The UK Statute Law Database. Office of Public Sector Information.