How to Convert Grams to Moles and Moles to Grams

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.

Grams to Moles Conversion Problem

Problem

Determine the number of moles of CO₂ in 454 grams of CO₂.

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 CO₂ is:

12.01 + 2(16.00) = 44.01

Thus, one mole of CO₂ 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 CO₂ = 454 g x 1 mol/44.01 g = 10.3 moles

Answer

There are 10.3 moles of CO₂ 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, H₂O₂.

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 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, and 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 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 H₂SO₄ = 3.60 mol x 98.08 g / 1 mol = 353 g H₂SO₄

Answer

There are 353 grams of H₂SO₄ in 3.60 moles of H₂SO₄.

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.