Converting Between Mass and Moles
To convert between mass and moles, use the molar mass as a conversion factor: moles = mass (g) ÷ molar mass (g/mol), and mass (g) = moles × molar mass (g/mol). In brief: 25.0 g of sodium chloride (58.44 g/mol) is 25.0 ÷ 58.44 = 0.428 mol, and 0.500 mol of water (18.015 g/mol) has a mass of 0.500 × 18.015 = 9.01 g.
This conversion is the most common step in chemistry calculations. A balance measures mass, but chemical equations relate moles, so mass has to be converted into moles before the equation can be applied. This article explains the method with dimensional analysis, gives a step-by-step procedure, shows a table of sample conversions, works through eight examples including formulas with parentheses and hydrates, explains how to handle significant figures and gives some practical tips.
What is the method?
The molar mass tells how many grams there are in one mole, so it can be written as two conversion factors: (1 mol ÷ M grams) and (M grams ÷ 1 mol). Choose the one that cancels the unit you start with.
- From grams to moles: n = m × (1 mol ÷ M).
- From moles to grams: m = n × (M ÷ 1 mol).
What are the steps?
- Write the formula of the substance and calculate its molar mass.
- Identify the given quantity (mass or moles) and what is asked.
- Set up the conversion so that the starting unit cancels.
- Calculate and round to the right number of significant figures.
- Check that the answer is reasonable: a mass in grams is larger than the number of moles for substances with a molar mass greater than 1 g/mol.
Sample conversions
| Substance | Molar mass (g/mol) | Given | Result |
|---|---|---|---|
| NaCl | 58.44 | 25.0 g | 0.428 mol |
| H2O | 18.015 | 0.500 mol | 9.01 g |
| CaCO3 | 100.09 | 1.00 kg | 9.99 mol |
| Fe | 55.845 | 0.250 mol | 13.96 g |
| C6H12O6 | 180.16 | 5.00 g | 0.0278 mol |
| H2SO4 | 98.07 | 2.50 mol | 245 g |
Worked examples
- Grams to moles. How many moles are in 25.0 g of NaCl? n = 25.0 g × (1 mol ÷ 58.44 g) = 0.428 mol.
- Moles to grams. What is the mass of 0.500 mol of water? m = 0.500 mol × (18.015 g ÷ 1 mol) = 9.01 g.
- Kilograms. How many moles are in 1.00 kg of CaCO3? Convert to grams first: 1.00 kg = 1,000 g. n = 1,000 ÷ 100.09 = 9.99 mol.
- Milligrams. How many moles of caffeine, C8H10N4O2 (194.19 g/mol), are in a 95.0 mg dose? 95.0 mg = 0.0950 g. n = 0.0950 ÷ 194.19 = 4.89 × 10−4 mol.
- Compound with parentheses. What is the mass of 0.200 mol of Ca(OH)2? M = 40.078 + 2(15.999 + 1.008) = 74.092 g/mol. m = 0.200 × 74.092 = 14.8 g.
- Hydrate. How many moles of CuSO4·5H2O are in 12.5 g? M = 249.68 g/mol. n = 12.5 ÷ 249.68 = 0.0501 mol. This contains 0.0501 mol of CuSO4 and 5 × 0.0501 = 0.250 mol of H2O.
- Mass of a sample for a given amount. A reaction needs 0.0250 mol of Na2CO3 (105.99 g/mol). m = 0.0250 × 105.99 = 2.65 g. Weigh 2.65 g.
- Two-step problem. What mass of H2O is formed from 4.00 g of H2 burning in oxygen? n(H2) = 4.00 ÷ 2.016 = 1.984 mol. From 2H2 + O2 → 2H2O, n(H2O) = 1.984 mol. m = 1.984 × 18.015 = 35.7 g.
How do you find the amount of one element in a compound?
The subscripts in a formula give the moles of each element per mole of compound. For aluminum sulfate, Al2(SO4)3, 1 mol contains 2 mol of Al, 3 mol of S and 12 mol of O.
Example: How many grams of oxygen are in 10.0 g of Al2(SO4)3 (342.13 g/mol)? n(compound) = 10.0 ÷ 342.13 = 0.02923 mol. n(O) = 0.02923 × 12 = 0.3508 mol. m(O) = 0.3508 × 15.999 = 5.61 g.
How many significant figures should the answer have?
The answer should have the same number of significant figures as the measurement with the fewest (the molar mass should have at least one more). In 25.0 g ÷ 58.44 g/mol, the mass has three significant figures, so the answer is 0.428 mol. Defined numbers such as the 1,000 g in a kilogram are exact and do not limit the answer.
Why does the conversion matter?
- Stoichiometry: chemical equations relate moles of substances, so every mass calculation goes through moles.
- Preparing solutions: to make a solution of known molarity, calculate the moles needed and convert to a mass to weigh.
- Pharmacy and nutrition: doses of drugs and vitamins are converted between mass and amount.
- Environmental chemistry: concentrations of pollutants are reported in moles or in mass.
Which mistakes are common?
Mistake 1: Multiplying instead of dividing
Moles = mass ÷ molar mass. Check the units: g ÷ (g/mol) = mol.
Mistake 2: Using the wrong molar mass
Use the molar mass of the exact species: O2 is 32.00 g/mol, O is 16.00 g/mol.
Mistake 3: Not converting units to grams
Convert kg and mg to g before using the molar mass.
Mistake 4: Rounding too early
Keep extra digits in the intermediate steps and round only the final answer.