Molar Mass and Mole Calculations
The molar mass (g/mol) converts between the mass of a substance and the number of moles — the chemist's counting unit for atoms and molecules.
Calculating Molar Mass
M = Σ (number of atoms × atomic mass)
Water (H₂O):
2 × H (1.008) + 1 × O (16.00) = 18.016 g/mol
Glucose (C₆H₁₂O₆):
6×12.011 + 12×1.008 + 6×16.00 = 180.16 g/mol
Mole Conversions
n = m / M (moles from mass)
m = n × M (mass from moles)
N = n × Nₐ (number of molecules)
Nₐ = 6.022×10²³ mol⁻¹ (Avogadro's number)
100g of NaCl (M=58.44 g/mol):
n = 100/58.44 = 1.71 mol
N = 1.71 × 6.022×10²³ = 1.03×10²⁴ molecules
Common Molar Masses (g/mol)
- H₂O (water): 18.02
- CO₂ (carbon dioxide): 44.01
- NaCl (salt): 58.44
- C₆H₁₂O₆ (glucose): 180.16
- CaCO₃ (calcium carbonate): 100.09
- H₂SO₄ (sulfuric acid): 98.08
Calculate molar mass: Free Molar Mass Calculator
Common Molar Masses Quick-Reference Table
| Compound | Formula | Molar Mass (g/mol) |
|---|---|---|
| Water | H₂O | 18.015 |
| Carbon dioxide | CO₂ | 44.010 |
| Glucose | C₆H₁₂O₆ | 180.16 |
| Sodium chloride | NaCl | 58.44 |
| Ethanol | C₂H₅OH | 46.07 |
| Caffeine | C₈H₁₀N₄O₂ | 194.19 |
| Aspirin | C₉H₈O₄ | 180.16 |
How Molar Mass Works
Molar mass is the mass of one mole (6.022×10²³ units) of a substance, in grams per mole. It numerically equals the substance's atomic or molecular weight in atomic mass units (u). For an element, molar mass = atomic weight from the periodic table. For a compound, sum the atomic masses of all atoms: M(H₂O) = 2(1.008) + 15.999 = 18.015 g/mol.
Molar mass converts between the macroscopic (grams) and microscopic (molecules, atoms) worlds. n = m/M gives moles from mass; N = n × Nₐ gives number of molecules. In pharmaceutical manufacturing, precise molar mass calculations determine drug dosages. In stoichiometry, it allows calculation of theoretical yields from balanced equations.
Common Mistakes
- Using integer atomic masses: H = 1, O = 16 are rough approximations. Use 1.008 and 15.999 for precise results (especially in analytical chemistry).
- Miscounting atoms in complex formulas: Ca(OH)₂ has 1 Ca, 2 O, and 2 H — the subscript outside the parenthesis multiplies everything inside.
- Confusing molar mass with molarity: Molar mass is g/mol (a property of a substance). Molarity is mol/L (a concentration — depends on how much is dissolved in solution).
Frequently Asked Questions
They are numerically identical but differ in units: molecular weight (or relative molecular mass) is dimensionless (the ratio of molecular mass to 1/12 of C-12 mass). Molar mass has units of g/mol. In practice, chemists use them interchangeably — both equal the sum of atomic masses in the formula.
N = (m/M) × Nₐ, where m is the sample mass in grams, M is molar mass in g/mol, and Nₐ = 6.022×10²³ mol⁻¹ (Avogadro's number). Example: 18 g of water = 1 mol = 6.022×10²³ molecules. 9 g = 0.5 mol = 3.011×10²³ molecules.
Natural elements are mixtures of isotopes with different masses. The standard atomic weight is the weighted average: chlorine is 75.77% ³⁵Cl (34.969 u) and 24.23% ³⁷Cl (36.966 u), giving a weighted average of 35.45 g/mol. Stable isotope ratios can shift slightly by geography, which is why ultra-precise analytical chemistry uses isotope-specific masses.