Molar Mass, Avogadro's Number, and Moles - Quick Review

Molar Mass and Atomic Mass Unit

• Molar mass is the mass of one mole of a substance, expressed in g/mol. It is the sum of the atomic masses of all atoms in a formula.

• Atomic mass unit (AMU) is the scale used on the periodic table; when talking about compounds we use molar mass in g/mol.

• For a compound: $M = \sum<em>i (n</em>i \times M<em>i)$ where $ni$ is the number of atoms of element $i$ in the formula and $M_i$ is the atomic mass of element $i$.

• Examples (use standard atomic masses):

  • Carbon = 12.01; Hydrogen = 1.01.

  • CH$4$: $M(CH</em>4) = M(C) + 4\,M(H) = 12.01 + 4\times 1.01 = 16.05\ \text{g/mol}$

  • CHCl$3$: $M(CHCl</em>3) = M(C) + M(H) + 3\,M(Cl) = 12.01 + 1.01 + 3\times 35.45 \approx 119.36\ \text{g/mol}$

  • C$9$H$8$O$4$: $M(C</em>9H<em>8O</em>4) = 9\,M(C) + 8\,M(H) + 4\,M(O) = 9\times 12.01 + 8\times 1.01 + 4\times 16.00 \approx 180.17\ \text{g/mol}$

• One mole contains Avogadro’s number of particles: $N_A = 6.022 \times 10^{23}\ \mathrm{mol^{-1}}$

  • 1 mole of any substance has $N_A$ particles.

  • 12 g of carbon-12 contains exactly $N_A$ carbon atoms (definition of the mole).

• The average molecular mass (in AMU) is equal to the molar mass in g/mol.

• The mole is the amount of substance unit; its mass relation is given by:
  $n = \frac{m}{M}$ where $m$ is mass in g and $M$ is molar mass in g/mol.

• Dimensional analysis reminder: g / (g/mol) = mol.

Avogadro's Number and the Mole

• The mole relates mass to amount of substance via $n = \dfrac{m}{M}$ and $N_A = 6.022 \times 10^{23}$ particles per mole.

• For a given mass, you can find moles by dividing by the molar mass.

Worked Example: Moles in 5.62 g of water

• Molar mass of water: $M(H_2O) = 2\,M(H) + M(O) = 2\times 1.01 + 16.00 = 18.02\ \text{g/mol}$

• Compute moles: $n = \frac{m}{M} = \frac{5.62\ \text{g}}{18.02\ \text{g/mol}} \approx 0.312\ \text{mol}$