Chemical Formulae, Equations and Calculations

What a mole is

• A mole (symbol mol) is the chemist's unit for counting chemical particles
• One mole of any substance always contains exactly the same number of particles — the Avogadro constant:

$N_\text{A} = 6.02 \times 10^{23}$

• The "particles" can be atoms, molecules, ions, electrons or formula units — whichever the substance is made of
  • 1 mole of helium (He) → 6.02 × 10²³ atoms
  • 1 mole of water (H₂O) → 6.02 × 10²³ molecules
  • 1 mole of sodium chloride (NaCl) → 6.02 × 10²³ formula units

Molar mass

• The molar mass is the mass, in grams, of one mole of a substance
• Numerically:
  • For an element, molar mass = A_r in grams
  • For a compound, molar mass = M_r in grams
• Examples:
  • 1 mol of carbon (A_r = 12) weighs 12 g
  • 1 mol of water (M_r = 18) weighs 18 g
  • 1 mol of sodium chloride (M_r = 58.5) weighs 58.5 g

Converting between mass and moles

• The key relationship is:

$n = \frac{m}{M_r}$

• where n = number of moles, m = mass in grams, and M_r = molar mass in g/mol
• Rearranged:
  • mass = moles × M_r
  • M_r = mass ÷ moles

Example. How many moles are in 5.0 g of NaOH?

• M_r(NaOH) = 23 + 16 + 1 = 40
• n = 5.0 / 40 = 0.125 mol

Example. What is the mass of 2.5 mol of glucose, C₆H₁₂O₆?

• M_r(C₆H₁₂O₆) = (6 × 12) + (12 × 1) + (6 × 16) = 180
• m = 2.5 × 180 = 450 g