Chemical Formulae, Equations and Calculations

Avogadro's law

• Avogadro's law states that, at the same temperature and pressure, equal volumes of any gases contain equal numbers of molecules
• Consequence: at the same temperature and pressure, the mole ratio of any two gases is the same as the volume ratio of those gases

Molar gas volume

• RTP stands for room temperature and pressure, taken as 20 °C and 1 atm
• At RTP, one mole of any gas occupies a volume of 24 dm³ (equivalently 24 000 cm³)
• This value is called the molar gas volume at RTP

The key formula

• For a gas at RTP:

$n = \frac{V}{24} \qquad (V \text{ in dm}^3)$

• or equivalently, when V is given in cm³:

$n = \frac{V}{24\,000} \qquad (V \text{ in cm}^3)$

• Rearranged:
  • volume (dm³) = moles × 24
  • volume (cm³) = moles × 24 000

Example. What volume does 88 g of CO₂ occupy at RTP?

• M_r(CO₂) = 44, so moles = 88 / 44 = 2.0 mol
• Volume = 2.0 × 24 = 48 dm³

Example. Methane burns completely:

CH₄ (g) + 2O₂ (g) → CO₂ (g) + 2H₂O (g)

What volume of oxygen reacts with 100 cm³ of methane, and what total volume of gas products forms? All volumes are measured at the same temperature and pressure.

• Mole ratio CH₄ : O₂ = 1 : 2, so volume of O₂ needed = 2 × 100 = 200 cm³
• Total moles of products per mole of CH₄ = 1 (CO₂) + 2 (H₂O) = 3
• Total volume of products = 3 × 100 = 300 cm³