CLASS 11–12 CHEMISTRY · STATES OF MATTER

Ideal gas equation pV = nRT

pV = nRT with p in atm, V in L, T in kelvin and R = 0.0821 L atm mol⁻¹ K⁻¹. Always convert °C to K first (T = t + 273).

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Worked examples

Example 1 · level 1

What volume (in litres) does 1 mol of methane gas occupy at 0 °C and 2 atm? Treat it as an ideal gas and give the answer correct to 2 decimal places. Use R = 0.0821 L atm mol⁻¹ K⁻¹ and T(K) = t(°C) + 273.

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  1. T = 0 + 273 = 273 K.
  2. V = nRT ÷ p = (1 × 0.0821 × 273) ÷ 2.
  3. V = 22.4133 ÷ 2 = 11.21 L.

Answer: 11.21 L

Example 2 · level 2

0.25 mol of nitrogen is sealed in a steel cylinder of volume 10 L at 0 °C. What pressure (in atm) does it exert? Treat it as an ideal gas and give the answer correct to 2 decimal places. Use R = 0.0821 L atm mol⁻¹ K⁻¹ and T(K) = t(°C) + 273.

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  1. T = 0 + 273 = 273 K.
  2. p = nRT ÷ V = (0.25 × 0.0821 × 273) ÷ 10.
  3. p = 5.6033 ÷ 10 = 0.56 atm.

Answer: 0.56 atm

Example 3 · level 3

A 5 L flask contains 2.78 g of an unknown gas at 350 K and 1 atm. Find the molar mass of the gas in g/mol, to the nearest whole number. (R = 0.0821 L atm mol⁻¹ K⁻¹)

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  1. n = pV ÷ RT = (1 × 5) ÷ (0.0821 × 350) = 0.174 mol.
  2. M = 2.78 ÷ 0.174 ≈ 15.98 ≈ 16 g/mol.
  3. This matches methane (CH₄, M = 16 g/mol).

Answer: 16

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