Question 2 of 9beginner🔧 ApplyNumerical2 marks

Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP: 1 atmospheric pressure, 0 °C). Show that it is 22.4 litres.

Correct Answer

Given:

  • Number of moles, n = 1 mol
  • Temperature, T = 273 K (STP: 0 °C)
  • Pressure, P = 1 atm = 1.01×1.01 \times 10^{5}$$ Pa
  • Universal gas constant, R = 8.31 J mol⁻¹ K⁻¹

Formula: Using the ideal gas equation: PV = nRT

Calculation: V = nRT/P V = (1×8.311 \times 8.31 × 273) / (1.01×1.01 \times 10^{5}$$) V = 2268.63 / 101000 V = 0.0224 m³

Converting to litres (1 m³ = 1000 litres): V = 0.0224×10000.0224 \times 1000 = 22.4 litres

Thus, 1 mol of any ideal gas at STP occupies a volume of 22.4 litres. This universal volume is called the molar volume.

Exercise: EXERCISES | Q: 12.2
For More Understanding

Explanation

This numerical problem from NCERT Physics Class 11 Chapter 12 tests the application of the ideal gas equation. The textbook context provides all necessary values: STP conditions (T = 273 K, P = 1.01×1.01 \times 10^{5}$$ Pa), and the gas constant R = 8.31 J mol⁻¹ K⁻¹. The solution requires substituting these values into PV = nRT and solving for V. The result demonstrates that regardless of the type of ideal gas, 1 mole always occupies 22.4 litres at STP, which is a fundamental result known as molar volume.

Solution Steps

  1. Step 1: Write the ideal gas equation PV = nRT

  2. Step 2: Substitute n = 1 mol, T = 273 K, P = 1.01×1.01 \times 10^{5}$$ Pa, R = 8.31 J mol⁻¹ K⁻¹

  3. Step 3: Solve for V: V = nRT/P = (1×8.311 \times 8.31 × 273)/(1.01×1.01 \times 10^{5}$$)

  4. Step 4: Calculate V = 0.0224 m³ = 22.4 litres

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