Question 5 of 9intermediate🔧 ApplyNumerical3 marks

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m³ at a temperature of 27 °C and 1 atm pressure.

Correct Answer

The total number of air molecules in the room is approximately 6.10×106.10 \times 10²⁶ molecules.

Exercise: EXERCISES | Q: 12.6
For More Understanding

Explanation

This numerical problem applies the ideal gas law PV = μRT to find the number of moles, then multiplies by Avogadro's number to get the total molecules. The context confirms the ideal gas law and provides the molar volume concept at STP, along with the value of R = 8.31 J mol⁻¹ K⁻¹.

Solution Steps

  1. Step 1: Convert temperature to Kelvin T = 27 °C + 273 = 300 K

  2. Step 2: Apply ideal gas law to find number of moles Using PV = μRT μ = PV/RT μ = (1.01×101.01 \times 10⁵ Pa × 25.0 m³) / (8.31 J mol⁻¹ K⁻¹ × 300 K) μ = 2.525×102.525 \times 10⁶ / 2493 μ ≈\approx 1012.8 moles

  3. Step 3: Calculate total number of molecules Number of molecules = μ × N_A = 1012.8×6.0221012.8 \times 6.022 × 10²³ ≈\approx 6.10×106.10 \times 10²⁶ molecules

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