Question 29 of 37advanced🔧 ApplyNumerical3 marks

The following data were obtained during the first order thermal decomposition of SO2Cl2\text{SO}_2\text{Cl}_2 at a constant volume.

SO2Cl2(g)→SO2(g)+Cl2(g)\text{SO}_2\text{Cl}_2(\text{g}) \rightarrow \text{SO}_2(\text{g}) + \text{Cl}_2(\text{g})

Experiment | Time/s−1^{-1} | Total pressure/atm 1 | 0 | 0.5 2 | 100 | 0.6 Calculate the rate of the reaction when total pressure is 0.65 atm.

Correct Answer

Rate of reaction = 7.8×107.8 \times 10⁻⁴ atm s⁻¹

Exercise: EXERCISES | Q: 3.21 | (Page 27)
For More Understanding

Explanation

This is a first order reaction where SO₂Cl₂ decomposes into SO₂ and Cl₂. For gaseous reactions at constant volume, we use pressure terms instead of concentrations. The rate constant is first determined using the initial data, then the rate is calculated at the specified pressure.

Solution Steps

  1. Step 1: Calculate the rate constant (k) For the reaction: SO₂Cl₂(g) → SO₂(g) + Cl₂(g) At t = 0: Initial pressure pᵢ = 0.5 atm At t = 100 s: Total pressure pₜ = 0.6 atm Partial pressure of SO₂Cl₂ at t = 100 s: pₐ = 2pᵢ - pₜ = 2(0.5) - 0.6 = 0.4 atm

    k = (2.303/t) log(pᵢ/pₐ) k = (2.303/100) log(0.5/0.4) k = (2.303/100) log(1.25) k = 2.23×102.23 \times 10⁻³ s⁻¹

  2. Step 2: Find partial pressure of SO₂Cl₂ when total pressure is 0.65 atm pₐ = 2pᵢ - pₜ = 2(0.5) - 0.65 = 0.35 atm

  3. Step 3: Calculate rate of reaction For first order reaction: Rate = k × pₐ Rate = 2.23×102.23 \times 10⁻³ × 0.35 Rate = 7.8×107.8 \times 10⁻⁴ atm s⁻¹

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