Question 6 of 37intermediate🔧 ApplyNumerical2 marks

Time required to decompose SO2Cl2\text{SO}_2\text{Cl}_2 to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.

Correct Answer

Given: Half-life, t1/2=60t_{1/2} = 60 minutes Reaction is first order.

Formula: For a first order reaction, half-life is related to rate constant by:

t1/2=0.693kt_{1/2} = \frac{0.693}{k}

Calculation:

k=0.693t1/2k = \frac{0.693}{t_{1/2}}

k=0.69360=0.01155k = \frac{0.693}{60} = 0.01155 min−1^{-1}

Converting to seconds: k=0.69360×60=0.6933600=1.925×10−4k = \frac{0.693}{60 \times 60} = \frac{0.693}{3600} = 1.925 \times 10^{-4} s−1^{-1}

Rate constant k=1.15×10−2k = 1.15 \times 10^{-2} min−1^{-1} or 1.93×10−41.93 \times 10^{-4} s−1^{-1}

Exercise: Intext Questions | Q: 3.6 | (Page 18)
For More Understanding

Explanation

This is a direct application of the first-order half-life formula. For first-order reactions, the half-life is constant and independent of initial concentration. The relationship t₁/₂ = 0.693/k is derived from the integrated rate law for first-order reactions. The numerical constant 0.693 represents ln(2), which comes from the mathematical derivation involving the natural logarithm of 2 (the ratio of initial to half concentration).

Solution Steps

  1. Step 1: Identify that for a first order reaction, half-life formula is t1/2=0.693kt_{1/2} = \frac{0.693}{k}

  2. Step 2: Rearrange to find rate constant: k=0.693t1/2k = \frac{0.693}{t_{1/2}}

  3. Step 3: Substitute t1/2=60t_{1/2} = 60 min: k=0.69360=0.01155k = \frac{0.693}{60} = 0.01155 min−1^{-1}

  4. Step 4: Convert to SI units (seconds): k=0.6933600=1.93×10−4k = \frac{0.693}{3600} = 1.93 \times 10^{-4} s−1^{-1}

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