The reaction:
SO₂ + Cl₂ SO₂ + Cl₂is a first order reaction with k₁ = 2.2 x 10^–5 s^–1 at 575 K. What percentage of a initial amount of SO₂ Cl₂will get decomposed in 90 minutes when the reaction is carried out at 575 K?

Solution

The reaction:
SO₂ + Cl₂ SO₂ + Cl₂is a first order reaction with k₁ = 2.2 x 10^–5 s^–1 at 575 K
Thus using the first order equation

k = \frac{2.303}{t} \log \frac{[A_{0}]}{[A]}

2.2 \times 10^{- 5} = \frac{2.303}{90} \log \frac{100}{[A]} \log \frac{100}{[A]} = \frac{2.2 \times 10^{- 5} \times 90 \times 60}{2.303} = \frac{198 \times 10^{- 5} \times 60}{2.303} = \frac{19.8 \times 10^{- 4} \times 60}{2.303} = 8.597 \times 6 \times 10^{- 3} = 51.482 \times 10^{- 3}

\frac{100}{[A]} = 051482 Antilog = 1.126 [A] = \frac{100}{1.126} = 88.8 % % of {SO}_{2} {Cl}_{2} decomposed = 100 - 88.8 = 11.2 % .

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