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In the decomposition reaction C6H5N2Cl → C6H5Cl + N2 (catalysed by Cu, heated), the half-life is independent of the initial concentration. After 5 minutes, 15 litres of N2 are produced, and at complete reaction, 45 litres of N2 are produced in total. Which of the following statements are correct? (A) The reaction is first order (B) The rate constant is k = (2.303/5)*log(1.5) min⁻¹ (C) The rate constant is k = (2.303/5)*log(3) min⁻¹ (D) The half-life is t_(1/2) = 0.693/k
- It is a first order reaction.
- Rate constant k = (2.303/5)*log(1.5) min⁻¹
- Rate constant k = (2.303/5)*log(3) min⁻¹
- Half-life t_(1/2) = 0.693/k
Correct answer: It is a first order reaction.
Solution
Since half-life is constant, the reaction is first order (A and D are correct). k = (2.303/t)*log(a/(a-x)): a=45 L (total), at t=5 min, x=15 L, so a-x=30 L. k = (2.303/5)*log(45/30) = (2.303/5)*log(1.5). Statement B is correct. Statement C uses log(3) which would apply if x=30 at t=5 min — not the case here. So A, B, D are correct.
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