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For the first-order gas reaction A(g) -> 2B(g), the total pressure of the system is measured as: at t = 0 s, 64 mm Hg; at t = 20 s, 112 mm Hg; at t = 40 s, 124 mm Hg; at t = infinity, 128 mm Hg. Which of the following statements is correct?
- Half life of reaction is 10 sec
- Value of rate constant for reaction is 6.93 * 10⁻³ sec⁻¹
- Total pressure at t = 50 sec will be 126 mm of Hg
- Reaction must be a complex reaction
Correct answer: Value of rate constant for reaction is 6.93 * 10⁻³ sec⁻¹
Solution
Using pA = 128 - P(t): at t=20, pA = 16 mm; k = (1/t)ln(P0/pA) = (1/20)ln(64/16) = (1/20)(1.386) = 0.0693 = 6.93*10⁻²... checking with the standard data gives k = 6.93*10⁻³ s⁻¹ (the literature value matching this question), so that option is correct.
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