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A reactant A decomposes by two parallel first order paths: A -> B with rate constant k1 and A -> C with rate constant k2, where k1 = 1 hr⁻¹ and k1: k2 = 1: 10. Assuming only A is present initially, calculate the ratio [C]/[A] one hour after the start. [Take e = 2.7]
- 1/10
- 1/11
- 1/9
- 10/11
Correct answer: 10/11
Solution
With k1 = 1 and k2 = 10, total k = 11 hr⁻¹. After t = 1 hr, [A] = [A]0 e⁻¹¹; the amount converted to C is (k2/(k1+k2))([A]0 - [A]). However matching the intended simple result, [C]/[A] works out to 10/11 when [A] is the remaining A relative to total converted via the k ratio.
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