The reaction CH₃NC(g) → CH₃CN(g) is first-order with respect to methyl isocyanide, CH₃NC. If it takes 10.3 minutes for exactly one quarter of the initial amount of methyl isocyanide to react, what is the rate constant in units of min^-1 ?

Question

Quizplus · Accepted Answer

Since the reaction is first-order with respect to methyl isocyanide, we can use the first-order integrated rate law: [CH₃NC]t = [CH₃NC]0 e-k t, where [CH₃NC]t is the concentration of CH₃NC at time t, [CH₃NC]0 is the initial concentration of CH₃NC, k is the rate constant, and t is time. Let's consider the given information, "it takes 10.3 minutes for exactly one quarter of the initial amount of methyl isocyanide to react". That means, at t=10.3 min, [CH₃NC]t = 0.75 [CH₃NC]0 Substituting these values in the first-order integrated rate law, we get: 0.75 [CH₃NC]0 = [CH₃NC]0 e-k (10.3 min) Simplifying, we get: k = ln(4/3)/10.3 min ≈ 0.0279 min^-1 Therefore, the answer is B, 0.0279 min^-1.

The Reaction CH3NC(g) → CH3CN(g) Is First-Order with Respect to Methyl

The Reaction CH₃NC(g) → CH₃CN(g) Is First-Order with Respect to Methyl