The isomerization reaction CH3NC → CH3CN obeys the first-order rate law, rate = k[CH3NC], in the presence of an excess of argon. Measurement at 500. K reveals that in 492 seconds, the concentration of CH3NC has decreased to 72% of its original value. Calculate the rate constant (k) of the reaction at 500. K.

Explanation:

The first-order rate law is:

The solution of that differential equation is:

You are given:

And you want to determine k.

Substitute into the solution of the differential equation and solve for t:

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explanation: