Question

A series of experiments investigating the reaction of (CH3)3CCl with H2O to create (CH3)3OH produces a plot of Ln[(CH3)3CCl] vs. time that is linear with a negative slope. Suppose the reaction is carried out under conditions such that the half-life of the reaction is 2.20 x 102 s. What is the instantaneous rate of reaction when [(CH3)3CCl] = 0.15 M?

Answer 1

Explanation:

There will occur a straight line for the curve of Ln[(CH_{3})_{3}CCl] Vs. time. Since, it is a first order reaction therefore, the formula of its half-life will be as follows.

         Half-life = $\frac{ln 2}{k}$

or,         k = $\frac{ln 2}{t_{\frac{1}{2}}}$

               = $\frac{ln 2}{220} sec^{-1}$

So, rate of the reaction will be as follows.

          Rate = $[(CH_{3})_{3}CCl]^{1}$

                   = $\frac{ln 2}{220} sec^{-1} \times 0.15 M$

                   = 0.000473 $Ms^{-1}$

                   = $4.73 \times 10^{-4} Ms^{-1}$

Thus, we can conclude that the instantaneous rate of given reaction is  $4.73 \times 10^{-4} Ms^{-1}$.