Consider the reaction 3A + B + C $\to$ D + E where the rate law is defined as .
An experiment is carried out where [B] 0 = [C] 0 = 1.00 M and [A] 0 = 1.00 $\times$ 10 - 4 M.
-The half-life for this experiment is

Question

Consider the reaction 3A + B + C $\to$ D + E where the rate law is defined as  .
An experiment is carried out where [B] 0 = [C] 0 = 1.00 M and [A] 0 = 1.00 $\times$ 10 - 4 M.
-The half-life for this experiment is

Quizplus · Accepted Answer

The half-life for a first-order reaction is given by the expression t1/2 = 0.693/k, where k is the rate constant. From the given rate law, we can see that the reaction is first order in A. Therefore, the rate constant k can be obtained using the initial concentration of A and the rate constant.

k = (ln 2) / t1/2 = (ln 2) / 87.0 s = 0.00797 M^-1*s^-1

Now, we can use this value of k to calculate the time required for the concentration of A to reduce to half its initial value.

ln [A]t/[A]0 = -kt

ln 0.5 = -0.00797 M^-1*s^-1 * t

t = 87.0 s

Therefore, the half-life of this reaction is 87.0 s, which is closest to choice (B).

Consider the Reaction 3A + B + C →\to→ D + E Where the Rate Law Is Defined as

Consider the Reaction 3A + B + C $\to$ D + E Where the Rate Law Is Defined as