Question

A particular reactant decomposes with a half‑life of 109 s when its initial concentration is 0.280 M. The same reactant decomposes with a half‑life of 231 s when its initial concentration is 0.132 M.
1. Determine the reaction order.
(A)1
(B)2
(C)0
2. What is the value and units of the rate constant for this reaction? ????=

Answer 1

Answer:

The order of reaction is 2.

Rate constant is 0.0328 (M s)⁻¹

Explanation:

The rate of a reaction is inversely proportional to the time taken for the reaction.

As we are decreasing the concentration of the reactant the half life is increasing.

a) For zero order reaction: the half life is directly proportional to initial concentration of reactant

b) for first order reaction: the half life is independent of the initial concentration.

c) higher order reaction: The relation between half life and rate of reaction is:

Rate = $\frac{1}{k[A_{0}]^{(n-1)}}$

Half life =$K\frac{1}{[A_{0}]^{(n-1)} }$

$\frac{(halflife_{1})}{(halflife_{2})}=\frac{[A_{2}]^{(n-1)}}{[A_{1}]^{(n-1)} }$

where n = order of reaction

Putting values

$\frac{109}{231}=\frac{[0.132]^{(n-1)}}{[0.280]^{(n-1)}}$

$0.472=(0.472)^{(n-1)}$

Hence n = 2

$halflife=\frac{1}{k[A_{0}]}$

Putting values

$231=\frac{1}{K(0.132)}$

K = 0.0328