A particular reactant decomposes with a half-life of 113 s when its initial concentration is 0.372 M. The same reactant decomposes with a half-life of 223 s when its initial concentration is 0.189 M. Calculate the rate constant (k) and reaction order?

Rate constant =  0.0237 M-1 s-1, Order = Second order

Explanation:

In this problem, it can be observed that as the concentration decreases, the half life increases. This means the concentration of the reactant is inversely proportional to the half life.

The order of reaction that exhibit this relationship is the second order of reaction.

In the second order of reaction, the relationship between rate constant and half life is given as;

t1/2 = 1 / k[A]o

Where;

k = rate constant

[A]o = Initial concentration

k = 1 / t1/2 [A]

Uisng the following values;

k = ?

t1/2 = 113

[A]o = 0.372M

k = 1 / (113)(0.372)

k = 1 / 42.036 = 0.0237 M-1 s-1

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