Question

A particular reactant decomposes with a half-life of 149s when its initial concentration is 0.352M.

The same reactant decomposes with a half-life of 237s when its initial concentration is 0.221M.

Determine the reaction order. What is the value and unit of the rate constant for this reaction?

Answer 1

We have, half-life = k/A_o^n-1

Where A_o is the initial concentration and n is the order

Now, by applying the two conditions,

149 = k/0.352^n-1                 Equation 1

237 = k/0.221^n-1                 Equation 2

Equation 2/ Equation 1= 237/149 = (0.352/0.221)^n-1

1.59 = 1.59^(n-1)

Therefore, n-1 = 1

n = 2

Thus, order of the reaction = 2

Bow, by using equation 1, and applying the order of the reaction,

149 = k/0.352^(2-1)

149 = k/0.352

Rate constant = k = 149 x 0.352 = 52.448

For second order reaction unit of rate constant = M^-1s^-1