Calculate the half-life (in s) of a first-order reaction if the concentration of the reactant is 0.0576 M 17.1 s after the reaction starts and is 0.0249 M 97.8 s after the reaction starts.

66.7s

Explanation:

Let's bring out the parameters we were given ...

Half life = ?

Initial Concentration = 0.0576 M

Final Concentration = 0.0249 M

Time for the concentration change to occur = 97.8s - 17.1s = 80.7s

Formular for half life (t1/2) is given as;

t1/2 = ln2 / k ≈ 0.693 / k

where k = rate constant

From the formular of first order reactions;

ln[A] = ln[A]o - kt

where [A] = Final Concentration and [A]o = Initial Concentration

Inserting the values, we have;

ln (0.0249) = ln (0.0576) - k (80.7)

Upon solving for k, we have;

-0.8387 = - k (80.7)

k = 0.01039 s-1

t1/2 = 0.693 / k = 0.693 / 0.01039 = 66.7s