Question

11. A reactant (A) decomposes by three different first order processes. The half-lives for A going to X is 2 Days, for A goingto Y 3.2 days, and for A going to Z 10 days. What is the half life of A?

Answer 1

Solution: If two or more than two reactions have the same order, the faster reaction will have a shorter half-life, and the slower reaction will have a longer half-life.The reacion is an example of first order parallel reaction.

For parallel reaction, rate (r) = -[dA/dt] = [K1+K2+K3] [A], means K = K1 +K2 +K3, then,

  t _1/2 = 0.6932 / (K1 + K2 + K3)

K1 = 0.6932/ 2, K2 = 0.6932/ 3.2 and K3 = 0.6932 / 10,

on putting these values, we get, t_1/2 = 0.6325 minutes