Question

A compound decomposes by a first-order process. If 36 %% of the compound decomposes in 60 minutes, the half-life of the compound is ________minutes. A compound decomposes by a first-order process. If 36 of the compound decomposes in 60 minutes, the half-life of the compound is ________minutes. -5 93 41 -18 39

Answer 1

Answer: The half-life of the compound is 93 minutes

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  

t = age of sample

a = let initial amount of the reactant =100

a - x = amount left after decay process = (100-36) = 64

a) for completion of 36 % of reaction

$60=\frac{2.303}{k}\log\frac{100}{100-36}$

$k=\frac{2.303}{60}\log\frac{100}{64}$

$k=0.0074min^{-1}$

b) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$t_{\frac{1}{2}}=\frac{0.693}{0.0074min^{-1}}=93min$

The half-life of the compound is 93 minutes