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

Step-by-step explanation:

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

`t=(2.303)/(k)\log(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=(2.303)/(k)\log(100)/(100-36)`

`k=(2.303)/(60)\log(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_{(1)/(2)}=(0.693)/(k)`

`t_{(1)/(2)}=(0.693)/(0.0074min^(-1))=93min`

The half-life of the compound is 93 minutes