Question

For the given first order reaction, \[\ce{A -> B}\]. the half-life of the reaction is 0.3010 min. The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min will be equal to ______ (Nearest integer).

Answer 1

For the given first order reaction, \[\ce{A -> B}\]. the half-life of the reaction is 0.3010 min. The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min will be equal to 100.

Explanation:

The given first order reaction is \[\ce{A -> B}\]

For a first-order reaction:

`t_(1//2) = 0.693/k`

⇒ `k = 0.693/t_(1//2)`

t_1/2 = 0.3010 min     ...[Given]

`k = 0.693/0.3010`

= 2.30 min⁻¹

By using the integrated first-order law:

`k = 2.303/t log_10  [A]_0/[A]_t`

`[A]_0/[A]_t = 10^((kt)/2.303)`

= `10^((2.30 xx 2.0)/2.303)`

= `10^(4.60/2.303)`

= 10²

= 100