Question

If the rate constant for a first-order reaction is k, the time (t) required for the completion of 99% of the reaction is given by:

Options

• t = 0.693/k

• t = 6.909/k

• t = 4.606/k

• t = 2.303/k

Answer 1

t = 4.606/k

Explanation:

For a first-order reaction,

t = `2.303/k log  ([A]_0)/([A])`

for 99% completion of the reaction,

This means only 1% of the reactant is left

`[A] = [A]_0/100`

⇒ `t = 2.303/k log  [A]_0/[A]`

= `2.303/k log  [A]_0/([A]_0//100)`

= `2.303/k log 100`

= `2.303/k xx 2`    ...(log 100 = 2)

t = `4.606/k`