The half-life of a first-order reaction is 6.93 minutes. Find the time required for 90% completion of the reaction.

A first-order reaction follows the rate law:

t = (2.303/k) log (a/(a-x))

For a first-order reaction:

t_1/2 = 0.693/k

Given:

t_1/2 = 6.93 min

Therefore:

k = 0.693/6.93

= 0.1 min^-1

For 90% completion:

Remaining reactant = 10%

a - x = 0.1a

Substituting in the first-order equation:

t = (2.303/0.1) log(10)

Since log(10)=1:

t = 23.03 min

Nearest integer:

23 min

First-order reactions are common in radioactive decay, decomposition reactions, and many biological processes. One important property of first-order reactions is that the half-life remains constant regardless of the initial concentration.

Time Required = 23 Minutes