Question

The rate of a first order reaction is $1.5 \times {10^{ - 2}}mol{L^{ - 1}}{\min ^{ - 1}}$ at $0.5M$ concentration of the reactant.
The half life of the reaction is:
A. $0.383\min $
B. $23.1\min $
C. $8.73\min $
D. $7.53\min $

Answer 1

Hint: A first-order reaction is one in which the rate of the reaction is linearly proportional to the concentration of only one reactant. In other terms, a first-order reaction is a chemical reaction whose rate is determined by changes in the concentration of one reactant. As a result, the order of these reactions is 1.
Formula Used:
Rate of reaction $ = k[A]$
$k = $Rate constant of first order reaction
$A = $ Concentration of first order reaction
Half life of first order reaction is given by:
${t_{0.5}} = \dfrac{{0.693}}{k}$

Complete answer:
Rate of reaction $ = 1.5 \times {10^{ - 2}}$
$A = 0.5M$
To find: Half life of the reaction
First, we need to find the rate constant of the reaction,
Using the above given formula,
$k = \dfrac{{1.5 \times {{10}^{ - 2}}}}{{0.5}}$
$k = 3 \times {10^{ - 2}}$
For Half – life of a reaction,
${t_{0.5}} = \dfrac{{0.693}}{k}$
Substituting the value of $k$ in the above equation,
${t_{0.5}} = \dfrac{{0.693}}{{3 \times {{10}^{ - 2}}}}$
${t_{0.5}} = 23.1\min $
Hence, the half life of the reaction is $23.1\min $.
Hence, the correct option is B. $23.1\min $.

Note:
The half-life of a chemical reaction is the amount of time it takes for the reactant concentration to reach half of its initial value. A unimolecular reaction is another name for a first-order reaction. As we know rate depends only on one reactant, other reactants may be present, but they will all be zero-order because their concentrations have no effect on the rate.