# Question 45035

Apr 12, 2017

We can understand it through the derivation of half life for 1st order reaction.

#### Explanation:

Equation for 1st order reaction is:

k = 2.303/t × log_10(["A"_0]/["A"])

Where,
$k$ = rate constant
$\left[\text{A}\right]$ = concentration after time $t$
$\left[{\text{A}}_{0}\right]$ = initial concentration

For half life, $\left[\text{A}\right]$ = $\frac{{\text{A}}_{0}}{2}$

Therefore,
k = 2.303/"t"_½ × log_10( ["A"_0]/(["A"_0]/2))

k = 2.303/"t"_½× log_10(2)

k = 2.303/"t"_½ × 0.301

k = 0.693/"t"_½#

Therefore, the equation for half life of first order reaction is independent of concentration and thus independent of stoichiometric ratio.