Question

The half-life period for a first order reaction is:

• A. Independent of concentration
• B. Proportional to concentration
• C. Inversely proportional to concentration
• D. Inversely proportional to the square of the concentration

Answer 1

Answer: (A)

Independent of concentration

Integrated rate law for a first order reaction is
$k=\frac{2.30}{t}log\frac{a}{a-x}$
For half-life, $t=t_{1/2},x=\frac{a}{2}$
On substituting the values,
$k=\frac{2.303}{t_{1/2}}log\frac{a}{a-\frac{a}{2}}$
$k=\frac{2.303log2}{t_{1/2}}=\frac{0.693}{t_{1/2}}$
or $t_{1/2}=\frac{0.693}{k}$
Thus, half-life period $\left(t_{1/2}\right)$ of a first order reaction does not depend upon the concentration.