Question

A first order reaction has a half life of $1$ min. The time required for $99.9\%$ completion of the reaction is ______$min.$
(Round off to the Nearest integer).

$[\text{Use : ln}2=0.69;ln10=2.3]$

• A. 10.00
• B. 10.0
• C. 10

Answer 1

Answer: (A), (B), (C)

For first order reaction,
$t=\frac{1}{k}ln\frac{A_0}{A_t}$

$\frac{t_{\text{99.9\%}}}{t_{\text{50\%}}}=\frac{\frac{1}{k}ln\frac{100}{0.1}}{\frac{1}{k}ln2}$

$t_{\text{99.9\%}}=\frac{ln1000}{ln2}\times t_{\text{50\%}}$

$t_{\text{99.9\%}}=3\frac{ln10}{ln2}\times 1$

$\frac{3\times 2.3}{0.69}=10min$