Question

The time of completion of $90\%$ of a first order reaction is approximately

• A. 1.1 times that of half-life
• B. 2.2 times that of half-life
• C. 3.3 times that of half-life
• D. 4.4 times that of half-life

Answer 1

Answer: (C)

Half-life period of first order reaction is
$t_{1/2}=\frac{2.303\times 0.3010}{k}\dots \text{ (i) }$
Time for completion of $90\%$ of a first order reaction is
$t_{90}=\frac{2.303}{k}\log \frac{100}{10}$
$\therefore t_{90}=\frac{2.303}{k}\dots$ (ii)
On dividing Eq. (i) by (ii), we get
$\frac{t_{1/2}}{t_{90}}=\frac{2.303\times 0.3010}{k}\times \frac{k}{2.303}$
$\Rightarrow \frac{t_{1/2}}{t_{90}}=\frac{0.3010}{1}$
$\Rightarrow t_{90}=\frac{1}{0.3010}\times t_{1/2}$
$\therefore t_{90}=3.322\times t_{1/2}$