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
$t_{1 / 2}=\frac{2.303 \times 0.3010}{k} \ldots \text { (i) }$
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} \ldots $ (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} $
$\Rightarrow t_{90}=\frac{1}{0.3010} \times t_{1 / 2}$
$\therefore t_{90}=3.322 \times t_{1 / 2}$