Question

For a reaction, $X\left(g\right)\to Y\left(g\right)+Z\left(g\right) $the half-life period is $10$ min. In What period of time would the concentration of $X$ be reduced to $10\%$ of original concentration

• A. 20 min
• B. 33 min
• C. 15 min
• D. 25 min

Answer 1

Answer: (B)

$X_{\left(g\right)}\to Y_{\left(g\right)}+Z_{\left(g\right)} $
The reaction is a first-order reaction hence,
$K=\frac{0.693}{t_{12}}=\frac{2.303}{t} log\frac{a}{a-x}$
$=\frac{0.693}{10 min}$
$=\frac{2.303}{t}log \frac{a}{a10}=\frac{0.693}{10}=\frac{2.303}{t}$ log 10
$\therefore t=\frac{2.303\times10}{693}=33\, min$