Question

Calculate the half-life of the first-order reaction, $C_2{H}_{4}O\left(g\right)\to C{H}_4\left(g\right)+CO\left(g\right)$, if the initial pressure of $C_2{H}_{4}O\left(g\right)$ is 80 mm and the total pressure at the end of 20 minutes is 120 mm.

• A. 40 min
• B. 120 min
• C. 20 min
• D. 80 min

Answer 1

The correct option is C 20 min

For first-order reaction,

$k=\frac{2.303}{t}log\frac{a}{a-x}$

$=\frac{2.303}{20}\times log\frac{80}{40}$

$=\frac{2.303}{20}\times 0.3010$

For half-life period,

$t_{\frac{1}{2}}=\frac{0.693}{k}=\frac{0.693\times 20}{2.303\times 3010}=20min$

Hence, option C is correct.