Question

Calculate the half-life of the first-order reaction

$C_{2}H_{4}O\left(g\right) \rightarrow CH_{4}\left(g\right)+CO\left(g\right)$

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

Answer: (C)

According to the question,

$p_{0}-p+p=120$ mm

or $p_{0}+p=120$ mm

or $p=120-80=40$ mm.

For a first order reaction,

$k=\frac{1}{t}ln \frac{p_{0}}{p_{0} - p}=\frac{1}{20}ln ⁡ \frac{80}{80 - 40}=\frac{1}{20}ln ⁡ 2$ …(i)

But we know that $t_{\frac{1}{2}}=\frac{1 n 2}{k}$ …(ii)

From equations (i) and (ii)

$k=\frac{1}{20}kt_{\frac{1}{2}}$

$t_{\frac{1}{2}}=20$ min.