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

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,

$k=\frac{1}{t}ln\frac{p_0}{p_0-p}=\frac{1}{20}ln\frac{80}{80-40}=\frac{1}{20}ln2$ …(i)

But we know that $t_{\frac{1}{2}}=\frac{1n2}{k}$ …(ii)

From equations (i) and (ii)

$k=\frac{1}{20}k{t}_{\frac{1}{2}}$

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