Question

If the initial pressure of $C{H}_{3}CHO\left(g\right)$ is 80 mm and the total pressure at the end of 20 min is 120 mm.

$C{H}_{3}CHO\left(g\right)\to C{H}_4\left(g\right)+CO\left(g\right)$

What is the half-life of the first-order reaction?

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

Answer 1

Answer: (C)

20 min

Let $p^o$ be the initial pressure. $p^o=80.$

At time t, the total pressure is $p^o+p=120.$

$p=120-80=40.$

The expression for the rate constant is $K=\frac{1}{t}\ln \frac{p^o}{p^o-p}$

$=\frac{1}{20}\ln \frac{80}{80-40}=\frac{1}{20}\ln 2.$

The expression for the half life period is $t_{1/2}=\frac{\ln 2}{K}.$

Hence, $t_{1/2}=\frac{\ln 2}{\ln 2}\times 20=20min.$