Question

Decomposition of $3A\left(g\right)\to 2B\left(g\right)+2C\left(g\right)$ follows first order kinetics. Initially only A is present in the container. Pressure developed after 20 min. and infinite time are 3.5 and 4 atm respectively. Which of the following is/are true?

• A. $t_{50}=20min$
• B. $t_{75}=40min$
• C. $t_{99}=64/3min$
• D. $t_{87.5}=60min$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $t_{75}=40min$
B $t_{50}=20min$
D $t_{87.5}=60min$

The decomposition reaction is $3A\left(g\right)\to 2B\left(g\right)+2C\left(g\right)$

Initially, let $P_0$ be the pressure of A.

After 20 minutes, the pressures of A, B and C are $P_0-x,\frac{2x}{3}and\frac{2x}{3}$ respectively.

After very large time, the pressures of A, B and C are $0,\frac{2P_0}{3}and\frac{2P_0}{3}$ respectively.

$\frac{4P_0}{3}=4$

Thus the initial pressure of A is $P_0=3atm$

$P_0+\frac{x}{3}=3.5$

$x=1.5$
Thus 20 minutes is the half life period. $t_{50}=20$

The time for 75% completion will be $t_{75}=2\times 20=40min.$

The time for 87.5% completion will be $t_{87.5}=3\times t_{50}=3\times 20=60min$

The time for 99% completion will be $t_{99}=\frac{2}{3}\times t_{99.9}=\frac{2}{3}\times 10\times t_{50}=\frac{400}{3}$.