Question

Decomposition of $3A\left(g\right)\to 2B\left(g\right)+2C\left(g\right)$ follows first-order kinetic. Initially, only $A$ is present in the container. The pressure developed after $20\text{min}$ and infinite time are $3.5$ and $4\text{atm}$, respectively. Which of the following is true?

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

Answer 1

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

$t_{87.5\text{\%}}=60\text{min}$

$3A\left(g\right)\to 2B\left(g\right)+2C\left(g\right)$
$\text{At}t=0\text{Pressure}=P_0$
$t=20\text{The pressure of A, B and C are}{P}_0-X,\frac{2x}{3},\frac{2x}{3}\text{respectively}.$
$t=\infty \text{The pressure of A, B and C are}\frac{2P_0}{3},\frac{2P_0}{3}\text{respectively}.$
$\Rightarrow \frac{4P_0}{3}=4$
$P_0=3\text{atm}$
$P_0+\frac{x}{3}=3.5$
$x=1.5$

$\to t_{50\%}=20\text{min}$ is the half life.
$t_{75\%}=2\times 20=40\text{min}$
$t_{87.5\text{\%}}=3\times t_{50\text{\%}}=3\times 20$
$=60\text{min}$
$t_{99\text{\%}}=\frac{2}{3}\times t_{99.9\text{\%}}=\frac{2}{3}\times 10\times t_{50\text{\%}}$
$=\frac{400}{3}\text{min}$