Question

$A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$ is observed to be a first order reaction. On starting with pure $A$, it is found that, at the end of 10 min, the total pressure of the system is $176mm$ of $Hg$ and after a long time, it is $270mm$ of $Hg$. Which of the following is /are correct for the given data?

• A. The initial pressure $A$ is $90mmHg$
• B. The partial pressure of $A$ after 10 min is $47mmHg$
• C. The rate constant of the reaction is $0.0649/min$
• D. None of the above

Answer 1

Answer: (A), (B), (C)

The initial pressure $A$ is $90mmHg$
The rate constant of the reaction is $0.0649/min$
The partial pressure of $A$ after 10 min is $47mmHg$

Let the initial pressure of $A$ will be a $mmHg$.

After a long time, the pressures of $A,B$ and $C$ will be $0,2a$ and $a$ atm respectively. Thus, $3a=270ora=90mmHg$.

Hence, the initial pressure $A$ is $90$ $mmHg$.

Option $A$ is correct.

After 10 min, the pressures of $A,B$ and $C$ will be $a-x,2x$ and $x$, respectively. Total pressure is $176mmHg$.

$a-x+2x+x=176orx=43mmHg$
$a-x=90-43=47mmHg$
Hence, the partial pressure of $A$ after 10 min is $47mmHg$.

Thus, the option $B$ is correct.

$k=\frac{2.303}{t}log\frac{a}{a-x}=\frac{2.303}{10}log\frac{90}{47}=0.0649/min$

Hence, the rate constant of the reaction is 0.0649 /min.

Thus, option $C$ is correct.