Question

In the following gaseous phase first order reaction
$A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$
initial pressure was found to be $400$ mm of $Hg$ and it changed to $1000$ mm of $Hg$ after $20$4 min. Then:

• A. half life for $A$ is $10$ min
• B. rate constant is $0.0693$ min${}^{-1}$
• C. partial pressure of $C$ at $30$ min is $350$ mm of $Hg$
• D. total pressure after $30$ min is $1100$ mm of $Hg$

Answer 1

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

The correct options are
A half life for $A$ is $10$ min
B rate constant is $0.0693$ min${}^{-1}$
C partial pressure of $C$ at $30$ min is $350$ mm of $Hg$
D total pressure after $30$ min is $1100$ mm of $Hg$

A(g) $\to$ 2B(g) + C(g)
t = 0 400 0 0
t = 20 min 400 - p 2p p
Given $400-p+2p+p=1000$
$400+2p=1000$
$p=300mm$
$k=\frac{1}{20}ln\frac{400}{400-300}=\frac{1}{20}ln4$
$k=fracln210mi{n}^{-1}$
$T_{1/2}=10min$
$ValueofK=0.0693mi{n}^{-1}$
After 30 min Partial Pressure of A is 50 mm
After 30 min Partial Pressure of B is 700 mm
After 30 min Partial Pressure of C is 350 mm
After 30 min total pressure become 1100 mm
So all of the above are correct.