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 min. Then:

• A. half life for A is $7.8min$
• B. rate constant is $0.0693mi{n}^{-1}$
• 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

The correct option is B rate constant is $0.0693mi{n}^{-1}$

$A\rightleftharpoons 2B+C$

$P$ $O$ $O$ ; $t=0$

$P-P_O$ $2P_O$ $P_O$ ; $t=20$

Initial $P_T=400mm$; Final $P_T=1000mm$

$\Rightarrow P-P_O+2P_O+P_O=P_T$

$\Rightarrow P+2P_O=P_T$

$\Rightarrow 400+2P_O=1000$

$\Rightarrow P_O=\frac{600}{2}=300mm$

$\Rightarrow P-P_O=400-300$

$=100mm$ of $Hg$

$K=\frac{2.303}{t}\log \left(\frac{P_1}{P_t}\right)$

$\Rightarrow K=\frac{2.303}{20}\log \frac{400}{100}$

$=0.0693mi{n}^{-1}$

$\Rightarrow t_{1/2}=\frac{0.693}{K}=\frac{0.693}{0.0693}=10min$ .