| A gaseous compound A reacts by three independent first-order processes (as shown in the figure) with rate constants \[2\times {{10}^{-3}},\,3\times {{10}^{-3}}\] and \[1.93\times {{10}^{-3}}{{s}^{-1}}\] products B, C and D respectively. If initially pure A was taken in a closed container with P = 8 atm, then the partial pressure of B (in atm) after 100 s from start of experiment will be: |
 |
A) 0.288
B) 0.577
C) 1.154
D) None of these
Correct Answer: C
Solution :
| Overall rate constant = |
| \[k={{k}_{1}}+{{k}_{2}}+{{k}_{3}}=6.93\times {{10}^{-3}}\] |
| \[{{t}_{1/2}}=\frac{0.693}{6.93\times {{10}^{-3}}}=100s\] |
| After half life, \[{{P}_{B}}+{{P}_{C}}+{{P}_{D}}=4atm\] |
| \[\frac{{{P}_{B}}}{{{P}_{B}}+{{P}_{C}}+{{P}_{D}}}=\frac{{{k}_{1}}}{{{k}_{1}}+{{k}_{2}}+{{k}_{3}}}=\frac{200}{693}\] |
| \[{{P}_{B}}=4\times \frac{200}{693}=1.154\,atm\] |
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