Q. Given below is a first-order homogeneous gaseous reaction:
$A \rightarrow 2B+C$
If the initial pressure was $P_{i}$ while total pressure after time $t$ was $P_{t},$ then what is the expression for rate constants $K$ in terms $P_{i}, \, P_{t}$ and $t?$

NTA AbhyasNTA Abhyas 2020Chemical Kinetics Report Error

A

$K=\frac{2 .303}{t}log \left(\frac{2 p_{i}}{3 p_{i} - p_{t}}\right)$

30%

B

$K=\frac{2 .303}{t}log \left(\frac{2 p_{i}}{2 p_{i} - p_{i}}\right)$

24%

C

$K=\frac{2 .303}{t}log \left(\frac{p_{i}}{p_{i} - p_{t}}\right)$

38%

D

None of these

9%

Solution:

Total $P_{t}=P_{i}-y+2y+y=P_{i}+2y$
$y=\frac{p_{t} - p_{i}}{2}$
$\because \, K=\frac{2 .303}{t}log \left(\frac{P_{i}}{P_{i} - \left(\frac{P_{t} - P_{i}}{2}\right)}\right)$
$=\frac{2 .303}{t}log \left(\frac{2 P_{i}}{3 P_{i} - P_{t}}\right)$

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