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Q. For a first order reaction $A(g) \to 2B(g) + C(g)$ at constant volume and $300\, K$, the total pressure at the beginning $(t = 0)$ and at time $t$ are $P_0$ and $P_t$, respectively. Initially, only $A$ is present with concentration $[A]0$, and $t_{1/3}$ is the time required for the partial pressure of $A$ to reach $1/3^{rd}$ of its initial value. The correct option(s) is (are)
(Assume that all these gases behave as ideal gases)

JEE AdvancedJEE Advanced 2018Chemical Kinetics

Solution:

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$P_0 + 2P = P_t$
$K = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - \frac{\left(P_{t} - P_{0}\right)}{2}}$
$ K = \frac{1}{t} In \frac{2P_{0}}{3P_{0} - P_{t}} \Rightarrow -Kt + In 2P_{0} = In \left(3P_{0} - P_{t}\right) $ and $t_{1/3} = \frac{1}{K} In \frac{P_{0}}{P_{0}/3}= \frac{1}{K} In 3 $ = constant
Rate constant does not depends on concentration