Question

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)

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

Answer 2

$\begin{matrix}&A&\to&2B&+&C\\\ t=0&P_{0}&&-&&-\\\ t=t&P_{0}-P&&2P&&P\end{matrix}$
$P_0 + 2P = P_t$
$K = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - P} = \frac{1}{t} In \frac{P_{0}}{P_{0} - \frac{\left(P_{t} - P_{0}\right)}{2}}$
$K = \frac{1}{t} In \frac{2P_{0}}{3P_{0} - P_{t}} \Rightarrow -Kt + In 2P_{0} = In \left(3P_{0} - P_{t}\right)$ 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