Question

For a first order reaction $A(g)\to 2B(g)+C(g)$ at constant volume and $300K$, 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: (A), (D)

$P_0+2P=P_t$
$K=\frac{1}{t}In\frac{P_0}{P_0-P}=\frac{1}{t}In\frac{P_0}{P_0-P}=\frac{1}{t}In\frac{P_0}{P_0-\frac{\left(P_t-P_0\right)}{2}}$
$K=\frac{1}{t}In\frac{2P_0}{3P_0-P_t}\Rightarrow -Kt+In2P_0=In\left(3P_0-P_t\right)$ and $t_{1/3}=\frac{1}{K}In\frac{P_0}{P_0/3}=\frac{1}{K}In3$ = constant
Rate constant does not depends on concentration