Question

$A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$
Initially at t = 0 gas A was present along with some amount of gas C. At At t = 0, the mole fraction of gas C is $\frac{1}{3}$. After some time $t=t_1$, the total pressure is half of the final total pressure at $t=t_x$ (a very long time). Assume this decomposition to follow first order kinetics (at a constant temperature). It is also given at $t=t_x$, the final total pressure is 35 bar.

Rate constant $\left(k\right)=(\log 64-\log 49)s^{-1}$. Value of $t_1$ in seconds is:

• A. 2.15 s
• B. 1.5 s
• C. 2.3 s
• D. 1.15 s

Answer 1

The correct option is D 1.15 s

$A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$
$\frac{2}{3}{P}_{i}0\frac{1}{3}{P}_i$ at $t=0$
$\frac{2}{3}{P}_i-p2p\frac{1}{3}{P}_i+p$ at $t_1$
$\frac{2}{3}{P}_i-p_{x}2p_x\frac{1}{3}{P}_i+p_x$ at $t_x$
from given data
$p_i+2p=\frac{35}{2}$
$p_i+2p_x=35$
after so long time
$\frac{2}{3}{P}_i-p_x=0$
by solving we get
$P_i=15$
$2p=2.5$
We know that for a first order reaction at time t,
$k=\frac{1}{t}ln\frac{\left[intial\right]}{\left[final\right]}$
$log64-log49=\frac{1}{t}ln\frac{\left[\frac{2}{3}{p}_i\right]}{[\frac{2}{3}{p}_i-p]}$
$t=1.15$