Chemistry - Chemical Kinetics Question with Solution | TestHub

Reaction:

A $\stackrel{k_1}{\to }$ 2B

A $\stackrel{k_2}{\to }$ C

Initial pressure $P_0=1$ atm, final pressure $P\infty =1.5$ atm.

For parallel reactions:

$P_t=P_0+(P\infty -P_0)(1-e^{-kt})$

At $t=10$ s:

$1.4=1+0.5(1-e^{-10k})$

$e^{-10k}=0.2$

$k=\frac{1}{10}\ln 5=\frac{1.6}{10}$

$k=0.16$ s⁻¹

Total rate constant:

$k=k_1+k_2$

At infinite time, the increase in pressure is due to the formation of products.

For A $\to$ 2B, the pressure increase is +1 mole, and for A $\to$ C, there is no mole change.

$\frac{k_1}{k_1+k_2}=\frac{P\infty -P_0}{P_0}=0.5$

$k_1=0.08$, $k_2=0.08$

Hence,

$k_1=8\times 10^{-2}$, $k_2=8\times 10^{-2}$

Given:

$k_1=x\times 10^{-2}$, $k_2=y\times 10^{-3}$

$x=8$, $y=80$

$x+y=88$