Chemistry - Chemical Kinetics Question with Solution | TestHub

$A(g)\to B(g)+C(g)$

Total pressure at time $t=P_2$

Total pressure at infinite time $\infty =P_3$

Let the initial pressure of A be $P_1$.

Since 1 mole of A gives 2 moles (B + C),

the total pressure increases during the reaction.

At completion:

$P_3=2P_1$

So,

$P_1=\frac{P_3}{2}$

The pressure of A remaining at time $t$:

$P_A=P_3-P_2$

Now, using the first-order formula:

$k=\frac{1}{t}\ln \left(\frac{P_1}{P_A}\right)$

Substitute the values:

$k=\frac{1}{t}\ln \left(\frac{P_3/2}{P_3-P_2}\right)$

$k=\frac{1}{t}\ln \left(\frac{P_3}{2(P_3-P_2)}\right)$