Question

In a closed system :$A\left(s\right)\leftrightharpoons 2B\left(g\right)+3C\left(g\right)$ if the partial pressure of C is doubled then partial pressure of B will be:

• A. Twice the original preasure
• B. Half of its original preasure
• C. $\frac{1}{\sqrt[2]{22}}$ times the original pressure
• D. $\frac{1}{2\times \sqrt{2}}$ times its original preasure

Answer 1

The correct option is D $\frac{1}{2\times \sqrt{2}}$ times its original preasure

Solution:- $\frac{1}{2\sqrt{2}}$ times its original pressure.

For a closed system-

$A_{\left(s\right)}\rightleftharpoons 2B_{\left(g\right)}+3C_{\left(g\right)}$

$K_p={\left(P_B\right)}^2\times {\left(P_C\right)}^3$

$\Rightarrow \frac{K_p}{{\left(P_C\right)}^3}={\left(P_B\right)}^2..........\left(1\right)$

Since, $K_p$ is constant, thus if the partial pressure of C is doubled then ${P_C}^{\prime }=2P_C$.

$\therefore K_p={\left({P_B}^{\prime }\right)}^2\times {\left({P_C}^{\prime }\right)}^3$

$K_p={\left({P_B}^{\prime }\right)}^2\times {\left(2P_C\right)}^3$

$\Rightarrow \frac{K_p}{{\left(P_C\right)}^3}=8\times {\left(P_B^{\prime }\right)}^2..........\left(2\right)$

From ${eq}^n\left(1\right)\&\left(2\right)$, we have

$8\times {\left(P_B^{\prime }\right)}^2={\left(P_B\right)}^2$

$\Rightarrow {\left(P_B^{\prime }\right)}^2=\frac{1}{8}\times {\left(P_B\right)}^2$

$\Rightarrow {P_B}^{\prime }=\frac{1}{2\sqrt{2}}\times P_B$

Hence, if the partial pressure of C is doubled then partial pressure of B will be $\frac{1}{2\sqrt{2}}$ times its original pressure.