Question

The value of $K_p$ for the reaction, $A\left(g\right)+2B\left(g\right)\rightleftharpoons C\left(g\right)$ is $25at{m}^{-2}$ at a certain temperature. The value of $K_p$ for the reaction, $\frac{1}{2}C\left(g\right)\rightleftharpoons \frac{1}{2}A\left(g\right)+B\left(g\right)$ at the same temperature would be:

• A. $25at{m}^{-1}$
• B. $\frac{1}{25}at{m}^{-1}$
• C. $\frac{1}{5}atm$
• D. $5atm$

Answer 1

Answer: (D)

$5atm$

We know,$K_c=\frac{[Products{]}^b}{[Reactants{]}^a}$ where a and b are stoichiometric co-efficients.

Also, $K_p=K_c(RT{)}^{\Delta n}$ where $\Delta n=b-a$

For first reaction,

$K_{c1}=\frac{\left[C\right]}{\left[A\right][B{]}^2}$

$\Delta n=1-3=-2$ So,$K_{p1}=K_{c1}(RT{)}^{-2}$

Now for the second reaction,

$K_{c2}=\frac{\left[A{]}^{0.5}\right[B]}{[C{]}^{0.5}}$

$\Delta n=1.5-0.5=1$ So, $K_{p2}=K_{c2}(RT{)}^1$

Now divide $K_{p1}$ and $K_{p2}$,

$⟹\frac{K_{p1}}{K_{p2}}=\frac{K_{c1}(RT{)}^{-2}}{K_{c2}\left(RT\right)}$

$⟹K_{p2}=5atm$