Question

The value of $\left(K_p/K_c\right)$ for the reversible reaction $S{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\iff S{O}_3\left(g\right)$ at constant temperature T is:

• A. $(RT{)}^{\frac{1}{2}}$
• B. RT
• C. $(RT{)}^{\frac{-1}{2}}$
• D. $\frac{1}{RT}$

Answer 1

The correct option is C $(RT{)}^{\frac{-1}{2}}$

The relationship between $K_p$ and $K_c$ is $K_p=K_c(RT{)}^{\Delta n}$.

For the reaction $S{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\iff S{O}_3\left(g\right)$,

The value of $\Delta n$ is $1-(1+\frac{1}{2})=-\frac{1}{2}$.

Substitute this value in the above expression.
$K_p=K_c(RT{)}^{\Delta n}=K_c(RT{)}^{-\frac{1}{2}}$.

Hence, $\frac{K_p}{K_c}=(RT{)}^{-\frac{1}{2}}$.

Option C is correct.