Question

In which of the following equilibrium, $K_c$ and $K_p$ are not equal?
(A) $2C_{(s)}+O_{2(g)}\rightleftharpoons 2C{O}_{(g)}$
(B) $2N{O}_{(g)}\rightleftharpoons N_{2(g)}+O_{2(g)}$
(C) $S{O}_{2(g)}+N{O}_{2(g)}\rightleftharpoons S{O}_{3(g)}+N{O}_{(g)}$
(D) $H_{2(g)}+I_{2(g)}\rightleftharpoons 2H{I}_{(g)}$

Answer 1

Hint: Recollect what is $K_c$ and $K_p$. Find out the relationship between $K_c$ and $K_p$. Then accordingly substitute the values from the chemical reaction and find out the answer.

Complete answer:
-$K_c$ and $K_p$ are both equilibrium constants. $K_c$ is measured in terms of molar concentration of reactants and products whereas, $K_p$ is measured in terms of partial pressures of reactants and products.
We know that, $${\text{K}}_{\text{c}}\text{=}{\displaystyle \frac{\left[\text{products}\right]}{\left[\text{reactants}\right]}}$$ and also, ${\text{K}}_{\text{p}}\text{=}{\displaystyle \frac{\text{partial pressure of products}}{\text{partial pressure of reactants}}}$
From ideal gas equation we have,
PV=nRT
$$P={\displaystyle \frac{n}{V}}RT$$
Concentration, $$C={\displaystyle \frac{n}{V}}$$. Substituting this in above equation, we get,
$$P=CRT$$
So, when we equate $K_c$ and $K_p$, we obtain the relation,
$$K_p=K_c\times {(RT)}^{\mathrm{\Delta }n}$$ where $\mathrm{\Delta }n$ is the change in number of moles of gaseous products to number of moles of gaseous reactants. $\mathrm{\Delta }n$ should be zero in order to get $K_p=K_c$.
Now, let’s calculate $\mathrm{\Delta }n$ for each reaction.
For option (A),
$$2C_{(s)}+O_{2(g)}\rightleftharpoons 2C{O}_{(g)}$$
$\mathrm{\Delta }n=2-3=-1$
So, $K_p\ne K_c$
For option (B),
$$2N{O}_{(g)}\rightleftharpoons N_{2(g)}+O_{2(g)}$$
$\mathrm{\Delta }n=2-2=0$
So, $K_p=K_c$
For option (C),
$$S{O}_{2(g)}+N{O}_{2(g)}\rightleftharpoons S{O}_{3(g)}+N{O}_{(g)}$$
$\mathrm{\Delta }n=2-2=0$
So, $K_p=K_c$
For option (D),
$H_{2(g)}+I_{2(g)}\rightleftharpoons 2H{I}_{(g)}$
$\mathrm{\Delta }n=2-2=0$
So, $K_p=K_c$
So, we can conclude that, in reaction,
(A) $$2C_{(s)}+O_{2(g)}\rightleftharpoons 2C{O}_{(g)}$$
$K_c$ and $K_p$ are not equal because $\mathrm{\Delta }n\ne 0$

Therefore, option (A) is the correct answer.

Note:
Remember the equilibrium concept thoroughly. Make a note of what is partial pressure of a gas and how to derive the relation between both the equilibrium constants. Also, see in which type of problems $K_c$ is used and where $K_p$ is used.