Chemical Equilibrium

$\begin{aligned} \text { Given, } \mathrm{N}_2 & =3.0 \times 10^{-3} \mathrm{M} \\ \mathrm{O}_2 & =4.2 \times 10^{-3} \mathrm{M} \\ \mathrm{NO} & =28 \times 10^{-3} \mathrm{M} \end{aligned}$

For the given reaction,

$\mathrm{N}_2(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{NO}(g)$

equilibrium constant $K_C$ can be written as

$\begin{aligned} & K_C=\frac{[\mathrm{NO}]^2}{\left[\mathrm{~N}_2\right]\left[\mathrm{O}_2\right]} \\ \therefore & \quad K_C=\frac{\left(2.8 \times 10^{-3} \mathrm{M}\right)^2}{\left(3.0 \times 10^{-3} \mathrm{M}\right)\left(4.2 \times 10^{-3} \mathrm{M}\right)}=0.622 \\ \because \quad & K_p=K_C \cdot(R T)^{\Delta n} \end{aligned}$

$\Delta n=$ Number of moles of gaseous products $-$ number of moles of gaseous reactants

$\therefore \quad \begin{aligned} \Delta n & =2-2=0 \\ & K_p=K_C \cdot(R T)^{\circ} \end{aligned}$

or, $\quad K_p=K_C$ or, $K_p=0.622 \mathrm{~atm}$

Both assertion and reason are correct and reason is the correct explanation of assertion.

$K_p=K_C(R T)^{\Delta n}$

$\Delta n$ = number of moles of gaseous products $-$ number of moles of gaseous reactants

When, $\Delta n>1, K_p>K_C$

When, $\Delta n<1, K_p< K_C$

When, $\Delta n=0, K_p=K_C$