Write the expression for the equilibrium constant for each of the following reactions. Write the pressure of a gas, X , as${\mathbf{P}}_{\mathbf{X}}$ .

(a)$\mathbf{3}{\mathbf{Ag}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{PO}}_{\mathbf{4}}^{\mathbf{3}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathbf{Ag}}_{\mathbf{3}}{\mathbf{PO}}_{\mathbf{4}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$

(b)${\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{6}}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{+}\frac{\mathbf{15}}{\mathbf{2}}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftharpoons }\mathbf{3}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

Equilibrium constant (K): In the equilibrium reaction, the ratio of the concentration of the reactant and the concentration of the product. If K's value is smaller than 1, the reaction should be moved to the left; if K is more than 1, the reaction should be moved to the right.

Example of an equilibrium reaction:

$aA+bB\stackrel{k}{\rightleftharpoons }KcC+dD$
$K=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left|B\right|}^b}$

The concentrations are replaced by pressure P to find pressure.

$K=\frac{P_C^C.{P_D}^d}{{P_A}^a{P_R}^b}$

The given reaction is:

$3{\mathrm{Ag}}^{+}\left(\mathrm{aq}\right)+{\mathrm{PO}}_{4\left(\mathrm{aq}\right)}^3\rightleftharpoons {\mathrm{Ag}}_3{\mathrm{PO}}_{\left(\mathrm{S}\right)}$

For the given reaction, the equilibrium constant is given as:

$K=\frac{1}{{\left[A{g}^{+}\right]}^3\left[P{O}_4^{3-}\right]}$

The product is represented as a unity because the concentration of pure solid is unity.

The given reaction is:

$C_6{H}_{6\left(1\right)}+\frac{15}{2}{O}_{2\left(g\right)}\rightleftharpoons 3H_2{O}_{\left(l\right)}+6C{O}_{2\left(g\right)}$

For the given reaction, the equilibrium constant is given as:

$K=\frac{{\left[H_{2}O\right]}^3{\left[C{O}_2\right]}^6}{\left[C_6{H}_6\right]{\left[O_2\right]}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

The pressure of a gas is$P_x$

$K=\frac{P_{CO2}^6}{P{O}_2^{15/2}}$