Question

Write expressions for K and K_p for the following reactions.

a. $\mathbf{2}\mathit{N}{\mathit{H}}_{\mathbf{3}}\left(\mathit{g}\right)\mathbf{+}\mathit{C}{\mathit{O}}_{\mathbf{2}}\left(\mathit{g}\right)\mathbf{}{\mathit{N}}_{\mathbf{2}}\mathit{C}{\mathit{H}}_{\mathbf{4}}\mathit{O}\left(\mathit{s}\right)\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\left(\mathit{g}\right)$

b. $\mathbf{2}\mathit{K}\mathit{C}\mathit{l}{\mathit{O}}_{\mathbf{3}}\left(s\right)\mathbf{2}\mathit{K}\mathit{C}\mathit{l}\left(s\right)\mathbf{+}\mathbf{3}{\mathit{O}}_{\mathbf{2}}\left(g\right)$

c. $\mathbf{2}\mathit{K}\mathit{C}\mathit{l}{\mathit{O}}_{\mathbf{3}}\left(\mathit{s}\right)\mathbf{2}\mathit{K}\mathit{C}\mathit{l}\left(\mathit{s}\right)\mathbf{+}\mathbf{3}{\mathit{O}}_{\mathbf{2}}\left(\mathit{g}\right)$

d. $\mathit{C}\mathit{u}\mathit{O}\left(\mathit{s}\right)\mathbf{+}{\mathit{H}}_{\mathbf{2}}\left(\mathit{g}\right)\mathit{C}\mathit{u}\left(\mathit{l}\right)\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\left(\mathit{g}\right)$

Short answer

a.$\text{K =}\frac{\left[{\text{H}}_{\text{2}}\text{O}\right]}{{\left[{\text{NH}}_{\text{3}}\right]}^{\text{2}}\left[{\text{CO}}_{\text{2}}\right]}$ and ${\text{K}}_{\text{p}}\text{=}\frac{{\text{P}}_{{\text{H}}_{\text{2}}\text{O}}}{\left({{\text{P}}_{{\text{NH}}_{\text{3}}}}^{\text{2}}\right)\left({\text{P}}_{{\text{CO}}_{\text{2}}}\right)}$

b.$\text{K =}\left[{\text{N}}_{\text{2}}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{3}}$ and ${\text{K}}_{\text{p}}\text{=}\left({\text{P}}_{{\text{N}}_{\text{2}}}\right)\left({{\text{P}}_{{\text{Br}}_{\text{2}}}}^{\text{3}}\right)$

c.$\text{K =}{\left[{\text{O}}_{\text{2}}\right]}^{\text{3}}$ and ${\text{K}}_{\text{p}}\text{=}{{\text{P}}_{{\text{O}}_{\text{2}}}}^{\text{3}}$

d. $\text{K =}\frac{\left[{\text{H}}_{\text{2}}\text{O}\right]}{\left[{\text{H}}_{\text{2}}\right]}$and ${\text{K}}_{\text{p}}\text{=}\frac{{\text{P}}_{{\text{H}}_{\text{2}}\text{O}}}{{\text{P}}_{{\text{H}}_{\text{2}}}}$

Step-by-step solution

Subpart a)

We know that the activities of pure liquids and solids are 1. Therefore, we neglected them in the equilibrium constant expressions.

The given balanced chemical equation is shown below:

${\text{2NH}}_{\text{3}}\left(\text{g}\right){\text{+CO}}_{\text{2}}\text{(g)}\rightleftharpoons {\text{N}}_{\text{2}}{\text{CH}}_{\text{4}}\text{O}\left(\text{s}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{g}\right)$

The expression for the equilibrium constant, K in terms of concentrations is written below:

${\text{K}}_{\text{p}}\text{=}\frac{{\text{P}}_{{\text{H}}_{\text{2}}\text{O}}}{\left({{\text{P}}_{{\text{NH}}_{\text{3}}}}^{\text{2}}\right)\left({\text{P}}_{{\text{CO}}_{\text{2}}}\right)}$

The expression for the equilibrium constant, K_p in terms of partial pressures is written below:

${\text{K}}_{\text{p}}\text{=}\frac{{\text{P}}_{{\text{H}}_{\text{2}}\text{O}}}{\left({{\text{P}}_{{\text{NH}}_{\text{3}}}}^{\text{2}}\right)\left({\text{P}}_{{\text{CO}}_{\text{2}}}\right)}$

Subpart b) 

The given balanced chemical equation is shown below:

${\text{2NBr}}_{\text{3}}\left(\text{s}\right){\text{N}}_{\text{2}}\left(\text{g}\right){\text{+ 3Br}}_{\text{2}}\left(\text{g}\right)$

The expression for the equilibrium constant, K in terms of concentrations is written below:

$\text{K =}\left[{\text{N}}_{\text{2}}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{3}}$

The expression for the equilibrium constant, K_p in terms of partial pressures is written below:

${\text{K}}_{\text{p}}\text{=}\left({\text{P}}_{{\text{N}}_{\text{2}}}\right)\left({{\text{P}}_{{\text{Br}}_{\text{2}}}}^{\text{3}}\right)$

Subpart c)

The given balanced chemical equation is shown below:

${\text{2KClO}}_{\text{3}}\left(\text{s}\right)\text{2KCl}\left(\text{s}\right){\text{+ 3O}}_{\text{2}}\left(\text{g}\right)$

The expression for the equilibrium constant, K in terms of concentrations is written below:

$\text{K =}{\left[{\text{O}}_{\text{2}}\right]}^{\text{3}}$

The expression for the equilibrium constant, K_p in terms of partial pressures is written below:

${\text{K}}_{\text{p}}\text{=}{{\text{P}}_{{\text{O}}_{\text{2}}}}^{\text{3}}$

Subpart d)

The given balanced chemical equation is shown below:

$\text{CuO}\left(\text{s}\right){\text{+H}}_{\text{2}}\left(\text{g}\right)\text{Cu}\left(\text{l}\right){\text{+H}}_{\text{2}}\text{O}\left(\text{g}\right)$

The expression for the equilibrium constant, K in terms of concentrations is written below:

$\text{K =}\frac{\left[{\text{H}}_{\text{2}}\text{O}\right]}{\left[{\text{H}}_{\text{2}}\right]}$

The expression for the equilibrium constant, K_p in terms of partial pressures is written below:

${\text{K}}_{\text{p}}\text{=}\frac{{\text{P}}_{{\text{H}}_{\text{2}}\text{O}}}{{\text{P}}_{{\text{H}}_{\text{2}}}}$