Question

For which of the reactions in Exercise 13.15 does\({K_c}\)(calculated using concentrations) equal\({K_p}\)(calculated using pressures)?

(a) \(C{H_4}(g) + C{l_2} \rightleftharpoons C{H_3}CI(g) + HCI(g)\)

(b) \({N_2}(g) + {O_2}(g)\rightleftharpoons 2NO(g)\)

(c) \(2S{O_2}(\;g) + {O_2}(\;g)\rightleftharpoons 2S{O_3}(\;g)\)

(d) \(BaS{O_3}(s)\rightleftharpoons BaO(s) + S{O_2}(g)\)

(e) \({P_4}(g) + 5{O_2}(g)\rightleftharpoons{P_4}{O_{10}}(s)\)

(f) \(B{r_2}(\;g)\rightleftharpoons 2Br(g)\)

(g) \(C{H_4}(g) + 2{O_2}(g)\rightleftharpoons C{O_2}(g) + 2{H_2}O(l)\)

(h)\(CuS{O_4} \times 5{H_2}O(s)\rightleftharpoons CuS{O_4}(s) + 5{H_2}O(g)\)

Short answer

1. The values are equal \({{\rm{K}}_{\rm{p}}} = {{\rm{K}}_{\rm{c}}}\).
2. The values are equal \({{\rm{K}}_{\rm{p}}} = {{\rm{K}}_{\rm{c}}}\)
3. The values are not equal \({{\rm{K}}_{\rm{p}}} \ne {{\rm{K}}_{\rm{c}}}\)
4. The values are not \({{\rm{K}}_{\rm{p}}} \ne {{\rm{K}}_{\rm{c}}}\)
5. The values are not equal \({{\rm{K}}_{\rm{p}}} \ne {{\rm{K}}_{\rm{c}}}\)
6. The values are not equal \({{\rm{K}}_{\rm{p}}} \ne {{\rm{K}}_{\rm{c}}}\)
7. The values are not equal \({{\rm{K}}_{\rm{p}}} \ne {{\rm{K}}_{\rm{c}}}\)
8. The values are not equal \({{\rm{K}}_{\rm{p}}} \ne {{\rm{K}}_{\rm{c}}}\)

Step-by-step solution

Definition of equilibrium constant 

The forward and backward (reverse) processes have identical rates in the equilibrium mixture.

For a chemical reaction is

\(A \to B + C\)

The equilibrium constant will be expressed as:

\({K_C} = \frac{{({\rm{B}})({\rm{C}})}}{{({\rm{A}})}}\)

Where,\((A),\;(B)\)and\((C)\)are equilibrium concentration of A, B and C respectively.

When there are an equal number of gas components on both sides of the reaction arrow, the value of\({K_c}\)equals the value of\({K_p}.\)

Both are related to each other as follows:

\({{\rm{K}}_{\rm{p}}} = {{\rm{K}}_{\rm{c}}}{({\rm{RT}})^{\Delta {\rm{n}}}}\)

Check\({K_c}\)and \({K_p}\)are equal or not for part (a)

a.\({\rm{C}}{{\rm{H}}_4}(\;{\rm{g}}) + {\rm{C}}{{\rm{l}}_2}(\;{\rm{g}})\rightleftharpoons{\rm{C}}{{\rm{H}}_3}{\rm{Cl}}({\rm{g}}) + {\rm{HCl}}({\rm{g}})\)

So, both sides contain equal number of gaseous components which is two. Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are equal.

\({{\rm{K}}_{\rm{p}}} = {{\rm{K}}_{\rm{c}}}{({\rm{RT}})^{\Delta {\rm{n}}}}\)

Check \({K_c}\)and \({K_p}\)are equal or notfor part (b)

b.\({N_2}(g) + {O_2}(g)\rightleftharpoons 2NO(g)\)

So, both sides contain equal number of gaseous components. Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are equal.

Check \({K_c}\)and \({K_p}\)are equal or notfor part (c)

c. \(2{\rm{S}}{{\rm{O}}_2}(\;{\rm{g}}) + {{\rm{O}}_2}(\;{\rm{g}}) \to 2{\rm{S}}{{\rm{O}}_3}(\;{\rm{g}})\)

\(2{\rm{S}}{{\rm{O}}_2}(\;{\rm{g}}) + {{\rm{O}}_2}(\;{\rm{g}}) \to 2{\rm{S}}{{\rm{O}}_3}(\;{\rm{g}})\)

So, both sides does not contain equal number of gaseous components. Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are not equal.

Check \({K_c}\)and \({K_p}\) are equal or notfor part (d)

d. \({\rm{BaS}}{{\rm{O}}_3}(\;{\rm{s}})\rightleftharpoons {\rm{BaO}}({\rm{S}}) + {\rm{S}}{{\rm{O}}_2}(\;{\rm{g}})\)

So, both sides does not contain equal number of gaseous components. Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are not equal.

Check \({K_c}\)and \({K_p}\) are equal or notfor part (e)

e. \({{\rm{P}}_4}(\;{\rm{g}}) + 5{{\rm{O}}_2}(\;{\rm{g}})\rightleftharpoons {{\rm{P}}_4}{{\rm{O}}_{10}}(\;{\rm{S}})\)

So, both sides does not contain equal number of gaseous components. Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are not equal..

Check \({K_c}\) and \({K_p}\) are equal or notfor part (f)

f. \({\rm{B}}{{\rm{r}}_2}(\;{\rm{g}})\rightleftharpoons 2{\rm{Br}}({\rm{g}})\)

So, both sides does not contain equal number of gaseous components.

Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are not equal.

Check \({K_c}\) and \({K_p}\) are equal or not for part (g)

g. \({\rm{C}}{{\rm{H}}_4}(\;{\rm{g}}) + 2{{\rm{O}}_2}(\;{\rm{g}})\rightleftharpoons {\rm{C}}{{\rm{O}}_2}(\;{\rm{g}}) + {{\rm{H}}_2}{\rm{O}}({\rm{l}})\)

So, both sides does not contain equal number of gaseous components.

Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are not equal.

Check \({K_c}\) and \({K_p}\) are equal or not for part (h)

h. \({\rm{CuS}}{{\rm{O}}_4}.5{{\rm{H}}_2}{\rm{O}}({\rm{s}})\rightleftharpoons {\rm{CuS}}{{\rm{O}}_4}(\;{\rm{s}}) + 5{{\rm{H}}_2}{\rm{O}}({\rm{l}})\)

So, both sides does not contain equal number of gaseous components.

Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are not equal.