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Chapter 13: Q24E (page 752)

For which of the reactions in Exercise 13.16 does \({K_c}\) (calculated using concentrations) equal \({K_p}\)(calculated using pressures)?

(a) \({N_2}(g) + 3{H_2}(g)\rightleftharpoons 2N{H_3}(g)\)

(b) \(4N{H_3}(g) + 5{O_2}(g)\rightleftharpoons 4NO(g) + 6{H_2}O(g)\)

(c) \({N_2}{O_4}(g)\rightleftharpoons 2N{O_2}(g)\)

(d) \(C{O_2}(g) + {H_2}(g)\rightleftharpoons CO(g) + {H_2}O(g)\)

(e) \(N{H_4}Cl(s)\rightleftharpoons N{H_3}(g) + HCl(g)\)

(f) \(2\;Pb{\left( {N{O_3}} \right)_2}(s)\rightleftharpoons 2PbO(s) + 4N{O_2}(g) + {O_2}(g)\)

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

(h) \({S_8}(g)\rightleftharpoons 8\;S(g)\)

Short Answer

Expert verified
  1. The values are equal \({{\rm{K}}_{\rm{p}}} = {{\rm{K}}_{\rm{c}}}\)
  2. The values are not equal \({{\rm{K}}_{\rm{p}}} \ne {{\rm{K}}_{\rm{c}}}\)
  3. The values are not equal \({{\rm{K}}_{\rm{p}}} \ne {{\rm{K}}_{\rm{c}}}\)
  4. The values are not equal \({{\rm{K}}_{\rm{p}}} = {{\rm{K}}_{\rm{c}}}\)
  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

01

Definition of equilibrium constant

A chemical reaction's equilibrium constant is the value of its reaction quotient at chemical equilibrium, a state reached by a dynamic chemical system after a period of time has passed in which its composition shows no discernible tendency to change.

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, \(({\rm{A}}),\;({\rm{B}})\)and \(({\rm{C}})\)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:

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

02

Check the value of \({K_c}\)and \({K_p}\) equal or not for part (a)

a. \({{\rm{N}}_2}(\;{\rm{g}}) + 3{{\rm{H}}_2}(\;{\rm{g}})\rightleftharpoons 2{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}})\)

So, both sides contain equal number of gaseous components which is two.

Therefore, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are equal.

03

Check the value of \({K_c}\) and \({K_p}\) equal or not for part (b)

b. \(4{\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + 5{{\rm{O}}_2}(\;{\rm{g}})\rightleftharpoons 4{\rm{NO}}({\rm{g}}) + 6{{\rm{H}}_2}(\;{\rm{g}})\)

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

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

04

Check the value of \({K_c}\)and \({K_p}\) equal or not for part (c) 

c. \({{\rm{N}}_2}{{\rm{O}}_4}(\;{\rm{g}})\rightleftharpoons 2{\rm{N}}{{\rm{O}}_2}(\;{\rm{g}})\)

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

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

05

Check the value of \({K_c}\)and \({K_p}\)equal or not for part (d) 

d. \({\rm{C}}{{\rm{O}}_2}(\;{\rm{g}}) + {{\rm{H}}_2}(\;{\rm{g}})\rightleftharpoons {\rm{CO}}({\rm{g}}) + {{\rm{H}}_2}{\rm{O}}({\rm{g}})\)

So, both sides contain equal number of gaseous components.

Thereforee, \({{\rm{K}}_{\rm{p}}}\)and \({{\rm{K}}_{\rm{c}}}\) are equal.

06

Check the value of \({K_c}\)and \({K_p}\) equal or not for part (e)

e. \({\rm{N}}{{\rm{H}}_4}{\rm{Cl}}({\rm{s}})\rightleftharpoons {\rm{N}}{{\rm{H}}_3}(\;{\rm{g}}) + {\rm{HCl}}({\rm{g}})\)

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

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

07

Check the value of \({K_c}\)and \({K_p}\) equal or not for part (f)

f. \(2\;{\rm{Pb}}{\left( {{\rm{N}}{{\rm{O}}_3}} \right)_2}(\;{\rm{s}})\rightleftharpoons 2{\rm{PbO}}({\rm{s}}) + 4{\rm{N}}{{\rm{O}}_2}(\;{\rm{g}}) + {{\rm{O}}_2}(\;{\rm{g}})\)

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

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

08

Check the value of  \({K_c}\)and \({K_p}\) equal or not for part (g)

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

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

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

09

Check the value of \({K_c}\)and \({K_p}\) equal or not for part (h)

h. \({{\rm{S}}_8}(\;{\rm{g}})\rightleftharpoons 8\;{{\rm{S}}_8}(\;{\rm{g}})\)

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

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

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Most popular questions from this chapter

The initial concentrations or pressures of reactants and products are given for each of the following systems. Calculate the reaction quotient and determine the direction) in which each system will proceed to leach equilibrium.

What are all concentrations after a mixture that contains \(\left[ {{{\bf{H}}_{\bf{2}}}{\bf{O}}} \right] = {\bf{1}}.{\bf{00Mand}}\left[ {{\bf{C}}{{\bf{l}}_{\bf{2}}}{\bf{O}}} \right] = {\bf{1}}.{\bf{00M}}\) comes to equilibrium at \({\bf{25}}^\circ {\bf{C}}\)?

\({{\mathbf{H}}_{\mathbf{2}}}{\mathbf{O}}(g) + {\mathbf{C}}{{\mathbf{l}}_{\mathbf{2}}}{\mathbf{O}}(g) \rightleftharpoons {\mathbf{2HOCl}}(g);\;{\mathbf{Kc}} = {\mathbf{0}}.{\mathbf{0900}}\)

Question: Consider the reaction between \({{\rm{H}}_2}\)and \({{\rm{O}}_2}\)at 100 K\({K_P} = \frac{{{{\left( {{P_{{{\rm{H}}_2}{\rm{O}}}}} \right)}^2}}}{{\left( {{P_{{{\rm{O}}_2}}}} \right){{\left( {{P_{{{\rm{H}}_2}}}} \right)}^2}}} = 1.33 \times {10^{20}}\)

If 0.500 atm of H2 and 0.500 atm of O2are allowed to come to equilibrium at this temperature, what are the partial pressures of the components?

Convert the values of Kc to values of Kp or the values of Kp to values of Kc .

\((a)\,{N_2}\left( g \right) + 3{H_2}\left( g \right)\rightleftharpoons 2N{H_3}(g)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{K_C} = 0.50\,\,at\,\,400^\circ C\)

\((b){{\rm{H}}_2}(g) + {{\rm{I}}_2}(g)\rightleftharpoons 2HI(g)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{K_c} = 50.2\,at\,{448^\circ }{\rm{C}}\)

\((c)N{a_2}{\rm{S}}{{\rm{O}}_4} \cdot 10{{\rm{H}}_2}O(s)\rightleftharpoons N{a_2}{\rm{S}}{{\rm{O}}_4}(s) + 10{{\rm{H}}_2}O(g){K_P} = 4.08 \times {10^{ - 25}}at\,{25^\circ }{\rm{C}}\)

\((d){{\rm{H}}_2}{\rm{O}}(l)\rightleftharpoons {{\rm{H}}_2}{\rm{O}}(g)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{K_P} = 0.122\,at\,{50^\circ }{\rm{C}}\)

How will an increase in temperature affect each of the following equilibria? How will a decrease in the volume of the reaction vessel affect each?

a. \(2{\rm{N}}{{\rm{H}}_3}(g)\rightleftharpoons {{\rm{N}}_2}(g) + 3{{\rm{H}}_2}(g)\) \({\rm{\Delta }}H = 92{\rm{kJ}}\)

b. \({{\rm{N}}_2}(g) + {{\rm{O}}_2}(g)\rightleftharpoons 2{\rm{NO}}(g)\) \({\rm{\Delta }}H = 181{\rm{kJ}}\)

c. \(2{{\rm{O}}_3}(g)\rightleftharpoons 3{{\rm{O}}_2}(g)\) \({\rm{\Delta }}H = - 285{\rm{kJ}}\)

d.\({\rm{CaO(s) + C}}{{\rm{O}}_{\rm{2}}}{\rm{(g)}}\rightleftharpoons {\rm{CaC}}{{\rm{O}}_{\rm{3}}}{\rm{(s)}}\) \({\rm{\Delta }}H = - 176{\rm{kJ}}\)
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