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

Expert verified
  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

01

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:

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

02

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.

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

03

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.

04

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.

05

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.

06

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..

07

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.

08

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.

09

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.

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Most popular questions from this chapter

Question: At 25 °C and at 1 atm, the partial pressures in an equilibrium mixture of N2O4 and NO2 are PN2O4= 0.70 atm and PNO2 = 0.30 atm.

(a) Predict how the pressures of NO2 and N2O4 will change if the total pressure increases to 9.0 atm. Will they increase, decrease, or remain the same?

(b) Calculate the partial pressures of NO2 and N2O4 when they are at equilibrium at 9.0 atm and 25 °C

Question: A reaction is represented by this equation: \({K_c} = 1 \times 1{0^3}\)

(a) Write the mathematical expression for the equilibrium constant.

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

Write the mathematical expression for the reaction quotient, \({Q_c}\), for each of the following reactions:

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

What is the approximate value of the equilibrium constant KP for the change C2H5OC2H5 (l)⇌C2 H5OC2H5 (g) at 25 °C.

(Vapor pressure was described in the previous chapter on liquids and solids; refer back to this chapter to find the relevant information needed to solve this problem.)

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