13.2 Equilibrium Constants

Explain why an equilibrium between Br₂(l) and Br₂(g) would not be established if the container were not a closed vessel shown in the reference.

Among the solubility rules previously discussed is the statement: All chlorides are soluble except Hg₂Cl₂, AgCl, PbCl₂, and CuCl.

(a) Write the expression for the equilibrium constant for the reaction represented by the equation $\text{AgCl} \left(s\right) \rightleftharpoons \text{Ag}^{+} \left(a q\right) + \text{Cl}^{−} \left(a q\right) .$ Is K_c > 1, < 1, or ≈ 1? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by the equation $\text{Pb}^{2+} \left(a q\right) + 2 \text{Cl}^{−} \left(a q\right) \rightleftharpoons \text{PbCl}_{2} \left(s\right) .$ Is K_c > 1, < 1, or ≈ 1?…

Benzene is one of the compounds used as octane enhancers in unleaded gasoline. It is manufactured by the catalytic conversion of acetylene to benzene: $3 \text{C}_{2} \text{H}_{2} \left(g\right) \rightleftharpoons \text{C}_{6} \text{H}_{6} \left(g\right) .$ Which value of K_c would make this reaction most useful commercially? K_c ≈ 0.01, K_c ≈ 1, or K_c ≈ 10. Explain your answer.

For a titration to be effective, the reaction must be rapid and the yield of the reaction must essentially be 100%. Is K_c > 1, < 1, or ≈ 1 for a titration reaction?

Write the mathematical expression for the reaction quotient, Q_c, for each of the following reactions:

(a) $\text{CH}_{4} \left(g\right) + \text{Cl}_{2} \left(g\right) \rightleftharpoons \text{CH}_{3} \text{Cl} \left(g\right) + \text{HCl} \left(g\right)$

(b) $\text{N}_{2} \left(g\right) + \text{O}_{2} \left(g\right) \rightleftharpoons 2 \text{NO} \left(g\right)$

(c) $2 \text{SO}_{2} \left(g\right) + \text{O}_{2} \left(g\right) \rightleftharpoons 2 \text{SO}_{3} \left(g\right)$

(d) $\text{BaSO}_{3} \left(s\right) \rightleftharpoons \text{BaO} \left(s\right) + \text{SO}_{2} \left(g\right)$

(e) $\text{P}_{4} \left(g\right) + 5 \text{O}_{2} \left(g\right) \rightleftharpoons \text{P}_{4} \text{O}_{10} \left(s\right)$

(f) $\text{Br}_{2} \left(g\right) \rightleftharpoons 2 \text{Br} \left(g\right)$

(g) $\text{CH}_{4} \left(g\right) + 2 \text{O}_{2} \left(g\right) \rightleftharpoons \text{CO}_{2} \left(g\right) + 2 \text{H}_{2} \text{O} \left(l\right)$

(h) $\text{CuSO}_{4} \cdot 5 \text{H}_{2} \text{O} \left(s\right) \rightleftharpoons \text{CuSO}_{4} \left(s\right) + 5 \text{H}_{2} \text{O} \left(g\right)$

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 reach equilibrium.

(a) $2 \text{NH}_{3} \left(g\right) \rightleftharpoons \text{N}_{2} \left(g\right) + 3 \text{H}_{2} \left(g\right) K_{c} = 17 ;$ [NH₃] = 0.20 M, [N₂] = 1.00 M, [H₂] = 1.00 M

(b) $2 \text{NH}_{3} \left(g\right) \rightleftharpoons \text{N}_{2} \left(g\right) + 3 \text{H}_{2} \left(g\right) K_{P} = 6.8 \times 10^{4} ;$ NH₃ = 3.0 atm, N₂ = 2.0 atm, H₂ = 1.0 atm

(c) $2 \text{SO}_{3} \left(g\right) \rightleftharpoons 2 \text{SO}_{2} \left(g\right) + \text{O}_{2} \left(g\right) K_{c} = 0.230 ;$ [SO₃] = 0.00 M, [SO₂] = 1.00 M, [O₂] = 1.00 M

(d) $2 \text{SO}_{3} \left(g\right) \rightleftharpoons 2 \text{SO}_{2} \left(g\right) + \text{O}_{2} \left(g\right) K_{P} = 16.5 ;$ SO₃ = 1.00 atm,…

The following reaction has K_P = 4.50 $\times$ 10⁻⁵ at 720 K.
$\text{N}_{2} \left(g\right) + 3 \text{H}_{2} \left(g\right) \rightleftharpoons 2 \text{NH}_{3} \left(g\right)$

If a reaction vessel is filled with each gas to the partial pressures listed, in which direction will it shift to reach equilibrium? P(NH₃) = 93 atm, P(N₂) = 48 atm, and P(H₂) = 52 atm

Which of the systems described in the exercise are homogeneous equilibria? Which are heterogeneous equilibria?

For which of the reactions in the exercise does K_c (calculated using concentrations) equal K_P (calculated using pressures)?

Convert the values of K_c to values of K_P or the values of K_P to values of K_c.

(a) $\text{N}_{2} \left(g\right) + 3 \text{H}_{2} \left(g\right) \rightleftharpoons 2 \text{NH}_{3} \left(g\right) K_{c} = 0.50 \text{at} 400 °\text{C}$

(b) $\text{H}_{2} \left(g\right) + \text{I}_{2} \left(g\right) \rightleftharpoons 2 \text{HI} \left(g\right) K_{c} = 50.2 \text{at} 448 °\text{C}$

(c) $\text{Na}_{2} \text{SO}_{4} \cdot 10 \text{H}_{2} \text{O} \left(s\right) \rightleftharpoons \text{Na}_{2} \text{SO}_{4} \left(s\right) + 10 \text{H}_{2} \text{O} \left(g\right) K_{P} = 4.08 \times 10^{−25} \text{at} 25 °\text{C}$

(d) $\text{H}_{2} \text{O} \left(l\right) \rightleftharpoons \text{H}_{2} \text{O} \left(g\right) K_{P} = 0.122 \text{at} 50 °\text{C}$

What is the value of the equilibrium constant expression for the change $\text{H}_{2} \text{O} \left(l\right) \rightleftharpoons \text{H}_{2} \text{O} \left(g\right)$ at 30 °C? (See Appendix E.)

Write the reaction quotient expression for the ionization of NH₃ in water.