7.1 Equilibrium constants  (Page 7/14)

For a precipitation reaction to be useful in a gravimetric analysis, the product of the reaction must be insoluble. Is K _c >1,<1, or ≈ 1 for a useful precipitation reaction?

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

(a) ${\text{CH}}_4(g)+{\text{Cl}}_2(g)\rightleftharpoons {\text{CH}}_3\text{Cl}(g)+\text{HCl}(g)$

(b) ${\text{N}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2\text{NO}(g)$

(c) $2{\text{SO}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2{\text{SO}}_3(g)$

(d) ${\text{BaSO}}_3(s)\rightleftharpoons \text{BaO}(s)+{\text{SO}}_2(g)$

(e) ${\text{P}}_4(g)+5{\text{O}}_2(g)\rightleftharpoons {\text{P}}_4{\text{O}}_{10}(s)$

(f) ${\text{Br}}_2(g)\rightleftharpoons 2\text{Br}(g)$

(g) ${\text{CH}}_4(g)+2{\text{O}}_2(g)\rightleftharpoons {\text{CO}}_2(g)+2{\text{H}}_2\text{O}(l)$

(h) ${\text{CuSO}}_4\text{·}5{\text{H}}_2\text{O}(s)\rightleftharpoons {\text{CuSO}}_4(s)+5{\text{H}}_2\text{O}(g)$

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

(a) ${\text{N}}_2(g)+3{\text{H}}_2(g)\rightleftharpoons 2{\text{NH}}_3(g)$

(b) $4{\text{NH}}_3(g)+5{\text{O}}_2(g)\rightleftharpoons 4\text{NO}(g)+6{\text{H}}_2\text{O}(g)$

(c) ${\text{N}}_2{\text{O}}_4(g)\rightleftharpoons 2{\text{NO}}_2(g)$

(d) ${\text{CO}}_2(g)+{\text{H}}_2(g)\rightleftharpoons \text{CO}(g)+{\text{H}}_2\text{O}(g)$

(e) ${\text{NH}}_4\text{Cl}(s)\rightleftharpoons {\text{NH}}_3(g)+\text{HCl}(g)$

(f) $2\text{Pb}{\left({\text{NO}}_3\right)}_2(s)\rightleftharpoons 2\text{PbO}(s)+4{\text{NO}}_2(g)+{\text{O}}_2(g)$

(g) $2{\text{H}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2{\text{H}}_2\text{O}(l)$

(h) ${\text{S}}_8(g)\rightleftharpoons 8\text{S}(g)$

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) $2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)K_c=17;$ [NH ₃ ] = 0.20 M , [N ₂ ] = 1.00 M , [H ₂ ] = 1.00 M

(b) $2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)K_P=6.8\times {10}^4;$ initial pressures: NH ₃ = 3.0 atm, N ₂ = 2.0 atm, H ₂ = 1.0 atm

(c) $2{\text{SO}}_3(g)\rightleftharpoons 2{\text{SO}}_2(g)+{\text{O}}_2\left(g\right)K_c=0.230;$ [SO ₃ ] = 0.00 M , [SO ₂ ] = 1.00 M , [O ₂ ] = 1.00 M

(d) $2{\text{SO}}_3(g)\rightleftharpoons 2{\text{SO}}_2(g)+{\text{O}}_2(g)K_P=16.5;$ initial pressures: SO ₃ = 1.00 atm, SO ₂ = 1.00 atm, O ₂ = 1.00 atm

(e) $2\text{NO}(g)+{\text{Cl}}_2(g)\rightleftharpoons 2\text{NOCl}(g)K_c=4.6\times {10}^4;$ [NO] = 1.00 M , [Cl ₂ ] = 1.00 M , [NOCl] = 0 M

(f) ${\text{N}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2\text{NO}(g)K_P=0.050;$ initial pressures: NO = 10.0 atm, N ₂ = O ₂ = 5 atm

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) $2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)K_c=17;$ [NH ₃ ] = 0.50 M , [N ₂ ] = 0.15 M , [H ₂ ] = 0.12 M

(b) $2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)K_P=6.8\times {10}^4;$ initial pressures: NH ₃ = 2.00 atm, N ₂ = 10.00 atm, H ₂ = 10.00 atm

(c) $2{\text{SO}}_3(g)\rightleftharpoons 2{\text{SO}}_2(g)+{\text{O}}_2(g)K_c=0.230;$ [SO ₃ ] = 2.00 M , [SO ₂ ] = 2.00 M , [O ₂ ] = 2.00 M

(d) $2{\text{SO}}_3(g)\rightleftharpoons 2{\text{SO}}_2(g)+{\text{O}}_2(g)K_P=6.5\text{atm;}$ initial pressures: SO ₂ = 1.00 atm, O ₂ = 1.130 atm, SO ₃ = 0 atm

(e) $2\text{NO}(g)+{\text{Cl}}_2(g)\rightleftharpoons 2\text{NOCl}(g)K_P=2.5\times {10}^3;$ initial pressures: NO = 1.00 atm, Cl ₂ = 1.00 atm, NOCl = 0 atm

(f) ${\text{N}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2\text{NO}(g)K_c=0.050;$ [N ₂ ] = 0.100 M , [O ₂ ] = 0.200 M , [NO] = 1.00 M

The following reaction has K _P = 4.50 $\times$ 10 ⁻⁵ at 720 K.
${\text{N}}_2(g)+3{\text{H}}_2(g)\rightleftharpoons 2{\text{NH}}_3(g)$

If a reaction vessel is filled with each gas to the partial pressures listed, in which direction will it shift to reach equilibrium? P (NH ₃ ) = 93 atm, P (N ₂ ) = 48 atm, and P (H ₂ ) = 52

Determine if the following system is at equilibrium. If not, in which direction will the system need to shift to reach equilibrium?
${\text{SO}}_2{\text{Cl}}_2(g)\rightleftharpoons {\text{SO}}_2(g)+{\text{Cl}}_2(g)$

[SO ₂ Cl ₂ ] = 0.12 M , [Cl ₂ ] = 0.16 M and [SO ₂ ] = 0.050 M . K _c for the reaction is 0.078.

Which of the systems described in [link] give homogeneous equilibria? Which give heterogeneous equilibria?

Which of the systems described in [link] give homogeneous equilibria? Which give heterogeneous equilibria?

For which of the reactions in [link] does K _c (calculated using concentrations) equal K _P (calculated using pressures)?

For which of the reactions in [link] 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) ${\text{N}}_2(g)+3{\text{H}}_2(g)\rightleftharpoons 2{\text{NH}}_3(g)K_c=0.50\text{at}400\text{°C}$

(b) ${\text{H}}_2+{\text{I}}_2\rightleftharpoons 2\text{HI}{K}_c=50.2\text{at}448\text{°C}$

(c) ${\text{Na}}_2{\text{SO}}_4\text{·}10{\text{H}}_2\text{O}(s)\rightleftharpoons {\text{Na}}_2{\text{SO}}_4(s)+10{\text{H}}_2\text{O}(g)K_P=4.08\times {10}^{\mathrm{-25}}\text{at}25\text{°C}$

(d) ${\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)K_P=0.122\text{at}50\text{°C}$

Convert the values of K _c to values of K _P or the values of K _P to values of K _c .

(a) ${\text{Cl}}_2(g)+{\text{Br}}_2(g)\rightleftharpoons 2\text{BrCl}(g)K_c=4.7\times {10}^{\mathrm{-2}}\text{at}25\text{°C}$

(b) $2{\text{SO}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2{\text{SO}}_3(g)K_P=48.2\text{at}500\text{°C}$

(c) ${\text{CaCl}}_2\text{·}6{\text{H}}_2\text{O}(s)\rightleftharpoons {\text{CaCl}}_2(s)+6{\text{H}}_2\text{O}(g)K_P=5.09\times {10}^{\mathrm{-44}}\text{at}25\text{°C}$

(d) ${\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)K_P=0.196\text{at}60\text{°C}$

What is the value of the equilibrium constant expression for the change ${\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)$ at 30 °C?

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

Write the reaction quotient expression for the ionization of NH ₃ in water.

What is the approximate value of the equilibrium constant K _P for the change ${\text{C}}_2{\text{H}}_5{\text{OC}}_2{\text{H}}_5(l)\rightleftharpoons {\text{C}}_2{\text{H}}_5{\text{OC}}_2{\text{H}}_5(g)$ 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.)