Equilibrium Problems Sorted by Topics

Calculating Equilibrium Concentration: Given K

  1. Given initial conc. of 0.10 M of COCl2, what are the equilibrium concentrations of CO and Cl2 given Kc= 2.19 X 10-10 and COCl2(g)  CO(g) + Cl2(G). Ans:
  2. The equilibrium constant K (=55.64) for H2(g) + I2(g)> 2HI(g) is determined at 425°C. What are the concentrations of H2, I2 and HI at equilibrium, if initial concentration of H2 is 2.0 M? [H2]= [I2]=0.42M, [HI]= 3.16 M
  3. For the decomposition of PCl5 PCl3+ Cl2, if the initial concentration of PCl5 is 1.60 M, what will be the concentrations of the products at equilibrium? K=1.20 at that temp. Ans: [PCl5]= 0.69M, [PCl3]= [Cl2]= 0.91 M

Calculating Equilibrium Concentrations (or change in conc.) and K: Given Initial Concentrations

1.Refer to the system PCl3(g) + Cl2(g) ↔ PCl5(g). To an empty 15.0-L cylinder, 0.500 moles of gaseous PCl5 are added and allowed to reach equilibrium. The conc. of PCl3 is found to be 0.0220M. Assume a temperature of 375 K.
a) How many moles of PCl5 remain at equilibrium?

b) Write the equilibrium constant expression for the above reaction.

c) Determine the value of K.

d) Determine the value of Kp for this same system at the same temperature.

e) How would the value of Kp be effected by increasing the temperature of the system at equilibrium for this exothermic reaction?

2. For the reaction PCl3(g) + Cl2(g) ↔ PCl5(g), Kp = 0.0870 at 300 degrees Celsius. A flask is charged with 0.30 atm PCl3, 060 atm Cl2, and 0.10 atm PCl5 at this temperature.

a) Determine whether the above conditions (the added gases) are at equilibrium. If not, determine to which direction the reaction must proceed to reach equilibrium.

b) Calculate the equilibrium partial pressures of the gases.

c) Calculate Kc for the above equation.

d) Predict and justify what effect increasing the volume of the system will have on the mole fraction of PCl5 in the mixture.

e) The reaction as written is exothermic. Predict and justify what effect that decreasing the temperature of the system will have on the mole fraction of PCl5 in the mixture.

Ans:

1.a) 0.170 mole PCl5

b) Kc = [ PCl5] \ [PCl3] [Cl2]

c) 23.4

d) 0.760

e) Raising the temperature of an exothermic reaction opposes the forward reaction. Further, from Kp = Kc (RT)delta n, if T increases, the value of Kp decreases.

2.a) The reaction proceeds to the left.

b) PPCl3 = 0.02 atm

PPCl5 = 0.38 atm

PPCl2 = 0.68 atm

c) 4.09

d) Increasing the volume of the container favors the process where more moles of gas are produced, so the reverse reaction is favored; the equilibrium shifts to the left; the mole fraction of PCl5 decreases.

e) For an exothermic reaction, decreasing the temperature increases the value of K, favoring the products. The partial pressure of PCl5 increases.

Converting between Kc, Kp and Q

1.The brown gas NO2, will exist in equilibrium with the colorless gas N2O4. K=170 at 298 K.

2 NO2(g) N2O4(g) K=170

If at a specific time concentration of NO2 is 0.015 M, and the concentration of N2O4 is o.025 M. Is Q larger, smaller or equal to K? Which direction should the reaction proceed to achieve equilibrium?

Ans: Q <K (Q= 110), forward rxn.

2.. The synthesis of Ammonia from elemental Nitrogen and Hydrogen proceeds according to the exothermic reaction given by the balanced equation:

N2(g) + 3 H2(g) 2 NH3(g)

The reaction has an equilibrium constant value, Kp, of 1260 at a temperature of 400 oC.

a. What is the value of Kc for the reaction equation given?

b. Give the expression of the reaction quotient, Q, expressed in terms of the partial pressures of each gas?

c. The Pressures of Nitrogen, Hydrogen, and Ammonia in a system (not necessarily at equilibrium) are: pp(N2) = 1.00 atm; pp(H2) = 4.00 atm; and : pp(NH3) = 2.00 atm.

i. Determine the value of Q for these conditions and predict how the system will shift in attaining equilibrium.

ii. Set up (but do not solve) a polynomial equation to determine the equilibrium pressures of all substances:

N2(g) + 3 H2(g)  2 NH3(g)

Po1.00 atm4.00 atm2.00 atm

 P

Peq



The value of Q is less that Keq, so the reaction will shift to the right, producing more NH3 and consuming N2 and H2



N2(g) + 3 H2(g)  2 NH3(g)

Po1.00 atm4.00 atm2.00 atm

 P -x -3x +2x

Peq1.00 –x4.00 – 3x2.00 + 2x


Peq0.01141.03423.9772

Calculating overall K given two reactions

  1. Calculate K for the reaction

SnO2 + 2CO → Sn(s) + 2CO2, given the following equation:

SnO2(s) + 2H2(g) → Sn (s)+2H2O(g) K=8.12

H2 + CO2--> H2O (g) + CO(g) K=0.771

  1. At a given temperature, K = 1.3 x 10-2 for the reaction

N2(g) + 3H2(g) ↔ 2NH3(g)

Calculate values of K for the following reactions at this temperature

a) ½ N2(g) + 3/2 H2(g) ↔ NH3(g)

b) 2NH3(g) ↔ N2(g) + 3H2(g)

c) NH3(g) ↔ ½ N2(g) + 3/2 H2(g)

d) 2N2(g) + 6H2(g) ↔ 4NH3(g)

Calculating Equilibrium Concentrations/Pressures Given K

  1. Consider the isomerization of butane with an equilibrium constant of K=2.5. The system is originally at equilibrium with [butane]=1.0M and [isobutane]=2.5M
  1. If 0.50 mol/L of isobutance is suddenly added and the system shifts to a new equilibrium position, what is the equilibrium concentration of each added gas?
  2. If 0.50 mol/L of butane is added and the system shifts to a new equilibrium position, what is the equilibrium concentration of each gas?

2.The equilibrium constant, Kp, for N2O4(g) → 2NO2(g) is at 0.15 at 25°C. If the pressure of N2O4 at equilibrium is 0.85 atm, what is the total pressure of the gas mixture at equilibrium?

  1. Kc for the decomposition of ammonium hydrogen sulfide is 1.8 x 10^-4 at 25°C.

NH4HS--> NH3(g) +H2S(g)

a. When the pure salt decomposes in a flask, what are the equilibrium concentrations of NH3 and H2S.

b. If NH4HS is placed in a flask already containing 0.020 mol/L of NH3 and the system is allowed to come to equilibrium, what are the equilibrium concentrations of NH3 and H2S?

  1. The equilibrium constant, K, for the reaction

H2(g) + F2(g)↔ 2HF(g) has

has the value 2.1 x 103 at a particular temperature. When the system is analyzed at equilibrium at this temperature, the concentrations of H2(g) and F2(g) are both found to be 0.0021 M. What is the concentration of HF(g) in the equilibrium system under these conditions?

  1. At 35◦C, K = 1.6 x 10-5 for the reaction

2 NOCl(g) ↔ 2 NO(g) + Cl2(g)

Calculate the concentrations of all species at equilibrium for each of the following original mixtures.

a) 2.0 mol pure NOCl in a 2.0-L flask

b) 1.0 mol NOCl and 1.0 mol NO in a 1.0-L flask

c) 2.0 mol NOCl and 1.0 mol Cl2 in a 1.0-L flask

Calculating K given Concentrations

  1. Ammonium iodide dissociates reversibly to ammonia and hydrogen iodide if the salt is heated to a sufficiently high temperature.

NH4I--> NH3(g) + HI (g)

Some ammonium iodide is placed in a flask, which is then heated to 400°C. If the total pressure in the flask when equilibrium has been achieved in 705 mmHg, what is the value of Kp(when partial pressure are in the atmosphere)?

Answers:

  1. K = 13.7
  2. a) 0.11

b) 77

c) 8.8

d) 1.7 x 10-4

Calculating Equilibrium Concentrations/Pressure Given K

3.a. Equilibrium concentrations are the same under both circumstances: [butane] = 1.1 M and [isobutane] = 2.9 M

b. Ptotal = 180 atm

4. a) [NH3] = [H2S] = 0.013

b) [NH3] = 0.027 M and [H2S] = 0.067 M

5. 0.096 M

6. a) [NO] = 0.032 M, [Cl2] = 0.016 M, [NOCl] = 1.0 M

b) [NO] = [NOCl] = 1.0 M, [Cl2] = 1.6 x 10-5 M

c) [NO] = 8.0 x 10-3 M, [Cl2] = 1.0 M, [NOCl] = 2.0 M

Calculating K given Concentrations

7. Kp = 0.215

Detailed Worked Out Problems