EXTRA PROBLEMS for UNIT 10: Equilibrium.

1. Determine the equilibrium constant for the reaction H₂ + I₂ = 2HI if the equilibrium concentrations are: H₂, 0.9 M; I₂, 0.4 M; HI, 0.6 M.

2. What is the equilibrium constant expression for the following reaction?

4NH₃(g) + 5 O₂(g) = 4NO(g) + 6H₂O(g)

3. At a certain temperature, K_eq for the reaction 3C₂H₂ = C₆H₆ is 4. If the equilibrium concentration of C₂H₂ is 0.5 M, what is the concentration of C₆H₆? .

4. You are given a box in which PCl₅(g), PCl₃(g), and Cl₂(g) are in equilibrium with each other at 546 K. Assuming that the decomposition of PCl₅ to PCl₃ and Cl₂ is endothermic, what effect would there be on the concentration of PCl₅ in the box if each of the following changes were made? (a) Add Cl₂ to the box, (b) Reduce the volume of the box, (c) Raise the temperature of the system.

5.A chemist dissolves BaSO₄ in pure water at 25⁰C. If its K_sp = 1 x 10^-10 , what is the solubility of the barium sulfate in the water?

6. Calculate the solubility product constant of pure PbSO₄ in water. The solubility of PbSO₄ in water at 25⁰C is 1.25 x 10^-4 M.

7. How many grams of calcium oxalate, CaC₂O₄ , will disslove in water to form 1.0 L of saturated solution? K_sp of CaC₂O₄ is 2.5 x 10^-9.

8.Calculate the concentration of calcium ion and fluoride ion in a saturated solution of calcium fluoride. K_sp of CaF₂ = 4.00 x 10^-11.

The following problems are for Honors only:

9. Given the reaction A + B = C + D , find the equilibrium constant if 0.7 moles of C are formed when 1 mole of A and 1 mole of B are initially present. For this same equilibrium, find the equilibrium composition when 1 mole each of A, B, C, and D are initially present.

10. Two moles of gaseous NH₃ are introduced into a 1.0 L vessel and allowed to undergo partial decomposition at high temperatures according to the reaction

2NH₃(g) = N₂(g) + 3H₂(g)

At equilibrium, 1.0 mole of NH₃(g) remains. What is the value of the equilibrium constant?

11. Four moles of PCl₅ are placed in a 2-liter flask. When the following equilibrium is established

PCl₅ = PCl₃ + Cl₂, the flask is found to contain 0.8 mole of Cl₂. What is the equilibrium constant?

12. For the reaction : CO₂(g) + H₂(g) = CO(g) + H₂O(g)

the value of the equilibrium constant at 825 K is 0.137. If 5.0 moles of CO₂ , 5.0 moles of H₂ , 1.0 mole of CO , and 1.0 mole of H₂O are initially present, what is the composition of the equilibrium mixture?

13. For the reaction : 2HI(g) = H₂(g) + I₂(g) , the value of the equilibrium constant at 700 K is 0.0183. If 3.0 moles of HI are placed in a 5-liter vessel and allowed to decompose according to the above equation, what percentage of the original HI would remain undissociated at equilibrium?

14. The solubility product constant of magnesium hydroxide is 8.9 x 10^-12. Calculate its solublity in (a) water, (b) 0.05 M NaOH.

15. Assuming the K_sp for RaSO₄ is 4 x 10^-11 , what is its solubilty in (a) pure water, and (b) 0.1 M Na₂SO₄?

16. A saturated solution of CaF₂ contains 0.00168 g of CaF₂ per 100 g of water. Determine the K_sp.

17. A chemist has a saturated solution of CaSO₄ in 0.0100 M Na₂SO₄. The K_sp of CaSO₄ is 2.4 x 10^-5, calculate the concentration of Ca⁺² ion in this saturated solution. .

18. Calculate the minimum concentration of Br^- ion necessary to bring about the precipitation of AgBr from a solution in which the concentration of Ag⁺ ion is 1.0 x 10^-5 M. K_sp for AgBr = 4.0 x 10^-13.

19. If you mix 50. mL of 5.0 x 10^-4 M Ca(NO₃)₂ and 50. mL of 2.0 x 10^-4 M NaF to give 100. mL of solution, will precipitation occur? The K_sp of CaF₂ is 1.7 x 10^-10.

20. A chemist mixes equal volumes of 0.01 M Na₂C₂O₄ and 0.001 M BaCl₂ together. Assuming the K_sp of BaC₂O₄ is 1.2 x 10^-7 , will a precipitate form?

Answers:

1. 1.0 ; 2. [NO]⁴[H₂O]⁶/[NH₃]⁴[O₂]⁵ ; 3. 0.5 M ; 4. increase; increase; decrease ; 5. 1 x 10^-5 M ; 6. 1.6 x 10^-8 M ; 7. 0.0064 g ; 8. [Ca^+2] = 2.15 x 10^-4 M ; [F^-] = 4.30 x 10^-4 M ; 9. 5.44; 0.6 M, 0.6 M, 1.4 M ; 1.4 M ; 10. 1.69 ; 11. 0.1 ; 12. CO₂ = H₂ = 4.38 mol ; CO = H₂O = 1.62 mol ; 13. 2.36/3.0 ; 14. 1.3 x 10^-4 M ; 3.6 x 10^-9 M ; 15. 6 x 10^-6 M; 4 x 10^-10 M ; 16. 3.98 x 10^-11 ; 17. 2.4 x 10^-3 M ; 18. [Br^-] = 4.0 x 10^-8 M ; 19. No ; 20. Yes

The following is an example of an Honors test for the Equilibrium unit:

Multiple Choice:

1. If a reaction has an equilibrium constant just greater than 1, what type of reaction is it?

(a) irreversible (b) reversible, favoring products (c) reversible, favoring reactants (d) spontaneous

2. At equilibrium, what is the rate of production of reactants compared with the rate of production of products?

(a) much higher (b) higher (c) the same (d) lower

3. Which compound would produce the largest concentration of OH^- ions in a saturated aqueous solution at 25^oC?

(a) 1 (b) 2 (c) 3 (d) 4

4. Which of the changes listed below would shift the following reaction to the right?

(a) addition of Cl₂ (b) increase of pressure (c) removal of O₂ (d) addition of H₂O

5. Identify the correct equilibrium expression (K_c) for the following reaction.

(a) [C₆H₁₂O₆][O₂]⁶/[CO₂][H₂O]⁶ (b) [O₂]⁶/[CO₂]⁶ (c) [CO₂]⁶/[O₂]⁶ (d) [O₂]⁶/[CO₂]⁶[H₂O]⁶

6. What is the consequence of heating the following equilibrium system at constant pressure?

(a) the concentration of SO₃ will increase (b) the partial pressure of SO₂ will increase (c) the equilibrium constant will increase (d) the total volume of the system will decrease

7. The equilibrium constant for reaction (1) is K. What is the equilibrium constant for equation (2)?

(1) 1/3 N₂(g) + H₂(g) <----> 2/3 NH₃(g)

(2) 2NH₃(g) <----> N₂(g) + 3H₂(g)

(a) K³ (b) 3K (c) K/3 (d) 1/K³

8. The dissociation constant expression for the equilibrium expressed by the equation: PbSO₄(s) <----> Pb⁺²(aq) + SO₄^-2(aq) would be

(a) [Pb⁺²] (b) [Pb⁺²][SO₄^-2] (c) [SO₄^-2] (d) [Pb⁺²] + [SO₄^-2]

9. The following reaction was carried out at 25^oC with the initial concentration of NO₂(g) being 0.70 M and no NO(g) or O₂(g) initially present. At equilibrium the NO₂(g) concentration was found to be 0.28 M. Calculate K_c for the reaction:

(a) 1.9 (b) 0.94 (c) 0.47 (d) 0.14

10. Consider the following chemical reaction:

at equilibrium, the concentration of H₂, I₂, and HI were found to be 0.15 M, 0.033 M, and 0.55 M respectively. What is the value of K_c for this reaction?

(a) 23 (b) 111 (c) 0.0090 (d) 61

11. Which one of the following will cause a change in the value of the equilibrium constant for a reaction?

(a) addition of a catalyst (b) addition of excess product (c) addition of excess reactant (d) changing the temperature

12. The solubility of PbCl₂ is 1.6 x 10^-2 mol/L. The concentration of chloride ions, Cl^-, in a saturated solution of PbCl₂ would be

(a) 0 M (b) 3.2 x 10^-2 M (c) 1.6 x 10^-2 M (d) 4.8 x 10 ^-2 M

13. The volume of the reaction vessel containing an equilibrium mixture in the reaction SO₂Cl₂(g) <----> SO₂(g) + Cl₂(g) is increased. When equilibrium is reestablished,

(a) the amount of SO₂(g) will have decreased (b) the amount of Cl₂(g) will have increased (c) the amount of Cl₂(g) will have remained unchanged (d) the amount of SO₂Cl₂(g) will have increased

14. Given the equilibrium expression: K = [A][B]/[C][D] , which pair represents the reactants for the forward reaction?

(a) A and B (b) B and D (c) C and D (d) A and C

15. The value of K represents a compromise between

(a) maximum enthalpy and maximum entropy (b) minimum enthalpy and maximum entropy (c) maximum enthalpy and minimum entropy (d) minimum enthalpy and minimum entropy

16. What is the maximum concentration of Cd⁺² that can exist in a solution in which the S^-2 concentration is 2.5 x 10^-6? (K_sp for CdS is 8.0 x 10^-27)

(a) 3.2 x 10^-21 (b) 8.9 x 10^-14 (c) 2.0 x 10^-32 (d) 2.2 x 10^-19

17. A slightly soluble ionic compound AB₂ dissociates according to the equation: AB₂(s) <----> A⁺²(aq) + 2B^-(aq). If the solubility of AB₂ at a particular temperature is 2.0 x 10^-4 M, then the value of K_sp at this temperature is

(a) 3.2 x 10^-11 (b) 8.0 x 10^-12 (c) 4.0 x 10^-8 (d) 2.0 x 10^-4

18. Which equilibrium constant indicates a reaction which is essentially complete?

(a) K = 1.0 x 10^-10 (b) K = 1.0 x 10^o (c) K = 2.0 x 10^o (d) K = 1.0 x 10¹⁰

19. Which salt would have the smallest Ksp?

(a) NaCl (b) FeCl₃ (c) MgCl₂ (d) AgCl

20. Which one of the following substances, when added to a saturated solution of Pb(OH)₂, will decrease the solubility of Pb(OH)₂ in the solution?

(a) NaNO₃ (b) HNO₃ (c) AgNO₃ (d) Pb(NO₃)₂

Problems:

21. Consider the following equilibrium system: C(s) + CO₂(g) <----> 2CO(g) ; delta H^o = 119.8 kJ

If the reaction is at equilibrium, what would be the effect on the equilibrium yield of CO(g) of (a) adding CO₂(g) ; (b) adding C(s) ; (c) adding heat ; (d) increasing the pressure on the system by decreasing the volume; (e) addition of a catalyst

22. For the reaction I₂(g) + Br₂(g) <----> 2IBr(g) , K_c = 280 at 150^oC. Suppose that 0.500 mol IBr is placed in a 0.250 L flask and allowed to reach equilibrium at this temperature. What are the equilibrium concentrations of IBr, I₂, and Br₂?

23. The value of K_sp for cerium hydroxide, Ce(OH)₃, is 1.5 x 10^-20. (a) What is the molar solubility of Ce(OH)₃ in pure water? (b) What will be the concentration of Ce⁺³ in a solution that contains 0.10 M NaOH?

24. Will AgIO₃ precipitate when 100. mL of 0.010 M AgNO₃ solution is mixed with 10.0 mL of 0.015 M NaIO₃ solution? (K_sp of AgIO₃ is 3.0 x 10^-8).

Answers: 1 b, 2 c, 3 a, 4 b, 5 b, 6 b, 7 d, 8 b, 9 c, 10 d, 11 d, 12 b, 13 b, 14 c, 15 b, 16 a, 17 a, 18 d, 19 d, 20 d.

21, (a) increase , (b) nothing , (c) increase , (d) decrease , (e) nothing

22, [IBr] = 1.79 M , [I₂] = 0.107 M , [Br₂] = 0.107 M

23, (a) 4.9 x 10^-6 M; (b) 1.5 x 10^-17M

24, Q = 1.24 x 10^-5 ; Q > K_sp , therefore there is a precipitate.