Exercises: 2, 8, 14, 20, 24, 26, 30, 34, 36, 38, 44, 48

2. (a) At equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction. Reactants are still being transformed into products and products are still being transformed into reactants. It is just that the rates exactly balance, leaving no net change in the concentrations in the reactants and products.

(b) It is the rates of the forward and reverse reactions that are equal at equilibrium, not the rate constants for the forward and reverse reactions.

© At equilibrium, there is no net change in concentrations of reactants and products. However, it is not necessary that the concentrations of reactants and products are equal. Therefore, there need not be equal amounts of reactants and products at equilibrium.

8. (a) This is a homogeneous reaction:

(b) This is a heterogeneous reaction. Solids and liqiuds do not appear in equilibrium expressions.

© This is a homogeneous reaction:

(d) This is a heterogeneous reaction. Again, solids and liquids do not appear in equilibrium expressions.

(e) This is a homogeneous reaction.

14. (a) The reaction

is the reverse of the reaction given in the problem. When you reverse the direction of a reaction, the equilibrium constant goes to its reciprocal:

(b) The reaction

is ½ times the reaction given in the problem. When you multiply a reaction by a number, the equilibrium is raised to the power of that number:

© The reaction

is the reverse of the reaction in part (b). The equilibrium constant for this reaction is equal to:

20. The expression for K_eq is:

The equilibrium partial pressures of each gas may be calculated using the ideal gas law:

Placing these equilibrium partial pressures into the expression for K_eq:

24. The expression for K_eq is:

Calculate the initial partial pressures of H₂ and Br₂ by determining the number of moles of each and using the ideal gas law to calculate the partial pressures:

Given the equilibrium amount of H₂, calculate the equilibrium partial pressure of H₂ by determining the equilibrium number of moles then the ideal gas law:

Setting up an equilibrium table:

The change in pressure for H₂ is equal to:

Since the changes in pressure are related by the stoichiometry of the reaction, then the change in pressure for Br₂ is also equal to –11.5 and the change in pressure of HBr is 2 × 11.5 = 23.0. Adding the changes in pressures to the initial pressures to calculate the equilibrium partial pressures of Br₂ and HBr:

The equilibrium partial pressures of H₂, Br₂, and HBr are 8.07 atm, 1.1 atm, and 23.0 atm, respectively.

(b) The equilibrium expression is:

26. (a) Setting up an equilibrium table with the given initial partial pressures and the equilibrium partial pressure:

Since the changes in partial pressures are related by the stoichiometry of the reaction, the partial pressure of N₂O₄ will increase by ½ times the change in NO₂ (or be equal to +0.25). Adding the initial and the change in pressure of N₂O₄, the equilibrium pressure of N₂O₄ is equal to:

(b) The value of K_eq is:

30. Using the given partial pressures, calculate the value of the reaction quotient, Q, then compare its value to the value of the equilibrium constant. If Q < K_eq, the reaction shifts towards products to get to equilibrium. If Q > K_eq, the reaction shifts towards reactants to get to equilibrium. If Q = K_eq, then the reaction is already at equilibrium.

(a) Calculate the value of Q:

Since Q < K_eq [(2.6 ´ 10^-6)<(4.51 ´ 10^-5)], the reaction will move towards products to get to equilibrium.

(b) Since there is no N₂ in the system (zero pressure), the reaction must move towards reactants to get to equilibrium.

(c) Calculate the value of Q:

Since Q = K_eq, this mixture is at equilibrium.

(d) Calculate the value of Q:

Since Q > K_eq [(1.3 ´ 10^-2)>(4.51 ´ 10^-5)], the reaction must move towards reactants to get to equilibrium.

34. (a) Calculate the equilibrium partial pressure of I(g) given the mass of I(g), the volume of the vessel, and the temperature. Convert the mass of I(g) to number of moles:

The equilibrium partial pressure of I is equal to:

Use the equilibrium constant to calculate the equilibrium partial pressure of I₂:

Use the ideal gas law to calculate number of moles of I₂:

Converting from moles to grams:

(b) Convert the masses of SO₃ and O₂ to number of moles:

Using the ideal gas law, convert moles of each to a partial pressure given the volume of 2.00 L and temperature of 700 K:

Use the equilibrium expression to calculate the partial pressure of SO₂:

Use the ideal gas law to calculate number of moles of SO₂:

Converting from moles to grams:

36. Calculate the initial partial pressures of Br₂ and Cl₂ given the number of moles, the volume, and the temperature of the vessel:

Setting up an equilibrium table:

Let 2x = D P_BrCl, then –x = and –x = . Place these changes in pressure in the equilibrium table. Add the initial pressure to the change in pressure to calculate expressions for the equilibrium pressures in terms of x. Place the equilibrium partial pressures into the equilibrium expression and solve for x:

The equilibrium partial pressure of BrCl is equal to: P_BrCl = 2x = 11 atm