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Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium
All textbooksMcMurry 8th EditionCh.18 - Thermodynamics: Entropy, Free Energy & EquilibriumProblem 14
Chapter 18, Problem 14

A 1.00 L volume of gaseous ammonia at 25.0 °C and 744 mm Hg was dissolved in enough water to make 500.0 mL of aqueous ammonia at 2.0 °C. What is the Kb for NH3 at 2.0 °C, and what is the pH of the solution? Assume that ∆H° and ∆S° are independent of temperature.

Verified step by step guidance
1
Step 1: Use the ideal gas law to calculate the number of moles of gaseous ammonia (NH_3) initially present. The ideal gas law is given by PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.
Step 2: Convert the initial conditions to appropriate units: pressure from mm Hg to atm, and temperature from Celsius to Kelvin. Use these values in the ideal gas law to find the moles of NH_3.
Step 3: Calculate the concentration of NH_3 in the aqueous solution. Since the gaseous ammonia is dissolved in 500.0 mL of water, use the moles of NH_3 from Step 2 and the volume of the solution to find the molarity (M = moles/volume in liters).
Step 4: Use the expression for the base dissociation constant (K_b) for NH_3. The reaction is NH_3 + H_2O ⇌ NH_4^+ + OH^-. Write the expression for K_b in terms of the concentrations of the products and reactants at equilibrium.
Step 5: Calculate the pH of the solution. Use the concentration of OH^- ions from the equilibrium expression to find the pOH, and then use the relationship pH + pOH = 14 to find the pH of the solution.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kb)

The base dissociation constant (Kb) quantifies the strength of a base in solution. It is defined as the ratio of the concentration of the products to the concentration of the reactants at equilibrium, specifically for the reaction of a base with water to form hydroxide ions. A higher Kb value indicates a stronger base, which is crucial for determining the pH of the solution.
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Equilibrium Constant K

pH and pOH Relationship

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. In basic solutions, pOH can also be calculated, and the relationship pH + pOH = 14 holds at 25 °C. Understanding this relationship is essential for calculating the pH of the ammonia solution after determining its Kb.
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pH and pOH Calculations

Temperature Dependence of Kb

The base dissociation constant (Kb) can vary with temperature, affecting the equilibrium position of the dissociation reaction. In this problem, it is assumed that the values of ∆H° and ∆S° are independent of temperature, allowing for the use of Kb values at different temperatures without needing to account for changes in enthalpy or entropy. This assumption simplifies the calculation of Kb and pH at the specified temperature.
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Related Practice
Textbook Question
Calculate ∆Stotal, and determine whether the reaction is spon-taneous or nonspontaneous under standard-state conditions. (a) -429 J/K; nonspontaneous (b) -123 J/K; spontaneous (c) +3,530 J/K; nonspontaneous (d) +184 J/K; nonspontaneous
Textbook Question
Consider the following endothermic reaction of gaseous AB3 molecules with A2 molecules.

Identify the true statement about the spontaneity of the reaction. (a) The reaction is likely to be spontaneous at high temperatures. (b) The reaction is likely to be spontaneous at high temperatures. (c) The reaction is always spontaneous.(d) The reaction is always spontaneous.
Textbook Question
Nitrogen reacts with fluorine to form nitrogen trifluoride: Calculate ∆G°, and determine whether the equilibrium composition should favor reactions or products at 25 °C(a) ∆G° = -6.7 kJ; the equilibrium composition should favor products. (b) ∆G° = -332 kJ; the equilibrium composition should favor reactants (c) ∆G° = -166 kJ; the equilibrium composition should favor products (d) ∆G° = +82.6 kJ; the equilbirum composiiton should favor reactants.
Textbook Question
Ammonium hydrogen sulfide, a stink bomb ingredient, decomposes to ammonia and hydrogen sulfide: Calculate the standard free-energy change for the rection at 25 °C if the total pressure resulting from the solid NH4S placed in an evacuated container is 0.658 atm at 25 °C.(a) -43.8 kJ(b) +1.04 kJ(c) -462 kJ(d) +5.51 kJ
Textbook Question
Consider the following graph of total free energy of reactants and products versus reaction progress for the general reaction, Reactants -> Products. At which of the four points (labeled a, b, c, and d) is Q < K?

(a) Point a(b) Point c and d(c) Point a, c, and d(d) Point b
Textbook Question

Spinach contains a lot of iron but is not a good source of dietary iron because nearly all the iron is tied up in the oxalate complex [Fe(C2O4)3]3-.

(b) Under the acidic conditions in the stomach, the Fe3+ concentration should be greater because of the reaction

[Fe(C2O4)3]3-(aq) + 6 H3O+(aq) ⇌ Fe3+(aq) + 3 H2C2O4(aq) + 6 H2O(l)

Show, however, that this reaction is nonspontaneous under standard-state conditions. (For H2C2O4, Ka1 = 5.9 × 10-2 and Ka2 = 6.4 × 10-5.)