Textbook Question
A 1.000 L sample of HF gas at 20.0 °C and 0.601 atm pressure was dissolved in enough water to make 50.0 mL of hydrofluoric acid. (a) What is the pH of the solution?
Ch.16 - Aqueous Equilibria: Acids & Bases
Chapter 16, Problem 159
A 200.0 mL sample of 0.350 M acetic acid (CH3CO2H) was allowed to react with 2.000 L of gaseous ammonia at 25 °C and a pressure of 650.8 mm Hg. Assuming no change in the volume of the solution, calculate the pH and the equilibrium concentrations of all species present (CH3CO2H, CH3CO2-, NH3, NH4+, H3O+, and OH-). Values of equilibrium constants are listed in Appendix C.
Verified step by step guidance1
Step 1: Calculate the initial moles of acetic acid (CH3CO2H) using its concentration and volume. Use the formula: \( \text{moles} = \text{concentration} \times \text{volume} \).
Step 2: Determine the moles of gaseous ammonia (NH3) using the ideal gas law, \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
Step 3: Write the balanced chemical equation for the reaction between acetic acid and ammonia, and use stoichiometry to find the limiting reactant and the moles of products formed.
Step 4: Use the equilibrium constant expressions for the dissociation of acetic acid (\( K_a \)) and the ionization of ammonia (\( K_b \)) to set up equations for the equilibrium concentrations of all species.
Step 5: Solve the equilibrium expressions simultaneously to find the concentrations of \( \text{CH}_3\text{CO}_2^- \), \( \text{NH}_4^+ \), \( \text{H}_3\text{O}^+ \), and \( \text{OH}^- \). Use these to calculate the pH of the solution.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Acid-Base Equilibria
Acid-base equilibria involve the transfer of protons (H+) between species in a solution. In this context, acetic acid (a weak acid) can donate a proton to ammonia (a weak base), forming acetate ions and ammonium ions. Understanding the equilibrium constant (Ka for acetic acid and Kb for ammonia) is crucial for calculating the concentrations of all species at equilibrium.
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Arrhenius Acids and Bases
pH Calculation
pH is a measure of the hydrogen ion concentration in a solution, defined as pH = -log[H3O+]. To calculate the pH of the solution after the reaction, one must determine the concentration of hydronium ions (H3O+) at equilibrium. This involves using the equilibrium concentrations of the reactants and products, which can be derived from the initial concentrations and the changes that occur during the reaction.
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Ideal Gas Law and Partial Pressure
The Ideal Gas Law (PV = nRT) relates the pressure, volume, and temperature of a gas to the number of moles. In this scenario, the gaseous ammonia's partial pressure must be converted to moles to determine its contribution to the reaction. Additionally, understanding how to calculate the concentration of gases in solution is essential for determining the equilibrium state of the system.
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Related Practice
Textbook Question
A 1.000 L sample of HF gas at 20.0 °C and 0.601 atm pressure was dissolved in enough water to make 50.0 mL of hydrofluoric acid. (b) To what volume must you dilute the solution to triple the percent dissociation?
Textbook Question
You may have been told not to mix bleach and ammonia. The reason is that bleach (sodium hypochlorite) reacts with ammonia to produce toxic chloramines, such as NH2Cl. For example, in basic solution: OCl-1aq2 + NH31aq2S OH-1aq2 + NH2Cl1aq2 (b) The following mechanism has been proposed for this reaction in basic solution: H2O + OCl-HOCl + OH- Fast, equilibrium constantK1 HOCl + NH3 S H2O + NH2Cl Slow, rate constantk2 Assuming that the first step is in equilibrium and the second step is rate-determining, calculate the value of the rate constant k2 for the second step. Ka for HOCl is 3.5 * 10-8.
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