(b) Calculate the percent ionization of 0.125 M lactic acid in a solution containing 0.0075 M sodium lactate.

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Identify the chemical equilibrium involved: Lactic acid (CH₃CH(OH)COOH) partially ionizes in water to form lactate ions (CH₃CH(OH)COO⁻) and hydrogen ions (H⁺). The presence of sodium lactate provides a common ion (lactate ion) which affects the equilibrium.

Write the expression for the acid dissociation constant (Kₐ) for lactic acid: \( K_a = \frac{[CH_3CH(OH)COO^-][H^+]}{[CH_3CH(OH)COOH]} \).

Use the given concentrations to set up the initial conditions for the equilibrium: [CH₃CH(OH)COOH] = 0.125 M, [CH₃CH(OH)COO⁻] = 0.0075 M, and [H⁺] = 0 M initially.

Apply the ICE (Initial, Change, Equilibrium) table method to determine the changes in concentration at equilibrium. Assume the change in concentration of lactic acid is \( -x \), and the change in concentration of lactate and hydrogen ions is \( +x \).

Substitute the equilibrium concentrations into the Kₐ expression and solve for \( x \), which represents the concentration of hydrogen ions at equilibrium. Calculate the percent ionization using the formula: \( \text{Percent Ionization} = \left( \frac{x}{0.125} \right) \times 100 \% \).

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Key Concepts

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

Ionization of Weak Acids

Weak acids, like lactic acid, do not completely dissociate in solution. Instead, they establish an equilibrium between the undissociated acid and its ions. The degree of ionization is crucial for understanding the acid's strength and its behavior in solution, which is essential for calculating percent ionization.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of the acid and its conjugate base. In this case, the presence of sodium lactate (the conjugate base of lactic acid) affects the pH and, consequently, the percent ionization of lactic acid, making this equation a vital tool for the calculation.

Percent Ionization Calculation

Percent ionization is calculated by taking the concentration of ionized acid at equilibrium, dividing it by the initial concentration of the acid, and multiplying by 100. This metric provides insight into the strength of the acid in the presence of a conjugate base, which is particularly relevant in buffer solutions.

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Calculating Percent Ionization of Weak Acids

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Textbook Question

(a) Calculate the percent ionization of 0.0075 M butanoic acid 1Ka = 1.5 * 10-52.

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(b) Calculate the percent ionization of 0.0075 M butanoic acid in a solution containing 0.085 M sodium butanoate.

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Textbook Question

(a) Calculate the percent ionization of 0.125 M lactic acid (K_a = 1.4 × 10^-4).

Textbook Question

Which of the following solutions is a buffer? (a) A solution made by mixing 100 mL of 0.100 M CH3COOH and 50 mL of 0.100 M NaOH, (b) a solution made by mixing 100 mL of 0.100 M CH3COOH and 500 mL of 0.100 M NaOH, (c) A solution made by mixing 100 mL of 0.100 M CH3COOH and 50 mL of 0.100 M HCl, (d) A solution made by mixing 100 mL of 0.100 M CH3COOK and 50 mL of 0.100 M KCl.

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Textbook Question

(a) Calculate the pH of a buffer that is 0.12 M in lactic acid and 0.11 M in sodium lactate.