Textbook Question
a. Calculate the percent ionization of 0.007 M butanoic acid (𝐾𝑎=1.5×10−5).
Ch.17 - Additional Aspects of Aqueous Equilibria
Chapter 17, Problem 18a
(a) Calculate the percent ionization of 0.125 M lactic acid (Ka = 1.4 × 10-4).
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Identify the given values: concentration of lactic acid (C) = 0.125 M, and the acid dissociation constant (Ka) = 1.4 \times 10^{-4}.
Set up the expression for the equilibrium constant (Ka) for the dissociation of lactic acid, which can be represented as: Ka = \frac{[H^+][A^-]}{[HA]}. Here, [HA] is the initial concentration of the acid, [H^+] is the concentration of hydrogen ions, and [A^-] is the concentration of the conjugate base at equilibrium.
Assume that the concentration of hydrogen ions produced, [H^+], is equal to x. Therefore, the concentration of the conjugate base [A^-] is also x. The concentration of the undissociated acid at equilibrium, [HA], will be the initial concentration minus x (0.125 - x).
Substitute these expressions into the Ka equation and simplify assuming x is much smaller than the initial concentration, which simplifies the denominator to just the initial concentration: Ka = \frac{x^2}{0.125}.
Solve for x, which represents the concentration of hydrogen ions at equilibrium. Then, calculate the percent ionization using the formula: \text{Percent Ionization} = \left(\frac{[H^+]}{[HA]_{initial}}\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 Acids
Ionization refers to the process by which an acid donates protons (H+) to water, forming hydronium ions (H3O+). For weak acids like lactic acid, this process is not complete, and only a fraction of the acid molecules ionize. The extent of ionization is crucial for calculating properties like percent ionization.
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Calculating Percent Ionization of Weak Acids
Percent Ionization
Percent ionization is a measure of the degree to which an acid ionizes in solution, expressed as a percentage. It is calculated using the formula: (concentration of ionized acid / initial concentration of acid) × 100%. This value helps in understanding the strength of the acid and its behavior in solution.
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Equilibrium Constant (Ka)
The equilibrium constant (Ka) quantifies the strength of an acid in solution, representing the ratio of the concentration of products to reactants at equilibrium. A smaller Ka value indicates a weaker acid, as seen with lactic acid's Ka of 1.4 × 10^-4, which suggests limited ionization and helps in calculating the percent ionization.
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Related Practice
Textbook Question
(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
(b) Calculate the percent ionization of 0.125 M lactic acid in a solution containing 0.0075 M sodium lactate.
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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