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

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

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