Calculate the pH of a solution prepared by dissolving 0.10 mol of solid NH4Cl in 0.500 L of 0.40 M NH3. Assume that there is no volume change.

Name: Chemistry
Author: McMurry
ISBN: 9781292336145

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Identify the components of the solution: NH4Cl is a salt that dissociates into NH4+ and Cl- ions, and NH3 is a weak base.

Recognize that NH4+ is the conjugate acid of NH3, and this forms a buffer solution. Use the Henderson-Hasselbalch equation for buffer solutions: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right) \).

Find the \( \text{pK}_a \) of NH4+ by using the relationship \( \text{pK}_a + \text{pK}_b = 14 \), where \( \text{pK}_b \) is for NH3. Look up or calculate \( \text{pK}_b \) for NH3.

Calculate the concentration of NH4+ in the solution: Since 0.10 mol of NH4Cl is dissolved in 0.500 L, the concentration \([\text{NH4}^+]\) is \( \frac{0.10 \text{ mol}}{0.500 \text{ L}} \).

Calculate the concentration of NH3 in the solution: The initial concentration is 0.40 M, and since there is no volume change, \([\text{NH3}]\) remains 0.40 M. Substitute these values into the Henderson-Hasselbalch equation to find the pH.

주요 개념

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

Acid-Base Chemistry

Acid-base chemistry involves the study of substances that can donate protons (acids) or accept protons (bases). In this context, NH4Cl acts as an acid, providing NH4+ ions, while NH3 is a weak base. The interaction between these species is crucial for determining the pH of the solution.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a formula used to calculate the pH of a buffer solution. It relates the pH to the pKa of the acid and the ratio of the concentrations of the conjugate base and acid. In this case, it helps to find the pH of the NH4+/NH3 buffer system formed by the dissolution of NH4Cl in NH3.

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH upon the addition of small amounts of acid or base. They typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid. The NH4+/NH3 system acts as a buffer, allowing for the calculation of pH based on the concentrations of NH4+ and NH3.