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.

Verified step by step guidance

1. Identify the components of the solution: NH4Cl is a salt that dissociates into NH4+ and Cl- ions, and NH3 is a weak base.
2. Recognize that NH4+ is the conjugate acid of NH3, and this forms a buffer solution. Use the Henderson-Hasselbalch equation for buffer solutions: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right) \).
3. 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.
4. 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 \( \frac{0.10 \text{ mol}}{0.500 \text{ L}} \).
5. 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.