What mass of ammonium chloride should be added to 2.55 L of 0.155 M NH3 to obtain a buffer with a pH of 9.55? (Assume no volume change.)

Verified step by step guidance

1. Identify the components of the buffer system: Ammonia (NH_3) is a weak base, and ammonium chloride (NH_4Cl) will provide the conjugate acid, NH_4^+.
2. Use the Henderson-Hasselbalch equation for a buffer solution: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right) \).
3. Find the \( \text{pK}_a \) of the ammonium ion (NH_4^+). The \( \text{pK}_a \) is related to the \( \text{pK}_b \) of NH_3 by the equation \( \text{pK}_a + \text{pK}_b = 14 \).
4. Rearrange the Henderson-Hasselbalch equation to solve for the ratio \( \frac{[\text{base}]}{[\text{acid}]} \): \( \frac{[\text{base}]}{[\text{acid}]} = 10^{(\text{pH} - \text{pK}_a)} \).
5. Calculate the moles of NH_3 in the solution using its concentration and volume, then use the ratio from the Henderson-Hasselbalch equation to find the moles of NH_4^+ needed. Convert this to mass using the molar mass of NH_4Cl.