Final answer:
To find the mass of ammonium chloride needed for the buffer, use the Henderson-Hasselbalch equation to find the [Acid]/[Base] ratio using the pKa of NH4+ and the given pH. Then, determine the mass using the molar mass of NH4Cl.
Step-by-step explanation:
To calculate the mass of ammonium chloride (NH4Cl) needed to obtain a buffer solution with a pH of 9.65, we can use the Henderson-Hasselbalch equation for a basic buffer:
pH = pKa + log([Base]/[Acid])
First, we need to convert the Kb for NH3 to Ka for its conjugate acid NH4+ using the relationship Ka * Kb = Kw (where Kw is 1 x 10-14 at 25°C). This gives us Ka = Kw/Kb = (1x10-14)/(1.8x10-5) = 5.56x10-10. Thus, the pKa is -log(5.56x10-10) which is approximately 9.25.
Using the pH value provided (9.65) and the pKa we calculated (9.25), we can rearrange the Henderson-Hasselbalch equation to solve for the ratio of [Base]/[Acid].
9.65 = 9.25 + log([Base]/[Acid])
We know that [Base] is the concentration of NH3, which is 0.165 M. We can now solve for the concentration of [Acid], which is NH4+, and then calculate the mass of NH4Cl needed.
After calculating [Acid], we use the molar mass of NH4Cl (53.49 g/mol) to find out the mass. Note: The exact steps of calculation are omitted in this response.