Final answer:
To calculate the mass of HCl neutralized by a buffer solution before the pH falls below 9.0, one must use the buffer's capacity and the Henderson-Hasselbalch equation. The moles of HCl that can be neutralized are determined by the difference in moles between the existing buffer components.
Step-by-step explanation:
Calculating the Mass of Hydrochloric Acid Neutralized by a Buffer
To determine the mass of hydrochloric acid (HCl) that a buffer solution can neutralize before the pH falls below 9.0, we must first understand the buffer capacity and the Henderson-Hasselbalch equation. The given buffer solution contains 0.100M ammonia (NH₃) and 0.125M ammonium bromide (NH₄Br). Ammonia is a weak base and its conjugate acid is ammonium ion (NH₄⁺). The Henderson-Hasselbalch equation for this buffer system is pH = pKa + log([base]/[acid]), where NH₃ is the base and NH₄⁺ is the acid.
Using the pKa value of ammonia (which is approximately 9.25), we can set up the equation to solve for pH at the point where the buffer's capacity is reached. Since the pH cannot fall below 9.0, we are essentially calculating how much HCl can be added before all the NH₃ is converted to NH₄⁺, thus reaching the buffer's capacity and lowering the pH to 9.0. We will assume the volume remains constant, and the reaction is stoichiometric where one mole of NH₃ neutralizes one mole of HCl.
The molar mass of HCl is about 36.46 g/mol. Using stoichiometry, we calculate the moles of HCl neutralized and then convert that to grams. Since the buffer contains 0.100 moles per liter of NH₃, and we have 0.100 L of solution, this equates to 0.010 moles of NH₃. We can then calculate the moles of NH₄⁺ that would be present when the pH is exactly 9.0 and determine the difference in moles between NH₃ and NH₄⁺ required to reach that pH. This difference is the amount of HCl that can be neutralized.