A buffer is prepared by mixng 150.0 mL of 0.500 M ammonia, 250.0 mL of 0.200 M ammonium chloride and 600.0 mL of water. To this solution is added 50.0 mL of 0400 M hydrochloric acid. What is the final pH?

To find the final pH of the solution, we need to determine the concentrations of the relevant species in the solution after the addition of hydrochloric acid. Let's break down the process step by step.

1. Calculate the moles of ammonia (NH₃) initially present in the solution:
moles of NH₃ = volume (L) × concentration (M)
moles of NH₃ = 0.150 L × 0.500 M = 0.075 mol

2. Calculate the moles of ammonium chloride (NH₄Cl) initially present in the solution:
moles of NH₄Cl = volume (L) × concentration (M)
moles of NH₄Cl = 0.250 L × 0.200 M = 0.050 mol

3. Since ammonia (NH₃) is a weak base and hydrochloric acid (HCl) is a strong acid, they will react to form ammonium chloride (NH₄Cl):
NH₃ + HCl → NH₄Cl

From the balanced equation, we can see that one mole of NH₃ reacts with one mole of HCl to form one mole of NH₄Cl.

4. Determine the moles of HCl added:
moles of HCl = volume (L) × concentration (M)
moles of HCl = 0.050 L × 0.400 M = 0.020 mol

5. Since the initial moles of NH₃ and NH₄Cl are greater than the moles of HCl added, NH₃ is in excess, and NH₄Cl will be completely converted to NH₃:
moles of NH₄Cl remaining = 0 mol

6. Calculate the total moles of NH₃ after the reaction:
moles of NH₃ = initial moles of NH₃ + moles of NH₄Cl remaining
moles of NH₃ = 0.075 mol + 0 mol = 0.075 mol

7. Calculate the total volume of the solution:
total volume = volume of NH₃ + volume of NH₄Cl + volume of water + volume of HCl
total volume = 0.150 L + 0.250 L + 0.600 L + 0.050 L = 1.050 L

8. Calculate the concentration of NH₃ in the final solution:
concentration of NH₃ = moles of NH₃ / total volume
concentration of NH₃ = 0.075 mol / 1.050 L = 0.071 M

9. Since NH₃ is a weak base, we can use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution:
pH = pKa + log([A-] / [HA])

In this case, NH₄Cl is the ammonium chloride and NH₃ is ammonia. The pKa for the NH₄⁺/NH₃ system is approximately 9.25.

[A-] = concentration of NH₃ = 0.071 M
[HA] = concentration of NH₄Cl = 0.050 M

pH = 9.25 + log(0.071/0.050)
pH ≈ 9.25 + 0.10
pH ≈ 9.35

Therefore, the final pH of the solution is approximately 9.35.