Calculate The Ph of A 0.20 M Solution of Nh4br.

Introduction

Ammonium bromide (NH4Br) is a weak electrolyte that dissociates in water to form NH4+ and Br- ions. The pH of a solution containing NH4Br can be calculated using the Henderson-Hasselbalch equation, which relates the pH to the concentration of the conjugate acid-base pair.

For a solution of NH4Br, the relevant acid-base pair is NH4+ and NH3. The equilibrium constant for the reaction NH4+ + H2O ⇌ NH3 + H3O+ is known, allowing us to calculate the pH.

Calculation Method

The pH of a solution containing NH4Br can be calculated using the following steps:

1. Determine the concentration of NH4+ and NH3 in the solution.
2. Use the equilibrium constant for the reaction NH4+ + H2O ⇌ NH3 + H3O+ to calculate the ratio [NH4+]/[NH3].
3. Apply the Henderson-Hasselbalch equation to find the pH.

The pKa for NH4+ is approximately 9.25. For a 0.20 M solution of NH4Br, the concentration of NH4+ is 0.20 M, and the concentration of NH3 is negligible at equilibrium.

Example Calculation

Let's calculate the pH of a 0.20 M solution of NH4Br:

1. Given: [NH4+] = 0.20 M, [NH3] ≈ 0 M (negligible at equilibrium)
2. pKa for NH4+ = 9.25
3. Apply the Henderson-Hasselbalch equation:
   pH = 9.25 + log(0.20 / 0.00) → Undefined (log(0) is undefined)
4. Since [NH3] is negligible, we must use the exact equilibrium calculation:
   pH = pKa - log([NH4+]/Ka) = 9.25 - log(0.20/5.6×10⁻¹⁰) ≈ 9.25 - log(3.57×10⁸) ≈ 9.25 - 8.55 ≈ 0.70

The exact calculation shows the pH is approximately 0.70, which is acidic due to the presence of NH4+ ions.

Interpretation

A pH of 0.70 indicates a strongly acidic solution. This is expected because NH4+ is a conjugate acid of NH3, which is a weak base. The solution contains more NH4+ ions than NH3 molecules, resulting in a low pH.

If you need to adjust the pH of the solution, you can add a strong base to convert NH4+ to NH3, or a strong acid to increase the concentration of NH4+.