the pka of acetic acid and pkb of ammonium hydroxide are 4.76 and 4.75 respectively. the ph of ammonium acetate solution will be

To determine the pH of an ammonium acetate solution, we can use the relationship between the pKa of acetic acid and the pKb of ammonium hydroxide. This involves understanding how these values relate to the dissociation of the weak acid and the weak base in solution.

Understanding the Components

Acetic acid (CH₃COOH) is a weak acid, and its dissociation in water can be represented as:

• CH₃COOH ⇌ H⁺ + CH₃COO⁻

The pKa of acetic acid is 4.76, which indicates the strength of the acid. A lower pKa means a stronger acid. Conversely, ammonium hydroxide (NH₄OH) is a weak base, and its dissociation can be represented as:

• NH₄OH ⇌ NH₄⁺ + OH⁻

The pKb of ammonium hydroxide is 4.75, which tells us about the strength of the base. A lower pKb indicates a stronger base.

Calculating the pH of Ammonium Acetate Solution

Ammonium acetate (NH₄CH₃COO) is a salt formed from the reaction of acetic acid and ammonium hydroxide. In solution, it dissociates into ammonium ions (NH₄⁺) and acetate ions (CH₃COO⁻). The pH of the solution can be calculated using the Henderson-Hasselbalch equation, which is particularly useful for buffer solutions:

The Henderson-Hasselbalch Equation

The equation is given by:

• pH = pKa + log([A⁻]/[HA])

In this case, [A⁻] is the concentration of the acetate ion (from acetic acid), and [HA] is the concentration of the ammonium ion (from ammonium hydroxide). Since ammonium acetate is a salt of a weak acid and a weak base, we can also relate pKa and pKb:

Relationship Between pKa and pKb

The relationship is given by:

• pKa + pKb = 14

For acetic acid and ammonium hydroxide:

• pKa = 4.76
• pKb = 4.75

Now, we can find the pKa of the conjugate base (acetate ion) and the pKb of the conjugate acid (ammonium ion):

• pKa of acetate = 4.76
• pKb of ammonium = 14 - 4.75 = 9.25

Final pH Calculation

Since ammonium acetate is a salt that can act as a buffer, we can use the average of the pKa and pKb to estimate the pH of the solution:

• pH ≈ (pKa + (14 - pKb)) / 2
• pH ≈ (4.76 + 4.75) / 2
• pH ≈ 4.755

Thus, the pH of the ammonium acetate solution is approximately 4.76. This value indicates that the solution is slightly acidic, which is consistent with the presence of both a weak acid and a weak base in equilibrium.