Calculate the degree of hydrolysis of 0.01 M solution of ammonium chloride if its pH is 5.28.

Explanation

To calculate the degree of hydrolysis of a 0.01 M solution of ammonium chloride (NH4Cl) given its pH of 5.28, we can follow these steps:

### Step 1: Calculate the concentration of H⁺ ions
The pH of the solution is given as 5.28. We can calculate the concentration of hydrogen ions [H⁺] using the formula:

\[ [H^+] = 10^{-\text{pH}} = 10^{-5.28} \]

Calculating this gives:

\[ [H^+] \approx 5.24 \times 10^{-6} \, \text{M} \]

### Step 2: Write the hydrolysis reaction
Ammonium chloride dissociates in water to form ammonium ions (NH4⁺) and chloride ions (Cl⁻). The ammonium ion can undergo hydrolysis as follows:

\[ NH_4^+ + H_2O \rightleftharpoons H^+ + NH_3 \]

### Step 3: Set up the equilibrium expression
Let \( x \) be the degree of hydrolysis. The initial concentration of NH4⁺ is 0.01 M. At equilibrium, the concentrations will be:

- [NH4⁺] = 0.01 - x
- [H⁺] = x
- [NH3] = x

From the pH, we found that [H⁺] = 5.24 × 10⁻⁶ M, which means \( x = 5.24 \times 10^{-6} \).

### Step 4: Calculate the degree of hydrolysis
The degree of hydrolysis (h) can be calculated using the formula:

\[ h = \frac{x}{C} \times 100\% \]

Where \( C \) is the initial concentration of NH4Cl, which is 0.01 M.

Substituting the values:

\[ h = \frac{5.24 \times 10^{-6}}{0.01} \times 100\% \]

Calculating this gives:

\[ h \approx 0.0524\% \]

### Final Answer
The degree of hydrolysis of the 0.01 M solution of ammonium chloride is approximately **0.0524%**.

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