Four solution of `NH_(4)Cl` are taken with concentration `1M,0.1M,0.01M & 0.001M`. Their degree of hydrolysis are `h_(1),h_(2) & h_(3),h_(4)`. What is the gradation of degree of hydrolysis

Options

A. `h_(1)gth_(2)gth_(3)gth_(4)`
B. `h_(1)=h_(2)=h_(3)=h_(4)`
C. `h_(4)gth_(3)gth_(2)gth_(1)`
D. None of these

Explanation

To solve the problem of determining the gradation of the degree of hydrolysis of four solutions of ammonium chloride (NH₄Cl) with different concentrations, we can follow these steps:

### Step 1: Understand Hydrolysis
Ammonium chloride (NH₄Cl) is a salt that undergoes hydrolysis in water, producing ammonium ions (NH₄⁺) and chloride ions (Cl⁻). The ammonium ions can further react with water to form ammonium hydroxide (NH₄OH) and release hydrogen ions (H⁺):
\[ NH₄^+ + H₂O \rightleftharpoons NH₄OH + H^+ \]

### Step 2: Define Degree of Hydrolysis
The degree of hydrolysis (α) is defined as the fraction of the salt that has undergone hydrolysis. For a salt like NH₄Cl, the degree of hydrolysis can be expressed in terms of the concentration of the salt (C) and the hydrolysis constant (K):
\[ K = \frac{C^2 \alpha^2}{C(1 - \alpha)} \]

### Step 3: Simplify the Expression
Assuming that the degree of hydrolysis (α) is much less than 1 (which is valid for dilute solutions), we can simplify the equation:
\[ K \approx C \alpha^2 \]
From this, we can derive the expression for the degree of hydrolysis:
\[ \alpha = \sqrt{\frac{K}{C}} \]

### Step 4: Analyze the Relationship
From the derived expression, we can see that the degree of hydrolysis (α) is inversely proportional to the square root of the concentration (C). This means that as the concentration of the solution decreases, the degree of hydrolysis increases.

### Step 5: Apply to Given Concentrations
Given the concentrations:
- \( C_1 = 1M \) (H₁)
- \( C_2 = 0.1M \) (H₂)
- \( C_3 = 0.01M \) (H₃)
- \( C_4 = 0.001M \) (H₄)

Using the relationship derived:
- For \( C_1 \): \( \alpha_1 \) is the smallest (least hydrolysis)
- For \( C_2 \): \( \alpha_2 \) is larger than \( \alpha_1 \)
- For \( C_3 \): \( \alpha_3 \) is larger than \( \alpha_2 \)
- For \( C_4 \): \( \alpha_4 \) is the largest (most hydrolysis)

### Step 6: Conclusion
Thus, the gradation of the degree of hydrolysis from highest to lowest is:
\[ \alpha_4 > \alpha_3 > \alpha_2 > \alpha_1 \]
or in terms of H values:
\[ H_4 > H_3 > H_2 > H_1 \]