Degree hydrolysis (h) of a salt of weak acid and a strong base is given by

Options

A. `h=sqrt((K_h)/c)`
B. `h=sqrt(K_h)`
C. `h=sqrt(c/(K_h))`
D. `h=sqrt((K_w)/(K_b))`

Answer

To find the degree of hydrolysis (h) of a salt formed from a weak acid and a strong base, we can follow these steps:

### Step 1: Identify the salt
The salt formed from a weak acid and a strong base can be represented as CH3COONa, where CH3COOH is acetic acid (weak acid) and NaOH is sodium hydroxide (strong base).

### Step 2: Dissociation of the salt
When the salt CH3COONa dissociates in water, it produces:
\[ \text{CH}_3\text{COO}^- + \text{Na}^+ \]
Here, CH3COO⁻ is the conjugate base of the weak acid.

### Step 3: Hydrolysis of the conjugate base
The conjugate base CH3COO⁻ will undergo hydrolysis in water:
\[ \text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^- \]
This reaction indicates that the conjugate base reacts with water to produce the weak acid and hydroxide ions.

### Step 4: Set up the equilibrium expression
Let the initial concentration of the salt be C. If h is the degree of hydrolysis, then at equilibrium:
- Concentration of CH3COOH = hC
- Concentration of OH⁻ = hC
- Concentration of CH3COO⁻ = C - hC = C(1 - h)

The equilibrium expression for the hydrolysis constant (K_h) is given by:
\[ K_h = \frac{[\text{CH}_3\text{COOH}][\text{OH}^-]}{[\text{CH}_3\text{COO}^-]} \]

### Step 5: Substitute the equilibrium concentrations into the expression
Substituting the equilibrium concentrations into the expression gives:
\[ K_h = \frac{(hC)(hC)}{C(1 - h)} \]
This simplifies to:
\[ K_h = \frac{h^2 C}{1 - h} \]

### Step 6: Assume low degree of hydrolysis
If we assume that the degree of hydrolysis (h) is small (which is often the case), we can approximate \(1 - h \approx 1\). Thus, the equation simplifies to:
\[ K_h \approx h^2 C \]

### Step 7: Solve for h
Rearranging the equation gives:
\[ h^2 = \frac{K_h}{C} \]
Taking the square root of both sides, we find:
\[ h = \sqrt{\frac{K_h}{C}} \]

### Conclusion
The degree of hydrolysis (h) of a salt of a weak acid and a strong base is given by:
\[ h = \sqrt{\frac{K_h}{C}} \]