`[H^(+)]` =`sqrt((K_(w)K_(a))/C)` is suitable for

Options

A. `NaCl,NH_(4)Cl`
B. `CH_(3)COONa,NaCN`
C. `CH_(3)COONa,(NH_(4))_(2)SO_(4)`
D. `CH_(3)COONH_(4),(NH_(4))_(2)CO_(3)`

Answer

To solve the question `[H^(+)] = sqrt((K_(w)K_(a))/C)` and determine for which scenario it is suitable, we will analyze the relationship between the concentrations of hydrogen ions, the dissociation constants of acids and bases, and the concentration of the solution.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation `[H^(+)] = sqrt((K_(w)K_(a))/C)` relates the concentration of hydrogen ions to the ion product of water (Kw), the acid dissociation constant (Ka), and the concentration (C) of the solution.

2. **Identifying the Components**:
- **Kw**: The ion product of water, which is constant at a given temperature (e.g., 1.0 x 10^-14 at 25°C).
- **Ka**: The acid dissociation constant, which measures the strength of an acid in solution.
- **C**: The concentration of the acid or salt solution.

3. **Analyzing the Types of Salts**:
We need to identify the types of salts or solutions that would lead to the given equation. The equation is typically applicable in cases involving:
- A weak acid and its salt.
- A weak base and its salt.

4. **Considering Strong and Weak Acids/Bases**:
- **Strong Acid + Strong Base**: This results in a neutral solution, and the concentration of H+ ions would not follow the given equation.
- **Weak Acid + Strong Base**: This will produce a basic solution, and the hydrolysis of the weak acid will lead to the formation of OH- ions, which is not suitable for the given equation.
- **Strong Acid + Weak Base**: This will produce an acidic solution, and the concentration of H+ ions can be derived from the hydrolysis of the weak base.
- **Weak Acid + Weak Base**: This scenario can lead to a more complex equilibrium, but the equation can still apply.

5. **Finalizing the Suitable Case**:
The equation `[H^(+)] = sqrt((K_(w)K_(a))/C)` is most suitable for the case of a weak acid and its salt, where the weak acid partially dissociates and contributes to the concentration of H+ ions in the solution.

### Conclusion:
The equation is suitable for a solution involving a weak acid and its salt, as it allows for the calculation of the hydrogen ion concentration based on the dissociation constants and the concentration of the solution.