The heats fo neutralization of `HCl` with `NH_(4) OH` and `NaOH` with `CH_(3) COOH` are `- 51.4 kJ eq^(-1)` and `- 50.6 kJ eq^(-1)`, respectively. The heat of neutralization of acetic acid with `NH_(4) OH` will be

Options

A. `- 44.6 kJ eq^(-1)`
B. `- 50.6 kJ eq^(-1)`
C. `- 51.4 kJ eq^(-1)`
D. `- 57.4 kJ eq^(-1)`

Explanation

To find the heat of neutralization of acetic acid (CH₃COOH) with ammonium hydroxide (NH₄OH), we can use the data provided for the heats of neutralization of other acid-base reactions.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Heat of neutralization of HCl with NH₄OH = -51.4 kJ/equiv (HCl is a strong acid)
- Heat of neutralization of NaOH with CH₃COOH = -50.6 kJ/equiv (CH₃COOH is a weak acid)

2. **Understand the Nature of the Reactants:**
- HCl is a strong acid and NH₄OH is a weak base.
- CH₃COOH is a weak acid and NaOH is a strong base.
- We need to find the heat of neutralization for the reaction between a weak acid (CH₃COOH) and a weak base (NH₄OH).

3. **Use the Concept of Heat of Neutralization:**
- The heat of neutralization is generally more exothermic (more negative) when a strong acid reacts with a strong base compared to when a weak acid or weak base is involved.
- The heat of neutralization for a weak acid with a weak base will be less negative than that of strong acid with strong base.

4. **Estimate the Heat of Neutralization:**
- Since HCl with NH₄OH has a heat of -51.4 kJ and NaOH with CH₃COOH has a heat of -50.6 kJ, we can estimate that the heat of neutralization for CH₃COOH with NH₄OH will be less negative than both.
- The approximate average of the two given heats can be considered as a rough estimate for the heat of neutralization of CH₃COOH with NH₄OH.

5. **Calculate the Approximate Value:**
- The average of -51.4 kJ and -50.6 kJ can be calculated as:
\[ \text{Average} = \frac{-51.4 + (-50.6)}{2} = \frac{-102.0}{2} = -51.0 \text{ kJ/equiv} \]
- However, since both reactants are weak (one weak acid and one weak base), we expect the heat of neutralization to be slightly less negative than this average.

6. **Final Estimation:**
- Therefore, we can estimate the heat of neutralization of acetic acid with NH₄OH to be around -49.0 kJ/equiv.

### Conclusion:
The heat of neutralization of acetic acid with NH₄OH is approximately **-49.0 kJ/equiv**.