The heat of neutralization of (i) `CHCl_(2)-COOH` by NaOH is 12830 cal, (ii) HCl by NaOH is 13680 cal and (iii) `NH_(4)OH` by HCl is 12270 cal. What is the heat of neutralization of dichloro acetic acid by `NH_(4)OH`? Calculate the heats of ionization of dichloro acetic acid and `NH_(4)OH`.

Answer

To solve the problem, we need to find the heat of neutralization of dichloroacetic acid (CHCl₂COOH) by ammonium hydroxide (NH₄OH) and calculate the heats of ionization for both substances.

### Step-by-Step Solution:

1. **Understanding the Given Data**:
- Heat of neutralization of CHCl₂COOH by NaOH: \( \Delta H_1 = -12830 \, \text{cal} \)
- Heat of neutralization of HCl by NaOH: \( \Delta H_2 = -13680 \, \text{cal} \)
- Heat of neutralization of NH₄OH by HCl: \( \Delta H_3 = -12270 \, \text{cal} \)

2. **Writing the Reactions**:
- For the neutralization of dichloroacetic acid by NaOH:
\[ \text{CHCl}_2\text{COOH} + \text{NaOH} \rightarrow \text{CHCl}_2\text{COONa} + \text{H}_2\text{O} \]
- For the neutralization of NH₄OH by HCl:
\[ \text{NH}_4\text{OH} + \text{HCl} \rightarrow \text{NH}_4\text{Cl} + \text{H}_2\text{O} \]
- For the neutralization of HCl by NaOH:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]

3. **Using Hess's Law**:
We can use Hess's law to find the heat of neutralization of dichloroacetic acid by NH₄OH. The equation can be set up as follows:
\[ \Delta H_{\text{neutralization of CHCl}_2\text{COOH by NH}_4\text{OH}} = -\Delta H_1 - \Delta H_3 + \Delta H_2 \]

4. **Substituting the Values**:
\[ \Delta H_{\text{neutralization}} = -(-12830) - (-12270) + (-13680) \]
\[ = 12830 + 12270 - 13680 \]
\[ = 11420 \, \text{cal} \]

5. **Calculating the Heats of Ionization**:
- For dichloroacetic acid (CHCl₂COOH):
\[ \Delta H_{\text{ionization}} = \Delta H_2 - \Delta H_1 \]
\[ = -13680 - (-12830) \]
\[ = -850 \, \text{cal} \]

- For ammonium hydroxide (NH₄OH):
\[ \Delta H_{\text{ionization}} = \Delta H_2 - \Delta H_3 \]
\[ = -13680 - (-12270) \]
\[ = -1410 \, \text{cal} \]

### Final Results:
- Heat of neutralization of dichloroacetic acid by NH₄OH: **11420 cal**
- Heat of ionization of dichloroacetic acid: **-850 cal**
- Heat of ionization of NH₄OH: **-1410 cal**