Heat of neutralization between HCl and NaOH is `-13.7 k.cal`. If heat of neutralization between `CH_(3)COOH` and `NaOH` is `-11.7 k.cal`. Calculate heat of ionization of `CH_(3)COOH`.

Explanation

To calculate the heat of ionization of acetic acid (CH₃COOH), we can use the given heats of neutralization for HCl and NaOH, as well as for CH₃COOH and NaOH. The heat of ionization can be determined using Hess's law.

### Step-by-Step Solution:

1. **Identify the reactions**:
- The neutralization reaction between HCl and NaOH can be written as:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]
The heat of this reaction (ΔH₁) is given as -13.7 kcal.

- The neutralization reaction between CH₃COOH and NaOH can be written as:
\[ \text{CH}_3\text{COOH} + \text{NaOH} \rightarrow \text{CH}_3\text{COONa} + \text{H}_2\text{O} \]
The heat of this reaction (ΔH₂) is given as -11.7 kcal.

2. **Set up the relationship using Hess's law**:
- The heat of ionization of acetic acid (ΔH₃) can be represented as:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]
- According to Hess's law:
\[ \Delta H_{\text{neutralization of HCl}} = \Delta H_{\text{ionization of CH}_3\text{COOH}} + \Delta H_{\text{neutralization of CH}_3\text{COOH}} \]
- This can be rearranged to find the heat of ionization:
\[ \Delta H_{\text{ionization of CH}_3\text{COOH}} = \Delta H_{\text{neutralization of HCl}} - \Delta H_{\text{neutralization of CH}_3\text{COOH}} \]

3. **Substitute the values**:
- Substitute the known values into the equation:
\[ \Delta H_{\text{ionization of CH}_3\text{COOH}} = -13.7 \, \text{kcal} - (-11.7 \, \text{kcal}) \]
- Simplifying this gives:
\[ \Delta H_{\text{ionization of CH}_3\text{COOH}} = -13.7 + 11.7 = -2.0 \, \text{kcal} \]

4. **Conclusion**:
- The heat of ionization of acetic acid (CH₃COOH) is -2.0 kcal.

### Summary of the Solution:
The heat of ionization of acetic acid (CH₃COOH) is calculated to be -2.0 kcal using the heats of neutralization for HCl and CH₃COOH with NaOH.