Given that the data for neutralization of a weak acid (HA) and strong acid with a strong base is:
`HA +OH^(-) rArr A^(-) + H_(2)O: DeltaH = -41.80kJ , H^(+) + OH^(-) rArr H_(2)O, Delta H= -55.90kJ`
The enthalpy of dissociation of weak acid would be

Answer

To find the enthalpy of dissociation of the weak acid (HA), we will use the given data for the neutralization reactions and apply Hess's law. Here’s the step-by-step solution:

### Step 1: Write down the reactions and their enthalpy changes
We have two reactions provided:

1. **Neutralization of weak acid (HA) with strong base (OH⁻):**
\[ \text{HA} + \text{OH}^- \rightarrow \text{A}^- + \text{H}_2\text{O} \quad \Delta H_1 = -41.80 \, \text{kJ} \]

2. **Neutralization of strong acid (H⁺) with strong base (OH⁻):**
\[ \text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O} \quad \Delta H_2 = -55.90 \, \text{kJ} \]

### Step 2: Set up the equation for the dissociation of the weak acid
The dissociation of the weak acid (HA) can be represented as:
\[ \text{HA} \rightarrow \text{H}^+ + \text{A}^- \]

### Step 3: Apply Hess's Law
According to Hess's law, the enthalpy change for the overall reaction can be found by summing the enthalpy changes of the individual steps. We can rearrange the reactions to find the enthalpy of dissociation of the weak acid.

We can express the dissociation of HA in terms of the two reactions we have:
\[ \text{HA} + \text{OH}^- \rightarrow \text{A}^- + \text{H}_2\text{O} \quad (\Delta H_1) \]
\[ \text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O} \quad (\Delta H_2) \]

To find the enthalpy of dissociation of HA, we can subtract the second reaction from the first:
\[ \Delta H_{\text{dissociation}} = \Delta H_1 - \Delta H_2 \]

### Step 4: Substitute the values
Now we substitute the values of \(\Delta H_1\) and \(\Delta H_2\):
\[ \Delta H_{\text{dissociation}} = (-41.80 \, \text{kJ}) - (-55.90 \, \text{kJ}) \]
\[ \Delta H_{\text{dissociation}} = -41.80 + 55.90 \]
\[ \Delta H_{\text{dissociation}} = 14.10 \, \text{kJ} \]

### Final Answer
The enthalpy of dissociation of the weak acid (HA) is:
\[ \Delta H_{\text{dissociation}} = +14.10 \, \text{kJ} \]

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