The heat of neutralization of HCN by NaOH is 13.3 KJ/mole, the energy of dissociation of HCN is

Options

A. 43.8 KJ
B. `-43.8` KJ
C. `-68 KJ`
D. `68 KJ`

Answer

To solve the problem of finding the energy of dissociation of HCN given the heat of neutralization with NaOH, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Neutralization Reaction**:
The neutralization reaction between HCN (a weak acid) and NaOH (a strong base) can be represented as:
\[ \text{HCN} + \text{NaOH} \rightarrow \text{NaCN} + \text{H}_2\text{O} \]

2. **Identify the Heat of Neutralization**:
The heat of neutralization (\(\Delta H_R\)) is given as \( -13.3 \, \text{kJ/mol} \). This value is negative because the reaction is exothermic.

3. **Understand the Dissociation of HCN**:
Since HCN is a weak acid, it does not fully dissociate in solution. The dissociation can be represented as:
\[ \text{HCN} \rightleftharpoons \text{H}^+ + \text{CN}^- \]
The energy required for this dissociation is denoted as \(\Delta H_{\text{dissociation}}\).

4. **Dissociation of NaOH**:
NaOH, being a strong base, dissociates completely in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
This process does not require additional energy input.

5. **Energy Change in the Reaction**:
The overall enthalpy change for the reaction can be expressed as:
\[ \Delta H_{\text{reaction}} = \Delta H_{\text{dissociation}} + \Delta H_{\text{neutralization}} \]
Here, \(\Delta H_{\text{neutralization}}\) for the reaction of \(\text{H}^+\) and \(\text{OH}^-\) is a constant value of \(-57.1 \, \text{kJ/mol}\).

6. **Set Up the Equation**:
Substitute the known values into the equation:
\[ -13.3 \, \text{kJ/mol} = \Delta H_{\text{dissociation}} + (-57.1 \, \text{kJ/mol}) \]

7. **Solve for \(\Delta H_{\text{dissociation}}\)**:
Rearranging the equation gives:
\[ \Delta H_{\text{dissociation}} = -13.3 \, \text{kJ/mol} + 57.1 \, \text{kJ/mol} \]
\[ \Delta H_{\text{dissociation}} = 43.8 \, \text{kJ/mol} \]

8. **Final Answer**:
The energy of dissociation of HCN is \(43.8 \, \text{kJ/mol}\).