If bond energy of `H_(2),F_(2)` and `HF` are in the ratio `2:1:3` and `DeltaH_(a)(H_(2))=400kJ//mol`. Then `DeltaH_(f)(HF)` is `:`

Options

A. `0 kJ //mol`
B. `-600kJ //mol`
C. `-1200kJ//mol`
D. None of these

Explanation

To find the heat of formation of HF (ΔH_f(HF)), we will follow these steps:

### Step 1: Define the Bond Energies
Given the bond energies of H₂, F₂, and HF are in the ratio 2:1:3, we can express them in terms of a variable \( X \):
- Bond energy of H₂ = \( 2X \)
- Bond energy of F₂ = \( X \)
- Bond energy of HF = \( 3X \)

### Step 2: Use the Given Information
We know that the heat of dissociation of H₂ (ΔH_a(H₂)) is 400 kJ/mol. Since the bond energy of H₂ is \( 2X \), we can set up the equation:
\[ 2X = 400 \text{ kJ/mol} \]
From this, we can solve for \( X \):
\[ X = \frac{400}{2} = 200 \text{ kJ/mol} \]

### Step 3: Calculate the Bond Energies
Now we can calculate the bond energies for each molecule:
- Bond energy of H₂ = \( 2X = 400 \text{ kJ/mol} \)
- Bond energy of F₂ = \( X = 200 \text{ kJ/mol} \)
- Bond energy of HF = \( 3X = 3 \times 200 = 600 \text{ kJ/mol} \)

### Step 4: Write the Formation Reaction
The formation of HF from its elements can be represented as:
\[ \frac{1}{2} \text{H}_2 + \frac{1}{2} \text{F}_2 \rightarrow \text{HF} \]

### Step 5: Apply the Heat of Formation Formula
The heat of formation (ΔH_f) can be calculated using the formula:
\[ \Delta H_f(HF) = \text{(Bond energy of reactants)} - \text{(Bond energy of products)} \]

Substituting the bond energies into the equation:
\[ \Delta H_f(HF) = \left( \frac{1}{2} \times 400 + \frac{1}{2} \times 200 \right) - 600 \]

### Step 6: Calculate the Values
Calculating the values:
1. For H₂: \( \frac{1}{2} \times 400 = 200 \)
2. For F₂: \( \frac{1}{2} \times 200 = 100 \)

Now substituting these into the equation:
\[ \Delta H_f(HF) = (200 + 100) - 600 \]
\[ \Delta H_f(HF) = 300 - 600 \]
\[ \Delta H_f(HF) = -300 \text{ kJ/mol} \]

### Final Answer
Thus, the heat of formation of HF is:
\[ \Delta H_f(HF) = -300 \text{ kJ/mol} \]

---