The standard heat of formation values of `SF_(6)(g), S(g)`, and `F(g)` are `-1100, 275`, and `80 kJ mol^(-1)`, respectively. Then the average `S-F` bond enegry in `SF_(6)`

Options

A. `310 kJ mol^(-1)`
B. `220 kJ mol^(-1)`
C. `309 kJ mol^(-1)`
D. `280 kJ mol^(-1)`

Explanation

To find the average S-F bond energy in SF6, we can use the standard heat of formation values provided for the substances involved in the reaction. Here’s a step-by-step solution:

### Step 1: Write the reaction for the formation of SF6
The formation reaction for SF6 from its elements in their standard states is:
\[ S(g) + 6F(g) \rightarrow SF_6(g) \]

### Step 2: Write the expression for the enthalpy change (ΔH) of the reaction
The enthalpy change for the formation of SF6 can be expressed using the standard heats of formation:
\[ \Delta H = \text{(Heat of formation of SF6)} - \left( \text{(Heat of formation of S)} + 6 \times \text{(Heat of formation of F)} \right) \]

### Step 3: Substitute the values into the equation
Using the given values:
- Heat of formation of SF6 = -1100 kJ/mol
- Heat of formation of S(g) = 275 kJ/mol
- Heat of formation of F(g) = 80 kJ/mol

Substituting these values into the equation:
\[ \Delta H = -1100 - \left( 275 + 6 \times 80 \right) \]

### Step 4: Calculate the total heat of formation for reactants
First, calculate \(6 \times 80\):
\[ 6 \times 80 = 480 \]
Now, add the heat of formation of S:
\[ 275 + 480 = 755 \]

### Step 5: Calculate ΔH
Now substitute back into the ΔH equation:
\[ \Delta H = -1100 - 755 = -1855 \text{ kJ} \]

### Step 6: Relate ΔH to bond energy
Since the reaction involves the formation of 6 S-F bonds, we can relate ΔH to the bond energy (X) as follows:
\[ \Delta H = 6X \]
Thus,
\[ -1855 = 6X \]

### Step 7: Solve for X (average bond energy)
Now, solve for X:
\[ X = \frac{-1855}{6} \approx -309.17 \text{ kJ/mol} \]
Since bond energies are typically reported as positive values, we take the absolute value:
\[ X \approx 309 \text{ kJ/mol} \]

### Final Answer
The average S-F bond energy in SF6 is approximately **309 kJ/mol**.

---