The average S-F bond energy in kJ `mol^(-1)` of `SF_(6)` is ________ (Rounded off to the nearest integer)
[Given : The values of standard enthalpy of formation of `SF_(6)(g),S(g)` and F(g) are -1100, 275 and 80 kJ `mol^(-1)` respectively. ]

Answer

To find the average S-F bond energy in \( SF_6 \), we will use the given standard enthalpy of formation values. Here’s the step-by-step solution:

### Step 1: Write the Reaction
The formation of \( SF_6 \) from its elements can be represented as:
\[ S(g) + 3F_2(g) \rightarrow SF_6(g) \]
However, since we need to find the bond energy of the S-F bond, we will consider the reverse reaction:
\[ SF_6(g) \rightarrow S(g) + 6F(g) \]

### Step 2: Use the Enthalpy of Formation Values
The standard enthalpy change (\( \Delta H \)) for the reaction can be calculated using the standard enthalpy of formation values:
\[ \Delta H = \text{Enthalpy of formation of products} - \text{Enthalpy of formation of reactants} \]
Given:
- Enthalpy of formation of \( SF_6(g) = -1100 \, \text{kJ/mol} \)
- Enthalpy of formation of \( S(g) = 275 \, \text{kJ/mol} \)
- Enthalpy of formation of \( F(g) = 80 \, \text{kJ/mol} \)

### Step 3: Calculate the Enthalpy Change
Substituting the values into the equation:
\[ \Delta H = [\Delta H_f(S) + 6 \times \Delta H_f(F)] - \Delta H_f(SF_6) \]
\[ \Delta H = [275 + 6 \times 80] - (-1100) \]
Calculating the right-hand side:
\[ \Delta H = [275 + 480] + 1100 \]
\[ \Delta H = 755 + 1100 = 1855 \, \text{kJ/mol} \]

### Step 4: Relate Enthalpy Change to Bond Energy
The enthalpy change calculated corresponds to the breaking of 6 S-F bonds:
\[ \Delta H = 6 \times \text{Bond Energy (S-F)} \]
Thus, we can express the bond energy as:
\[ \text{Bond Energy (S-F)} = \frac{\Delta H}{6} = \frac{1855}{6} \]

### Step 5: Calculate the Average Bond Energy
Calculating the average bond energy:
\[ \text{Bond Energy (S-F)} = 309.17 \, \text{kJ/mol} \]

### Step 6: Round to the Nearest Integer
Rounding \( 309.17 \) to the nearest integer gives:
\[ \text{Average S-F bond energy} \approx 309 \, \text{kJ/mol} \]

### Final Answer
The average S-F bond energy in \( SF_6 \) is **309 kJ/mol**.

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