If `triangleH_(f) (C_(2)H_(5)-S-C_(2)H_(5))=-147` kJ/mole and
`triangleH_(f) (C_(2)H_(5)-S-S-C_(2)H_(5))=-202` Kj/mole and
`triangleH_(f) (S) (g)=+ 223 kJ/mole then the S-S bond energy will be

Options

A. 168 kJ
B. 126 kJ
C. 278 kJ
D. 572 kJ

Answer

To find the S-S bond energy using the given enthalpies of formation, we can follow these steps:

### Step 1: Write the Reaction
We need to consider the formation of the compound \( C_2H_5-S-S-C_2H_5 \) from \( C_2H_5-S-C_2H_5 \) and sulfur (S).

The reaction can be written as:
\[ C_2H_5-S-C_2H_5 + S \rightarrow C_2H_5-S-S-C_2H_5 \]

### Step 2: Use the Enthalpy of Formation Values
We are given the following values:
- \( \Delta H_f (C_2H_5-S-C_2H_5) = -147 \, \text{kJ/mol} \)
- \( \Delta H_f (C_2H_5-S-S-C_2H_5) = -202 \, \text{kJ/mol} \)
- \( \Delta H_f (S) = +223 \, \text{kJ/mol} \)

### Step 3: Calculate the Change in Enthalpy for the Reaction
Using the enthalpy of formation values, we can calculate the change in enthalpy (\( \Delta H \)) for the reaction:
\[ \Delta H = \Delta H_f (\text{products}) - \Delta H_f (\text{reactants}) \]
Substituting the values we have:
\[ \Delta H = \Delta H_f (C_2H_5-S-S-C_2H_5) - \Delta H_f (C_2H_5-S-C_2H_5) - \Delta H_f (S) \]
\[ \Delta H = (-202) - (-147) - (223) \]
Calculating this gives:
\[ \Delta H = -202 + 147 - 223 = -278 \, \text{kJ/mol} \]

### Step 4: Relate the Change in Enthalpy to Bond Energies
The change in enthalpy can also be expressed in terms of bond energies:
\[ \Delta H = \text{Bond energy of reactants} - \text{Bond energy of products} \]
For our case, the bond energy of reactants includes the bond energy of the S-S bond we want to find. Therefore, we can express it as:
\[ -278 = \text{Bond energy of S} - \text{Bond energy of S-S} \]
Where the bond energy of sulfur (S) is given as \( +223 \, \text{kJ/mol} \).

### Step 5: Solve for the S-S Bond Energy
Rearranging the equation:
\[ \text{Bond energy of S-S} = \text{Bond energy of S} + 278 \]
Substituting the known value:
\[ \text{Bond energy of S-S} = 223 + 278 = 501 \, \text{kJ/mol} \]

### Final Answer
The bond energy of the S-S bond is \( 501 \, \text{kJ/mol} \).

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