`Delta H_(1)C_(2)H_(4) = 12.5 kcal`
Heat of atomisation of C = 171 Kcal
Bond energy of `H_(2)` = `104.3 kcal`
Bond energy C - H = 99.3 kcal
What is C = C bond energy?

Options

A. `140.9 kcal`
B. `49 kcal`
C. `40 kcal`
D. `76 kcal`

Answer

To find the bond energy of the C=C bond in ethylene (C2H4), we can use the given data and apply the concept of bond energies and heats of formation. Here’s a step-by-step solution:

### Step 1: Write the formation reaction of C2H4
The formation of ethylene (C2H4) from its elements in their standard states can be represented as:
\[ 2C(s) + 2H_2(g) \rightarrow C_2H_4(g) \]

### Step 2: Identify the given data
- Heat of formation of C2H4, \( \Delta H_{f} = 12.5 \, \text{kcal} \)
- Heat of atomization of C (for 1 mole of C), \( = 171 \, \text{kcal} \)
- Bond energy of H2, \( = 104.3 \, \text{kcal} \)
- Bond energy of C-H bond, \( = 99.3 \, \text{kcal} \)

### Step 3: Write the equation for the heat of formation in terms of bond energies
The heat of formation can be expressed as:
\[ \Delta H_{f} = \text{(Bond energies of reactants)} - \text{(Bond energies of products)} \]

### Step 4: Calculate the bond energies of reactants
For the reactants:
- The bond energy for 2 moles of C (atomization) is:
\[ 2 \times 171 \, \text{kcal} = 342 \, \text{kcal} \]
- The bond energy for 2 moles of H2 is:
\[ 2 \times 104.3 \, \text{kcal} = 208.6 \, \text{kcal} \]

Total bond energy of reactants:
\[ 342 \, \text{kcal} + 208.6 \, \text{kcal} = 550.6 \, \text{kcal} \]

### Step 5: Calculate the bond energies of products
For the products (C2H4):
- The bond energy for the C=C bond (which we need to find) is \( E_{C=C} \).
- The bond energy for 4 C-H bonds is:
\[ 4 \times 99.3 \, \text{kcal} = 397.2 \, \text{kcal} \]

Total bond energy of products:
\[ E_{C=C} + 397.2 \, \text{kcal} \]

### Step 6: Set up the equation
Using the heat of formation:
\[ 12.5 \, \text{kcal} = 550.6 \, \text{kcal} - (E_{C=C} + 397.2 \, \text{kcal}) \]

### Step 7: Rearranging the equation
Rearranging gives:
\[ E_{C=C} = 550.6 \, \text{kcal} - 397.2 \, \text{kcal} - 12.5 \, \text{kcal} \]
\[ E_{C=C} = 550.6 - 409.7 \]
\[ E_{C=C} = 140.9 \, \text{kcal} \]

### Final Answer
The bond energy of the C=C bond is:
\[ E_{C=C} = 140.9 \, \text{kcal} \]

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