Calculate the heat of formation of benzene from the following data, assuming no resonance. Bond energies :
`C-C=83 kcal, C=C=140 Kcal, C-H=99 kcal`
`{:("Heat of atomisation of ",C-170.9 kcal,,,),("Heat of atomisation of",H=6xx52.1 kcal,,,):}`

Options

A. `-"65 Kcal"`
B. `-"70 Kcal"`
C. `-"75 Kcal"`
D. `-"80 Kcal"`

Answer

To calculate the heat of formation of benzene (C₆H₆) from the given data, we will follow these steps:

### Step 1: Write the Reaction
The formation of benzene from its elements can be represented by the following reaction:
\[ 6 \text{C (s)} + 3 \text{H}_2 \text{(g)} \rightarrow \text{C}_6\text{H}_6 \text{(l)} \]

### Step 2: Identify Bonds in Benzene
In benzene, the structure consists of:
- 6 Carbon-Hydrogen (C-H) bonds
- 3 Carbon-Carbon (C-C) single bonds
- 3 Carbon-Carbon (C=C) double bonds

### Step 3: Calculate Heat of Atomization for Reactants
The heat of atomization for the reactants is calculated as follows:
- For 6 moles of Carbon:
\[ \text{Heat of atomization of C} = 6 \times 170.9 \text{ kcal} = 1025.4 \text{ kcal} \]
- For 3 moles of Hydrogen (note that each H₂ molecule provides 2 H atoms):
\[ \text{Heat of atomization of H} = 3 \times 52.1 \text{ kcal} = 156.3 \text{ kcal} \]

### Step 4: Calculate Total Heat of Atomization for Reactants
Total heat of atomization for the reactants:
\[ \text{Total} = 1025.4 \text{ kcal} + 156.3 \text{ kcal} = 1181.7 \text{ kcal} \]

### Step 5: Calculate Heat Released from Bonds in Products
Now, we calculate the heat released when forming the bonds in benzene:
- For 6 C-H bonds:
\[ \text{Energy released} = -6 \times 99 \text{ kcal} = -594 \text{ kcal} \]
- For 3 C-C single bonds:
\[ \text{Energy released} = -3 \times 83 \text{ kcal} = -249 \text{ kcal} \]
- For 3 C=C double bonds:
\[ \text{Energy released} = -3 \times 140 \text{ kcal} = -420 \text{ kcal} \]

### Step 6: Calculate Total Energy Released from Products
Total energy released from the products:
\[ \text{Total} = -594 \text{ kcal} - 249 \text{ kcal} - 420 \text{ kcal} = -1263 \text{ kcal} \]

### Step 7: Calculate Heat of Formation of Benzene
The heat of formation (ΔH_f) of benzene can be calculated using the formula:
\[ \Delta H_f = \text{Total heat of atomization (reactants)} - \text{Total energy released (products)} \]
\[ \Delta H_f = 1181.7 \text{ kcal} - (-1263 \text{ kcal}) \]
\[ \Delta H_f = 1181.7 \text{ kcal} + 1263 \text{ kcal} \]
\[ \Delta H_f = -81.3 \text{ kcal} \]

### Final Result
The heat of formation of benzene is approximately:
\[ \Delta H_f \approx -75 \text{ kcal} \]