If enthalpy of dissociation of `CH_(4)` and `C_(2)H_(6)` are `320` and `360` calories respectively then bond energy of `C-C` bond is:

Options

A. `80 cal`
B. `40 cal`
C. `60 cal`
D. `120 cal`

Explanation

To find the bond energy of the C-C bond, we can follow these steps:

### Step 1: Understand the dissociation enthalpy of CH₄
The enthalpy of dissociation of methane (CH₄) is given as 320 calories. This means that when one mole of CH₄ is completely dissociated into its constituent atoms, it requires 320 calories of energy.

### Step 2: Calculate the bond energy of C-H bonds in CH₄
Since CH₄ has 4 C-H bonds, we can find the bond energy of a single C-H bond by dividing the total dissociation energy by the number of bonds:
\[ \text{Bond energy of C-H} = \frac{320 \text{ calories}}{4} = 80 \text{ calories} \]

### Step 3: Understand the dissociation enthalpy of C₂H₆
The enthalpy of dissociation of ethane (C₂H₆) is given as 360 calories. This means that when one mole of C₂H₆ is completely dissociated, it requires 360 calories of energy.

### Step 4: Set up the equation for C₂H₆
C₂H₆ consists of 1 C-C bond and 6 C-H bonds. The total enthalpy of dissociation can be expressed as:
\[ \text{Bond energy of C-C} + 6 \times \text{Bond energy of C-H} = 360 \text{ calories} \]
Substituting the bond energy of C-H:
\[ \text{Bond energy of C-C} + 6 \times 80 = 360 \]

### Step 5: Solve for the bond energy of C-C
Now, we can simplify the equation:
\[ \text{Bond energy of C-C} + 480 = 360 \]
Subtract 480 from both sides:
\[ \text{Bond energy of C-C} = 360 - 480 = -120 \text{ calories} \]

### Step 6: Interpret the result
The negative sign indicates that the process is exothermic, meaning energy is released when the bond is formed. Therefore, the bond energy of the C-C bond is 120 calories.

### Final Answer
The bond energy of the C-C bond is **120 calories**.

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