If enthalpies of methane and ethane are respectively 320 and 360 calories then the bond energy of C - C bond is

Options

A. 0 calories
B. 40 calories
C. 60 calories
D. 120 calories

Answer

To find the bond energy of the C-C bond in ethane (C2H6), we can follow these steps:

### Step 1: Understand the dissociation of methane (CH4)
When methane (CH4) is dissociated, it breaks down into 1 carbon atom and 4 hydrogen atoms. The enthalpy change for this process is given as 320 calories.

The dissociation energy can be expressed as:
\[ \text{Dissociation energy of CH}_4 = 4 \times \Delta \text{bond energy of CH} \]
Where \(\Delta \text{bond energy of CH}\) is the bond energy of the C-H bond.

### Step 2: Calculate the bond energy of C-H in methane
From the equation above, we can rearrange it to find the bond energy of C-H:
\[ 320 = 4 \times \Delta \text{bond energy of CH} \]
\[ \Delta \text{bond energy of CH} = \frac{320}{4} = 80 \text{ calories} \]

### Step 3: Understand the dissociation of ethane (C2H6)
When ethane (C2H6) is dissociated, it breaks down into 2 carbon atoms and 6 hydrogen atoms. The enthalpy change for this process is given as 360 calories.

The dissociation energy can be expressed as:
\[ \text{Dissociation energy of C}_2\text{H}_6 = \Delta \text{bond energy of CC} + 6 \times \Delta \text{bond energy of CH} \]
Where \(\Delta \text{bond energy of CC}\) is the bond energy of the C-C bond.

### Step 4: Substitute the known values into the equation for ethane
We already calculated \(\Delta \text{bond energy of CH} = 80\) calories. Now we can substitute this value into the equation for ethane:
\[ 360 = \Delta \text{bond energy of CC} + 6 \times 80 \]
\[ 360 = \Delta \text{bond energy of CC} + 480 \]

### Step 5: Solve for the bond energy of C-C
Rearranging the equation gives us:
\[ \Delta \text{bond energy of CC} = 360 - 480 \]
\[ \Delta \text{bond energy of CC} = -120 \text{ calories} \]

### Step 6: Interpret the result
The bond energy of the C-C bond is -120 calories. However, since bond energies are typically expressed as positive values, we can state that the bond energy of the C-C bond is 120 calories.

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

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