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: Determine the bond energy of C-H bonds in methane (CH4).
- The enthalpy of methane (CH4) is given as 320 calories.
- Methane has 4 C-H bonds.
- Therefore, the energy for one C-H bond can be calculated as:
\[ \text{Energy per C-H bond} = \frac{\text{Enthalpy of CH4}}{\text{Number of C-H bonds}} = \frac{320 \text{ calories}}{4} = 80 \text{ calories} \]

### Step 2: Set up the equation for the enthalpy of ethane (C2H6).
- The enthalpy of ethane (C2H6) is given as 360 calories.
- Ethane has 6 C-H bonds and 1 C-C bond.
- The total enthalpy can be expressed as:
\[ \text{Enthalpy of C2H6} = \text{Energy of C-C bond} + 6 \times \text{Energy per C-H bond} \]
- Substituting the known values:
\[ 360 = \text{Energy of C-C bond} + 6 \times 80 \]

### Step 3: Calculate the energy of the C-C bond.
- Calculate the total energy contribution from the C-H bonds:
\[ 6 \times 80 = 480 \text{ calories} \]
- Substitute this back into the equation:
\[ 360 = \text{Energy of C-C bond} + 480 \]
- Rearranging gives:
\[ \text{Energy of C-C bond} = 360 - 480 = -120 \text{ calories} \]

### Step 4: Interpret the result.
- The negative value indicates that the bond energy is released when the bond is formed, which is typical in thermodynamics. However, since we are interested in the absolute value of the bond energy, we take:
\[ \text{Bond energy of C-C bond} = 120 \text{ calories} \]

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

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