If enthalpies of methane and enthane are respectively 320 and 560 calories, then the bond energy of C-C bond is :

Options

A. 50 calories
B. 80 calories
C. 40 calories
D. 120 calories

Explanation

To calculate the bond energy of the C-C bond in ethane (C2H6) using the given enthalpies of methane (CH4) and ethane, we can follow these steps:

### Step 1: Understand the enthalpy change for methane (CH4)
The enthalpy change (ΔH) for the formation of methane is given as 320 calories. When methane is broken down, it dissociates into its constituent atoms:
\[ \text{CH}_4(g) \rightarrow \text{C}(g) + 4\text{H}(g) \]

### Step 2: Calculate the bond energy of C-H bonds in methane
Since there are four C-H bonds in methane, the bond energy for each C-H bond can be calculated as:
\[ \text{Bond Energy of C-H} = \frac{\Delta H_{\text{CH}_4}}{4} = \frac{320 \text{ cal}}{4} = 80 \text{ cal} \]

### Step 3: Understand the enthalpy change for ethane (C2H6)
The enthalpy change (ΔH) for the formation of ethane is given as 560 calories. When ethane is broken down, it dissociates into its constituent atoms:
\[ \text{C}_2\text{H}_6(g) \rightarrow 2\text{C}(g) + 6\text{H}(g) \]

### Step 4: Calculate the total bond energy for ethane
In ethane, there are six C-H bonds and one C-C bond. The total bond energy can be expressed as:
\[ \Delta H_{\text{C}_2\text{H}_6} = \text{Bond Energy of C-C} + 6 \times \text{Bond Energy of C-H} \]

### Step 5: Substitute known values into the equation
We know:
- \(\Delta H_{\text{C}_2\text{H}_6} = 560 \text{ cal}\)
- \(\text{Bond Energy of C-H} = 80 \text{ cal}\)

Substituting these values into the equation gives:
\[ 560 = \text{Bond Energy of C-C} + 6 \times 80 \]

### Step 6: Solve for the bond energy of C-C
Calculating the total energy for the C-H bonds:
\[ 6 \times 80 = 480 \text{ cal} \]

Now substituting this back into the equation:
\[ 560 = \text{Bond Energy of C-C} + 480 \]
\[ \text{Bond Energy of C-C} = 560 - 480 = 80 \text{ cal} \]

### Final Answer
The bond energy of the C-C bond in ethane is **80 calories**.

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