Heat of combustion of `CH_4, C_2H_6 and C_3H_6` are respectively `-210, - 368.4 and -526.3 k cal mol^(-1)` . Hence, heat of combustion of `C_6H_14` is approximately.

Options

A. `-1310 kcal mol^(-1)`
B. `-684 kcal mol^(-1)`
C. `-840 kcal mol^(-1)`
D. `-1000 kcal mol^(-1)`

Explanation

To find the heat of combustion of \( C_6H_{14} \) (hexane) based on the provided heats of combustion for \( CH_4 \) (methane), \( C_2H_6 \) (ethane), and \( C_3H_8 \) (propane), we can follow these steps:

### Step 1: Write down the given heats of combustion
- Heat of combustion of \( CH_4 \): \( -210 \, \text{kcal/mol} \)
- Heat of combustion of \( C_2H_6 \): \( -368.4 \, \text{kcal/mol} \)
- Heat of combustion of \( C_3H_8 \): \( -526.3 \, \text{kcal/mol} \)

### Step 2: Determine the heat of combustion for the \( CH_2 \) unit
To find the heat of combustion for the \( CH_2 \) unit, we can calculate the difference in heats of combustion between successive alkanes:

1. **From \( CH_4 \) to \( C_2H_6 \)**:
\[ \Delta H_{C_2H_6} = H_{C_2H_6} - H_{CH_4} = -368.4 - (-210) = -158.4 \, \text{kcal/mol} \]

2. **From \( C_2H_6 \) to \( C_3H_8 \)**:
\[ \Delta H_{C_3H_8} = H_{C_3H_8} - H_{C_2H_6} = -526.3 - (-368.4) = -157.9 \, \text{kcal/mol} \]

### Step 3: Average the heat of combustion for the \( CH_2 \) unit
We can take the average of the two calculated values for the \( CH_2 \) unit:
\[ \Delta H_{CH_2} \approx \frac{-158.4 + (-157.9)}{2} \approx -158.15 \, \text{kcal/mol} \]

### Step 4: Calculate the heat of combustion for \( C_6H_{14} \)
Since \( C_6H_{14} \) can be viewed as \( C_3H_8 \) plus three \( CH_2 \) units, we can calculate its heat of combustion as follows:
\[ H_{C_6H_{14}} = H_{C_3H_8} + 3 \times \Delta H_{CH_2} \]
Substituting the values:
\[ H_{C_6H_{14}} = -526.3 + 3 \times (-158.15) \]
\[ H_{C_6H_{14}} = -526.3 - 474.45 = -1000.75 \, \text{kcal/mol} \]

### Step 5: Approximate the final value
Thus, the heat of combustion of \( C_6H_{14} \) is approximately:
\[ H_{C_6H_{14}} \approx -1000 \, \text{kcal/mol} \]

### Final Answer
The heat of combustion of \( C_6H_{14} \) is approximately \( -1000 \, \text{kcal/mol} \).

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