Enthalpy of combustion of `CH_(4)` , `C_(2)H_(6)` and `C_(3)H_(8)` are `-210-370` and `-530Kcal//mol` respectivaly. The approximate value of enthalpy of combustion of `n`-hexane is

Options

A. `-1170 (Kcal)/(mol)`
B. `-750(Kcal)/(mol)`
C. `-1010(Kcal)/(mol)`
D. `-590(Kcal)/(mol)`

Explanation

To find the approximate value of the enthalpy of combustion of n-hexane (C6H14), we can use the enthalpy values of combustion for methane (CH4), ethane (C2H6), and propane (C3H8) provided in the question. The enthalpy values are as follows:

- Enthalpy of combustion of CH4 = -210 kcal/mol
- Enthalpy of combustion of C2H6 = -370 kcal/mol
- Enthalpy of combustion of C3H8 = -530 kcal/mol

### Step-by-Step Solution:

1. **Identify the pattern in the enthalpy values**:
- The enthalpy of combustion increases in magnitude as we move from CH4 to C3H8. This suggests that the enthalpy of combustion is related to the number of CH2 groups in the molecule.

2. **Calculate the change in enthalpy for each addition of CH2**:
- From CH4 to C2H6:
\[ \Delta H = -370 \, \text{kcal/mol} - (-210 \, \text{kcal/mol}) = -160 \, \text{kcal/mol} \]
- From C2H6 to C3H8:
\[ \Delta H = -530 \, \text{kcal/mol} - (-370 \, \text{kcal/mol}) = -160 \, \text{kcal/mol} \]
- This indicates that each additional CH2 group contributes approximately -160 kcal/mol to the enthalpy of combustion.

3. **Determine the number of CH2 groups in n-hexane**:
- n-Hexane (C6H14) has 6 carbon atoms, which means it has 5 CH2 groups (since it can be represented as CH4 + 5(CH2)).
- Therefore, we need to account for the combustion of 5 additional CH2 groups starting from CH4.

4. **Calculate the total enthalpy of combustion for n-hexane**:
- Starting from the enthalpy of combustion of CH4:
\[ \text{Enthalpy of combustion of n-hexane} = -210 \, \text{kcal/mol} + 5 \times (-160 \, \text{kcal/mol}) \]
\[ = -210 \, \text{kcal/mol} - 800 \, \text{kcal/mol} \]
\[ = -1010 \, \text{kcal/mol} \]

5. **Final approximation**:
- The approximate value of the enthalpy of combustion of n-hexane is therefore -1010 kcal/mol.