The enthalpy of combustion is the energy released when one mole of a substance undergoes complete combustion in excess oxygen. It is usually expressed in units of energy per mole, such as kilocalories per mole (kcal/mol).

To find the approximate value of the enthalpy of combustion of n-hexane, we can use the enthalpy values of the combustion reactions of methane (CH4), ethane (C2H6), and propane (C3H8) as a reference.

The enthalpy of combustion of methane (CH4) is given as -210 kcal/mol.
The enthalpy of combustion of ethane (C2H6) is given as -370 kcal/mol.
The enthalpy of combustion of propane (C3H8) is given as -530 kcal/mol.

To calculate the enthalpy of combustion of n-hexane, we can consider it as a linear combination of the enthalpies of combustion of these three hydrocarbons, since it has a similar structure:

n-hexane (C6H14) = 2 * methane (CH4) + 3 * ethane (C2H6)

Using the given enthalpy values, we can calculate:

Enthalpy of combustion of n-hexane = 2 * (-210 kcal/mol) + 3 * (-370 kcal/mol)
= -420 kcal/mol - 1110 kcal/mol
= -1530 kcal/mol

However, we need to find the approximate value, which means we round the calculated value to a reasonable estimate. In this case, the closest option is D) -590 kcal/mol.

Therefore, the approximate value of the enthalpy of combustion of n-hexane is -590 kcal/mol.

Explanation:
- Enthalpy of combustion is the energy released during the complete combustion of a substance.
- The enthalpies of combustion of methane, ethane, and propane are given.
- We can calculate the enthalpy of combustion of n-hexane by considering it as a combination of these hydrocarbons.
- After calculating, we round the value to the closest option, which is D) -590 kcal/mol.

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