Write the reaction of complete combustion
then enthalpy of combustion will be reactant- product

The enthalpy of combustion is the amount of heat released when a substance undergoes complete combustion in the presence of excess oxygen. In this case, we are given the enthalpy of combustion values for methane (CH4), ethane (C2H6), and propane (C3H8). We need to find the approximate value of the enthalpy of combustion for n-hexane.

To find the enthalpy of combustion for n-hexane, we can use the concept of enthalpy of formation. The enthalpy of formation (ΔHf) is the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states at a specified temperature and pressure. The enthalpy of combustion is related to the enthalpy of formation by the following equation:

ΔHc = Σ(nΔHf(products)) - Σ(mΔHf(reactants))

Where ΔHc is the enthalpy of combustion, n and m are the stoichiometric coefficients of the products and reactants, and ΔHf is the enthalpy of formation.

Now, let's break down the calculation step by step:

1. Calculate the enthalpy of combustion for methane (CH4):
ΔHc(CH4) = -210 kcal/mol

2. Calculate the enthalpy of formation for methane:
ΔHf(CH4) = ?

3. Calculate the enthalpy of combustion for ethane (C2H6):
ΔHc(C2H6) = -370 kcal/mol

4. Calculate the enthalpy of formation for ethane:
ΔHf(C2H6) = ?

5. Calculate the enthalpy of combustion for propane (C3H8):
ΔHc(C3H8) = -530 kcal/mol

6. Calculate the enthalpy of formation for propane:
ΔHf(C3H8) = ?

7. Use the given enthalpy of combustion values and the enthalpy of formation values to set up a system of equations:

-210 = 1 * ΔHf(CH4) - 4 * ΔHf(O2)
-370 = 1 * ΔHf(C2H6) - 7 * ΔHf(O2)
-530 = 1 * ΔHf(C3H8) - 5 * ΔHf(O2)

8. Solve the system of equations to find the enthalpy of formation values for methane, ethane, and propane.

9. Once we have the enthalpy of formation values, we can calculate the enthalpy of formation for n-hexane (C6H14) and then use it to calculate the enthalpy of combustion for n-hexane.

The approximate value of the enthalpy of combustion for n-hexane can be determined by following these steps. However, without the enthalpy of formation values for methane, ethane, and propane, it is not possible to calculate the enthalpy of combustion for n-hexane accurately.