Given data:
- Combustion of a gaseous hydrocarbon produces 0.72 g of water and 3.08 g of CO2
- We need to find the empirical formula of the hydrocarbon

Empirical formula:
The empirical formula gives the simplest whole-number ratio of atoms in a compound. To find the empirical formula of a compound, we need to know the relative masses of the elements present in it.

Steps to find the empirical formula:
1. Calculate the moles of water and CO2 produced.
2. Calculate the number of moles of carbon and hydrogen atoms in the hydrocarbon using the moles of water and CO2.
3. Find the simplest whole-number ratio of carbon and hydrogen atoms to get the empirical formula.

Calculations:

1. Moles of water produced:
- The molar mass of water (H2O) = 2(1.01) + 16.00 = 18.02 g/mol
- Number of moles of water = mass/molar mass = 0.72/18.02 = 0.04 mol

2. Moles of CO2 produced:
- The molar mass of CO2 = 12.01 + 2(16.00) = 44.01 g/mol
- Number of moles of CO2 = mass/molar mass = 3.08/44.01 = 0.07 mol

3. Moles of carbon and hydrogen in the hydrocarbon:
- From the balanced chemical equation for the combustion of hydrocarbons, we know that 1 mole of hydrocarbon produces 1 mole of water and n moles of CO2, where n is the number of carbon atoms in the hydrocarbon.
- For the given data, we have:
- 0.04 mol of water produced = 0.04 mol of hydrocarbon
- 0.07 mol of CO2 produced = n mol of hydrocarbon
- From these equations, we can find the number of carbon atoms in the hydrocarbon:
- n = 0.07/0.04 = 1.75
- Since the number of carbon atoms must be a whole number, we can assume that the hydrocarbon has 2 carbon atoms.

- The total mass of carbon in the CO2 produced = 2(12.01) = 24.02 g
- The mass of carbon in the hydrocarbon = total mass of carbon - mass of carbon in CO2 = 24.02 - 3.08 = 20.94 g
- The mass of hydrogen in the hydrocarbon = mass of water produced = 0.72 g

4. Empirical formula:
- Number of moles of carbon in the hydrocarbon = 20.94/12.01 = 1.74 mol
- Number of moles of hydrogen in the hydrocarbon = 0.72/1.01 = 0.71 mol
- The simplest whole-number ratio of carbon and hydrogen atoms in the hydrocarbon is 1.74:0.71, which can be simplified to 7:2.
- The empirical formula of the hydrocarbon is C7H2.

Therefore, the correct answer is option D, C7H8.