A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO 2. The empirical formula of the hydrocarbon is: (1) C3H4 (2) C6H5 (3) C7H8 (4) C2H4

To determine the empirical formula of the gaseous hydrocarbon based on the combustion products, we need to analyze the amounts of water and carbon dioxide produced. The combustion of hydrocarbons typically yields carbon dioxide (CO2) and water (H2O), and from these products, we can deduce the ratio of carbon to hydrogen in the original compound.

Step 1: Calculate Moles of CO2 and H2O

First, we need to convert the masses of CO2 and H2O into moles. The molar mass of CO2 is approximately 44.01 g/mol, and for H2O, it is about 18.02 g/mol.

• Moles of CO2 = mass of CO2 / molar mass of CO2 = 3.08 g / 44.01 g/mol ≈ 0.0700 moles
• Moles of H2O = mass of H2O / molar mass of H2O = 0.72 g / 18.02 g/mol ≈ 0.0400 moles

Step 2: Determine Moles of Carbon and Hydrogen

From the moles of CO2 produced, we can find the moles of carbon in the hydrocarbon. Each mole of CO2 contains one mole of carbon:

• Moles of Carbon = Moles of CO2 = 0.0700 moles

From the moles of H2O produced, we can find the moles of hydrogen. Each mole of H2O contains two moles of hydrogen:

• Moles of Hydrogen = 2 × Moles of H2O = 2 × 0.0400 moles = 0.0800 moles

Step 3: Calculate the Simplest Ratio

Now, we have the moles of carbon and hydrogen:

• Carbon: 0.0700 moles
• Hydrogen: 0.0800 moles

To find the simplest whole number ratio, we divide both values by the smallest number of moles, which is 0.0700:

• Ratio of Carbon = 0.0700 / 0.0700 = 1
• Ratio of Hydrogen = 0.0800 / 0.0700 ≈ 1.14

Step 4: Adjust to Whole Numbers

The ratio of carbon to hydrogen is approximately 1:1.14. To convert this to whole numbers, we can multiply both by 7 (to eliminate the decimal):

• Carbon: 1 × 7 = 7
• Hydrogen: 1.14 × 7 ≈ 8

This gives us a ratio of 7:8, leading us to the empirical formula of C7H8.

Final Answer

Based on our calculations, the empirical formula of the hydrocarbon is C7H8, which corresponds to option (3).