A gaseous hydrocarbon gives upon combustion 0.72g of water and 3.08g of CO2.The empirical formula of the hydrocarbon is:

To find the empirical formula of the hydrocarbon, we need to analyze the products of its combustion, specifically the amount of water and carbon dioxide produced. From the given data, we can determine the moles of carbon and hydrogen present in the original compound. Let's break this down step by step.

Step 1: Analyzing the Products

During combustion, hydrocarbons react with oxygen to produce carbon dioxide (CO2) and water (H2O). From the problem, we know:

• Mass of water produced = 0.72 g
• Mass of carbon dioxide produced = 3.08 g

Step 2: Calculating Moles of Carbon and Hydrogen

Next, we need to convert these masses into moles to find the number of atoms of carbon and hydrogen in the hydrocarbon.

Calculating Moles of Carbon from CO2

The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol (12.01 g/mol for carbon and 32.00 g/mol for two oxygen atoms). To find the moles of CO2 produced:

• Number of moles of CO2 = mass of CO2 / molar mass of CO2
• Number of moles of CO2 = 3.08 g / 44.01 g/mol ≈ 0.0700 mol

Since each molecule of CO2 contains one carbon atom, the moles of carbon in the hydrocarbon is also 0.0700 mol.

Calculating Moles of Hydrogen from H2O

The molar mass of water (H2O) is approximately 18.02 g/mol (2.02 g/mol for hydrogen and 16.00 g/mol for oxygen). To find the moles of H2O produced:

• Number of moles of H2O = mass of H2O / molar mass of H2O
• Number of moles of H2O = 0.72 g / 18.02 g/mol ≈ 0.0399 mol

Each molecule of water contains two hydrogen atoms, so the moles of hydrogen in the hydrocarbon is:

• Moles of H = 2 × moles of H2O = 2 × 0.0399 mol ≈ 0.0798 mol

Step 3: Finding the Empirical Formula

Now we have the moles of carbon and hydrogen:

• Moles of Carbon (C) = 0.0700 mol
• Moles of Hydrogen (H) = 0.0798 mol

To find the simplest whole number ratio, we divide each by the smallest number of moles:

• Ratio of C = 0.0700 mol / 0.0700 mol = 1
• Ratio of H = 0.0798 mol / 0.0700 mol ≈ 1.14

Since we want whole numbers, we can multiply both ratios by a common factor to get whole numbers. In this case, multiplying by 7 gives us:

• C: 1 × 7 = 7
• H: 1.14 × 7 ≈ 8

Final Result

The empirical formula of the hydrocarbon is therefore:

This indicates that for every seven carbon atoms, there are eight hydrogen atoms in the simplest form of this hydrocarbon. This process illustrates how we can derive the empirical formula from the combustion products of a hydrocarbon.