To tackle this problem, we need to analyze the combustion products of the welding fuel gas, which consists solely of carbon and hydrogen. The combustion of this gas in oxygen produces carbon dioxide (CO2) and water (H2O). From the given data, we can derive the empirical formula, molar mass, and molecular formula of the gas step by step.
Step 1: Determine Moles of Carbon and Hydrogen
First, we need to find out how many moles of carbon and hydrogen are present in the combustion products. We can use the masses of carbon dioxide and water produced in the reaction.
Calculating Moles of Carbon
The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol. To find the moles of CO2 produced:
- Moles of CO2 = Mass of CO2 / Molar mass of CO2
- Moles of CO2 = 3.38 g / 44.01 g/mol ≈ 0.0768 mol
Since each mole of CO2 contains one mole of carbon, the moles of carbon in the gas is also 0.0768 mol.
Calculating Moles of Hydrogen
The molar mass of water (H2O) is approximately 18.02 g/mol. To find the moles of H2O produced:
- Moles of H2O = Mass of H2O / Molar mass of H2O
- Moles of H2O = 0.690 g / 18.02 g/mol ≈ 0.0383 mol
Each mole of water contains two moles of hydrogen, so the moles of hydrogen in the gas is:
- Moles of H = 2 × Moles of H2O = 2 × 0.0383 mol ≈ 0.0766 mol
Step 2: Finding the Empirical Formula
Now that we have the moles of carbon and hydrogen, we can find the simplest whole number ratio of these elements.
- Moles of C = 0.0768 mol
- Moles of H = 0.0766 mol
To find the ratio, we can divide both by the smallest number of moles:
- Ratio of C = 0.0768 / 0.0766 ≈ 1.003
- Ratio of H = 0.0766 / 0.0766 = 1
This gives us an approximate ratio of 1:1 for carbon to hydrogen, leading to the empirical formula of:
CH
Step 3: Calculating Molar Mass of the Gas
Next, we need to determine the molar mass of the gas. We know that 10.0 L of the gas weighs 11.6 g. At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 L. Therefore, we can calculate the number of moles in 10.0 L:
- Moles of gas = Volume / Molar volume at STP
- Moles of gas = 10.0 L / 22.4 L/mol ≈ 0.4464 mol
Now, we can find the molar mass:
- Molar mass = Mass / Moles
- Molar mass = 11.6 g / 0.4464 mol ≈ 26.0 g/mol
Step 4: Determining the Molecular Formula
Now that we have the empirical formula (CH) and the molar mass (26.0 g/mol), we can find the molecular formula. The molar mass of the empirical formula (CH) is:
- Molar mass of CH = 12.01 g/mol (C) + 1.008 g/mol (H) ≈ 13.018 g/mol
Next, we find the ratio of the molar mass of the gas to the molar mass of the empirical formula:
- Ratio = Molar mass of gas / Molar mass of empirical formula
- Ratio = 26.0 g/mol / 13.018 g/mol ≈ 2
This means the molecular formula is twice the empirical formula:
C2H2
Summary of Results
To summarize:
- Empirical Formula: CH
- Molar Mass of the Gas: 26.0 g/mol
- Molecular Formula: C2H2
This process illustrates how combustion analysis can be used to derive the composition of a compound based on its combustion products. If you have any further questions or need clarification on any of the steps, feel free to ask!
