A welding fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygen gas 3.38 g carbon dioxide, 0.690 g of water and no other products. A volume of 10.0 L (measured at STP) of this welding gas is found to weigh 11.6 g. Calcuate

Answer

To solve the problem, we need to determine the empirical formula of the welding fuel gas based on the combustion products (carbon dioxide and water) and the mass of the gas sample. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the mass of carbon from carbon dioxide
1. We know that the mass of carbon dioxide (CO₂) produced is 3.38 g.
2. The molar mass of CO₂ is calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Molar mass of CO₂ = 12 + (2 × 16) = 44 g/mol
3. To find the mass of carbon in the CO₂, we use the ratio of the molar mass of carbon to the molar mass of CO₂:
\[ \text{Mass of Carbon} = \left( \frac{12 \text{ g/mol}}{44 \text{ g/mol}} \right) \times 3.38 \text{ g} = 0.92 \text{ g} \]

### Step 2: Determine the mass of hydrogen from water
1. The mass of water (H₂O) produced is 0.690 g.
2. The molar mass of water is calculated as follows:
- Hydrogen (H) = 1 g/mol
- Oxygen (O) = 16 g/mol
- Molar mass of H₂O = (2 × 1) + 16 = 18 g/mol
3. To find the mass of hydrogen in the water, we use the ratio of the molar mass of hydrogen to the molar mass of water:
\[ \text{Mass of Hydrogen} = \left( \frac{2 \text{ g/mol}}{18 \text{ g/mol}} \right) \times 0.690 \text{ g} = 0.077 \text{ g} \]

### Step 3: Calculate the percentage composition of carbon and hydrogen
1. The total mass of the sample is the sum of the mass of carbon and hydrogen:
\[ \text{Total mass} = 0.92 \text{ g} + 0.077 \text{ g} = 0.997 \text{ g} \]
2. The percentage of carbon is calculated as:
\[ \text{Percentage of Carbon} = \left( \frac{0.92 \text{ g}}{0.997 \text{ g}} \right) \times 100 \approx 92.3\% \]
3. The percentage of hydrogen is calculated as:
\[ \text{Percentage of Hydrogen} = \left( \frac{0.077 \text{ g}}{0.997 \text{ g}} \right) \times 100 \approx 7.7\% \]

### Step 4: Determine the number of moles of carbon and hydrogen
1. Calculate the number of moles of carbon:
\[ \text{Moles of Carbon} = \frac{0.92 \text{ g}}{12 \text{ g/mol}} \approx 0.077 \text{ mol} \]
2. Calculate the number of moles of hydrogen:
\[ \text{Moles of Hydrogen} = \frac{0.077 \text{ g}}{1 \text{ g/mol}} \approx 0.077 \text{ mol} \]

### Step 5: Determine the simplest mole ratio
1. The mole ratio of carbon to hydrogen is:
\[ \text{Ratio} = \frac{0.077}{0.077} = 1 \]
2. Therefore, the empirical formula of the welding fuel gas is:
\[ \text{Empirical Formula} = \text{CH} \]

### Final Answer:
The empirical formula of the welding fuel gas is **CH**.

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