To determine the percent composition, by mass, of acetylene gas (C₂H₂), follow these detailed steps:
1. Identify the molecular formula: The molecular formula of acetylene gas is C₂H₂, which means it contains 2 carbon (C) atoms and 2 hydrogen (H) atoms.
2. Find the atomic masses:
- The atomic mass of carbon (C) is approximately 12.01 grams per mole.
- The atomic mass of hydrogen (H) is approximately 1.01 grams per mole.
3. Calculate the molar mass of C₂H₂:
- The molar mass contribution from carbon is calculated by multiplying the number of carbon atoms by the atomic mass of carbon:
[tex]\[
\text{Molar mass from C} = 2 \times 12.01 \, \text{g/mol} = 24.02 \, \text{g/mol}
\][/tex]
- The molar mass contribution from hydrogen is calculated similarly by multiplying the number of hydrogen atoms by the atomic mass of hydrogen:
[tex]\[
\text{Molar mass from H} = 2 \times 1.01 \, \text{g/mol} = 2.02 \, \text{g/mol}
\][/tex]
- Adding these together gives the total molar mass of acetylene gas:
[tex]\[
\text{Molar mass of C₂H₂} = 24.02 \, \text{g/mol} + 2.02 \, \text{g/mol} = 26.04 \, \text{g/mol}
\][/tex]
4. Calculate the mass percent of each element:
- For carbon:
[tex]\[
\text{Mass percent of carbon} = \left( \frac{\text{Molar mass of carbon}}{\text{Molar mass of C₂H₂}} \right) \times 100 = \left( \frac{24.02}{26.04} \right) \times 100 \approx 92.24\%
\][/tex]
- For hydrogen:
[tex]\[
\text{Mass percent of hydrogen} = \left( \frac{\text{Molar mass of hydrogen}}{\text{Molar mass of C₂H₂}} \right) \times 100 = \left( \frac{2.02}{26.04} \right) \times 100 \approx 7.76\%
\][/tex]
Hence, the percent composition by mass of acetylene gas (C₂H₂) is approximately 92.24% carbon and 7.76% hydrogen.
