Final answer:
The mole fraction of H2S in the gas mixture is approximately 0.170, calculated by dividing the moles of H2S by the total moles of all gases in the mixture.
Step-by-step explanation:
To calculate the mole fraction of H2S in a gas mixture, we first need to find the number of moles of each gas in the mixture. We use the molar mass of each gas to convert the given masses to moles. The molar mass of H2S is approximately 34.08 g/mol, of CH4 is 16.04 g/mol, and of O2 is 32.00 g/mol.
First, let's calculate the moles of each gas:
- H2S: moles = 7.0 g / 34.08 g/mol \approx 0.205 moles
- CH4: moles = 10.0 g / 16.04 g/mol \approx 0.623 moles
- O2: moles = 12.0 g / 32.00 g/mol \approx 0.375 moles
Next, we sum up the total moles in the mixture:
Total moles = 0.205 + 0.623 + 0.375 = 1.203 moles
Finally, the mole fraction of H2S is calculated by dividing the moles of H2S by the total moles:
Mole fraction of H2S = 0.205 moles / 1.203 moles \approx 0.170
Therefore, the mole fraction of H2S in the mixture is approximately 0.170.