Final answer:
To calculate the mole fraction of CO₂ in the gas mixture, the total number of moles in the mixture was first determined (7.397 moles), and then the moles of CO₂ (0.917 moles) were divided by this total to yield a mole fraction of 0.124.
Step-by-step explanation:
The question asks to calculate the mole fraction of CO₂ in a mixture of gases that includes 4.10 moles of O₂, 2.38 moles of N₂, and 0.917 moles of CO₂. First, we need to determine the total number of moles in the gas mixture. Adding up the moles of each gas, we get:
Total moles = 4.10 moles O₂ + 2.38 moles N₂ + 0.917 moles CO₂ = 7.397 moles
Next, we can find the mole fraction of CO₂ by dividing the moles of CO₂ by the total moles:
Mole fraction of CO₂ (X₂) = Moles of CO₂ / Total moles = 0.917 moles / 7.397 moles
X₂ = 0.124 (rounded to three decimal places).
Therefore, the mole fraction of CO₂ in the gas mixture is 0.124.