Final answer:
The correct mole fractions for the solution with 25g of ethanol and 40.0g of water are 0.196 for ethanol and 0.804 for water. None of the provided answer choices match these calculated values.
Step-by-step explanation:
To calculate the mole fractions of ethanol and water in the solution, you first need to find the number of moles of each substance using their masses and molar masses. The molar mass of ethanol (C₂H₅OH) is approximately 46.07 g/mol, and for water (H₂O), it is approximately 18.02 g/mol.
Calculation steps:
- Calculate the number of moles of ethanol: moles EtOH = mass (g) / molar mass (g/mol).
- Calculate the number of moles of water: moles H₂O = mass (g) / molar mass (g/mol).
- Calculate the total moles in the solution: total moles = moles EtOH + moles H₂O.
- Calculate the mole fraction of ethanol: mole fraction EtOH = moles EtOH / total moles.
- Calculate the mole fraction of water: mole fraction H₂O = moles H₂O / total moles.
Now applying these steps to the given data:
- Moles of ethanol: 25g / 46.07 g/mol ≈ 0.542 moles
- Moles of water: 40g / 18.02 g/mol ≈ 2.22 moles
- Total moles = 0.542 + 2.22 ≈ 2.762 moles
- Mole fraction of ethanol ≈ 0.542 / 2.762 ≈ 0.196
- Mole fraction of water ≈ 2.22 / 2.762 ≈ 0.804
Therefore, the mole fractions are ethanol: 0.196 and water: 0.804. None of the answer choices (a) through (d) match this correct calculation.