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Here's how to calculate the mole fraction of water in the solution:
1. Calculate the moles of each component:
Moles of CH3OH:
- Molar mass of CH3OH = 12.01 g/mol (C) + 3(1.01 g/mol) (H) + 16.00 g/mol (O) = 32.04 g/mol
- Moles of CH3OH = (128 g) / (32.04 g/mol) = 4 mol
Moles of H2O:
- Molar mass of H2O = 2(1.01 g/mol) (H) + 16.00 g/mol (O) = 18.02 g/mol
- Moles of H2O = (108 g) / (18.02 g/mol) = 6 mol
2. Calculate the mole fraction of water (X_H2O):
- X_H2O = (moles of H2O) / (total moles of solution)
- X_H2O = 6 mol / (4 mol + 6 mol) = 0.6
Therefore, the mole fraction of water in the solution is 0.6.