the percentage by weight of methanol in a mixture of methanol and ethanol is 50 percent. therefore, the mole fraction of methanol in the mixture is

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Solution

Mole fraction is determined by dividing the number of moles of a substance by the total number of moles. The sum of all the mole fractions should be 1. The symbol for mole fraction is chi , χ.
χx=moles xtotal moles
Since the masses are equal but not given in the question, we can assume any number of grams. I'm going to assume 100.0 g of each substance.
Calculate the molar mass of each substance.
CH4O: (1×12.011g/mol)+(4×1.008g/mol)+(1×15.999g/mol)=32.042 g/mol
C2H6O: (2×12.011g/mol)+(6×1.008g/mol)+(1×15.999g/mol)=46.069 g/mol
Calculate the moles of each substance by dividing 100.0 g of each substance by its molar mass.
CH4O: 100.0g32.042gmol=3.121 mol
C2H6O: 100.0g46.069gmol=2.171 mol
Calculate the mole fraction for each substance.
Total moles = 3.121 + 2.171=5.292 mol
Mole fraction of Methanol:
χmethanol=3.121mol5.292mol=0.5898
Mole fraction of Ethanol:
χethanol=2.171mol5.292mol=0.4102

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