Answer
0.0427
Work Step by Step
We have 14.6 g of CH3OH per 184g of H2O. To find the mole fraction, we need to convert both to moles:
CH3OH (Carbon is 12g/mol, H is 1g/mol, O is 16g/mol):
12 + 3*1 + 16 + 1 = 32 g/mol
H2O : 2*1 + 16 = 18 g/mol
Then we have 14.6 g * (1mol/32g) = 0.456 moles CH3OH
and then 184g * (1mol/18g) = 10.22 moles H2O
The total moles is 10.22 + 0.456 = 10.678 moles so then the mole fraction of CH3OH would be moles CH3OH/ total moles
0.456 / 10.678 = 0.0427