Question

Mole fraction of ethanol in ethanol and water mixture is 0.25. Hence percentage of ethanol by weight of mixture is:
A: 25%
B: 75%
C: 46%
D: 54%
THE ANSWER IS (C) BUT I NEED A DETAILED SOLUTION

Answer 1

mole fraction = no of mole of ethanol / total moles
If ethanol is 0.25, then H2O will be 0.75.
Mol wt of ethanol is 46.06g/mol,
So, 0.25 mol=11.515g of ethanol

Mol wt of H2O is 18.01528g/mol,
So, 0.75 mol=13.51g of H2O

Total wt=25.02646g
wt % of etanol is = 11.515 / 25.02646 * 100 = 46.011%
Approximately 46%

Answer 2

Answer:            C : 46 %

Explanation:         mole fraction = moles A / total mass

now,

mole fraction of ethanol is 0.25 so mole fraction of water will be .75

[ The sum of all mole fractions is 1 ]

moles of ethanole = mass(g)/ molar mass = mass (g)/ 46.07

so,     mass(g) of ethanol = 46.07 X 0.25 =  11.517 g

moles of water = mass(g)/ molar mass = mass (g)/18.02

and,   mass(g) of water = 18.02 X 0.75 = 13.515 g

then,

percentage concentration  = mass of solute/ mass of solvent X 100

by weight

                               11.517/13.515 + 11.517 X 100

                                11.517/25.032 X 100 = 46%

hopes it helps u,✔✔