Answer:
The solution is composed by 37.5 g of water and 28.5 g of methanol.
Explanation:
Total mass = 66 g
Mole fraction methanol: 0.3
Sum of mole fraction = 1
Therefore, mole fraction of water = 0.7
Let's find out the mass of each component by this two equations:
Methanol mass + Water mass = 66 g
Water mass = 66g - Methanol mass
Methanol mass = 66g - water mass
water mass / 18 g/mol = moles of water
methanol mass / 32 g/mol = moles of methanol
moles of water / total moles = 0.7
moles of methanol / total moles = 0.3
water mass / 18 g/mol / (water mass / 18 g/mol) + (methanol mass / 32 g/mol) = 0.7 ; let's replace methanol mass, as (66 - water mass)
water mass / 18 g/mol / (water mass / 18 g/mol) + (66 - water mass / 32 g/mol) = 0.7 → The unknown is water mass (X)
X / 18 / ( (X / 18) + ((66-X) / 32)) = 0.7
(X / 18) + ((66-X) / 32) = (16X + 594 - 9X)/288
X / 18 / (16X + 594 - 9X)/288 = 0.7
X/18 = 0.7 . ( (7X + 594 ) / 288)
X / 18 = 7/2880 ( 7X + 594)
X = 7/2880 ( 7X + 594) 18
X = 7/160 (7X + 594)
X = 49/160X + 2079/80
X - 49/160X = 2079/80
111/160X = 2079/80
X = 2079/80 . 160/111 = 37.5 g → mass of water
Therefore, mass of methanol → 66 g - 37.4 g = 28.5 g
