Question

Mole fraction of methanol in its aqueous solution is 0.5 . The concentration of solution in terms of percent by mass of methanol is

Answer 1

Given conditions ⇒
Mole Fraction of the Methanol = 0.5
∴ Mole Fraction of the Water = 1 - 0.5
   = 0.5 

For Methanol,
Molar mass of the methanol = 32 g/mole.

∵ No. of mole = Mass/Molar Mass
∴ Mass = No. of moles × Molar Mass
∴ Mass = 0.5 × 32
∴ Mass = 16 g.

Now, For the Water,
Molar Mass of the Water = 18 g/mole.
∴ No. of moles = Mass/Molar mass
∴ Mass = 0.5 × 18
∴ Mass = 9 g.


 Mass of the Solution = Mass of the Methanol + Mass of the Water.
∴ Mass of the solution = 16 + 9
∴ Mass of the solution = 25 g.

Now, Using the Formula,
% mass of the Methanol = (Mass of the Methanol/Mass of the solution) × 100%
 = (16/25) × 100%
 = 0.64 × 100%
 = 64%


Hence, the % mass of the Methanol in the solution is 64%.



Hope it helps.

Answer 2

Mole fraction of methanol = 0.5
Mole fraction of water = 1-0.5 = 0.5
MM of methanol = 32 g mol⁻¹
MM of H₂O = 18 g mol⁻¹
Mass of methanol present in the solution = 0.5×32 = 16 g
Mass of water present in the solution = 0.5×18 = 9 g
Mass of solution = 16+9 = 25 g
% by mass of methanol = mass of methanol/total mass of solution = 16/25 = 0.64