Question

Calculate mole fraction of ethanol to sample of spirit containing 92% ethanol by mass.?

Answer 1

Let weight of solution is 100g
∵ mass % of ethanol is 92 %
∴ mass of ethanol in solution = 92g
and mass of water = 100 - 92 = 8g

Now, mole fraction of ethanol = mole of ethanol /(mole of ethanol + mole of water )

Mole of ethanol = mass of ethanol/molar mass of ethanol
= 92/46 = 2 [ ∵ molar mass of ethanol (C₂H₅OH) is 46 g/mol ]
Mole of water = mass of water/molar mass of water
= 8/18 = 4/9 = 0.444

∴mole fraction of ethanol = 2/(2 + 0.444) = 2/2.444 = 0.818

Answer 2

Hello Dear.

Here is the answer---

Let the weight of the Solution be x.
∴ Mass of the Ethanol = 92% of x
   = 92x/100

Using the Formula,
 No. of moles = Mass/Molar mass
 ∵ Molar mass of the Ethanol is 46 g/mole.
∴ No. of Moles of Ethanol = (92x/100) ÷ 46
   = x/50 moles.

Now,
Weight of Solvent = Weight of Solution - Weight of Ethanol.
   = x - 92x/100
   = 8x/100
   = 2x/25 

∵ Molar mass of Water = 18 g/mole.
No of moles of Solvent(Water) = (2x/25) ÷ 18
 = x/225 moles.

Total Number of moles in a solution = Moles of Ethanol + Moles of Water
= x/50 + x/225
= (9x + 2x)/450
= 11x/450

Now, Using the Formula

Mole Fraction of Ethanol = Moles of Ethanol/Moles of Solution.
= $\frac{ \frac{x}{50} }{ \frac{11x}{450} }$
= 9/11
= 0.818


∴ Mole Fraction of Ethanol in a solution is 0.818.


Hope it helps.