Question

Mole fraction of ethyl alcohol in aqueous ethyl alcohol solution is 0.25. Hence percentage of ethyl alcohol by weight is
(A) 54%
(B) 25%
(C) 75%
(D) 46%

Answer 1

The basic concepts of concentration and mole basis can help us solve this problem. We would require the knowledge of molar weights, weight percent, etc.
Also, only one option amongst all the four options will be correct.

Complete step by step solution:
Let us firstly know about the mole concepts and concentration to be expressed in terms of weight percentage.
-The mole fraction of the components present in the mixture will add up to unity.
-The molar mass of a compound is the summation of the product of atomic mass and the subscripts on each atom.
-The weight percent is a type of determining the concentration of certain molecules or compounds in a mixture of compounds.
From this general information let us try to solve the given illustration:
Given data- Mole fraction of ethyl alcohol in aqueous ethyl alcohol solution = 0.25
Thus, as the mole fraction will add up to unity, Mole fraction of water in aqueous ethyl alcohol solution = 1-0.25 = 0.75
Considering 1 mole of mixture present we can say that, The moles of ethyl alcohol and water in the mixture will be 0.25 and 0.75 respectively.
We know, Molar mass of ethyl alcohol = 46 gm/mol
Molar mass of water = 18 gm/mol
Thus, the masses of water and ethyl alcohol present in the mixture can be given as,
Ethyl alcohol = $0.25mole\times 46gm/mole=11.5gm$
Water = $0.75mole\times 18gm/mole=13.5gm$
Thus, the weight percentage of ethyl alcohol = $\dfrac{11.5}{11.5+13.5}\times 100$ = 46%

Therefore, option (D) is correct.

Note: Do note to use proper units while solving the illustrations based on mole concepts and concentration. The mole fraction of all the components present in the mixture will always add up to one.