Question

What will be the mole fraction of ethanol in a sample of spirit containing $85\%$ ethanol by mass?
A. $0.69$
B. $0.82$
C. $0.85$
D. $0.60$

Answer 1

The number of molecules of a specific component in a mixture divided by the total number of moles in the mixture is known as the mole fraction. It is a means of expressing a solution's concentration.
Formula used:
$\text{Moles} = \dfrac{\text{Mass}}{\text{Molar mass}}$
Mole fraction of component $A$ = $\dfrac{{{N_A}}}{{{N_A} + {N_B}}}$
${N_A} =$ Number of moles substance $A$
${N_B} =$ Number of moles of substance $B$

Complete answer:
Given:
Mass of ethanol $= 85g$
Mass of solution$= 100g$
To find: Mole fraction of ethanol
Mass of water$= 100 - 85 = 15g$
Molar mass of ethanol$= 46g/mol$
Molar mass of water$= 18g/mol$
So now we can calculate the moles of ethanol and water.
Using the formula for calculating moles, we can find moles of ethanol and water:
$\text{Moles of ethanol} = \dfrac{\text{Moles of ethanol}}{\text{Molar mass of ethanol}}$
Moles of ethanol $= \dfrac{{85g}}{{46g/mole}}$
Moles of ethanol$= 1.85mole$
$\text{Moles of Water} = \dfrac{\text{Moles of water}}{\text{Molar mass of water}}$
Moles of water$= \dfrac{{15}}{{18g/mole}}$
Moles of water$= 0.83mole$
Now, from the number of moles we can calculate the mole fraction of ethanol.
Substituting the values in the formula of mole fraction,
$\text{Mole fraction of ethanol} = \dfrac{\text{Moles of ethanol}}{\text{Moles of ethanol + Moles of water}}$
Mole fraction of ethanol $= \dfrac{{1.85mole}}{{1.85mole + 0.83mole}}$
Mole fraction of ethanol $= 0.690$
Therefore, the mole fraction of ethanol is $0.690$.
Hence, the correct option is A. $0.69$.

Note:
The mole fraction is a fraction of molecules, and it differs from the mass fraction because different molecules have different masses. Spirit is an alcoholic beverage that can be made by distilling alcohol.