Question

A mixture has $18g$ water and $414g$ ethanol. The mole fraction of water in the mixture is (assume ideal behaviour of the mixture)
A. $0.1$
B. $0.4$
C. $0.7$
D. $0.9$

Answer 1

Hint: Mole fraction is defined as the ratio of the number of moles of one component to the number of moles of all the components in a mixture. Whereas, moles of a component are represented by the ratio of given mass by the molecular mass of the component. The Sum of all mole fractions is equivalent to 1.

Complete answer:
Mole fraction delineates the number of molecules in a specific compound in a mixture divided by the total number of moles in the mixture.
Mole fraction$ = \dfrac{{Number{\text{ of moles of that specific component}}}}{{Total{\text{ number of moles of all components}}}}$ ….(I)
So, according to the question, let the mole fraction of water be $x{H_2}O$.
Mole fraction of water will be equal to moles of water divided by the total moles in the mixture i.e. moles of water + the moles of ethanol.
Mathematically, the number of moles can be calculated by dividing the given mass of the substance by the molecular mass of that substance.
The mixture had $18g$ water and the molar mass of water is $18{\text{ g/mol}}$, so $n{H_2}O = \dfrac{{18}}{{18}}$
$n{H_2}O = 1$
Similarly, the mixture had $414g$ ethanol and the molar mass of ethanol is $2(12) + 6(1) + 16 = 46{\text{ g/mol}}$
$n{C_2}{H_5}OH = \dfrac{{414}}{{46}}$
$n{C_2}{H_5}OH = 9$
Substituting the values in equation (I)
$x{\text{ }}{{\text{H}}_2}O = \dfrac{1}{{1 + 9}} = 0.1$

So the correct answer is option A.
The mole fraction of water in the given mixture of water and ethanol is $0.1$

Note:
Molality has a unit of moles/Kg but molarity has a unit of moles/liter.
A homogeneous mixture of one or more solutes dissolved in the solvent is known as a solution, the substance that is dissolved in a solution is known as solute and the dissolving medium is known as a solvent.