Question

A solution contains \[1\] mole of water and \[4\] mole of ethanol. The mole fraction of water and ethanol will be
A. \[0.2\] Water + \[0.8\] ethanol
B. \[0.4\]water + \[0.6\] ethanol
C. \[0.6\]Water + \[0.8\] ethanol
D. \[0.8\] Water + \[0.2\] ethanol

Answer 1

Hint: Before we proceed into the problem, it is important to know the definition of mole fraction of a substance.
By dividing the component's mole by the sum of the moles of all the other components in the solution, the component's mole fraction can be computed. Calculating the component's moles requires dividing the component's stated mass by its molecular mass. By doing this we will get the desired answer of the mole fraction of water and ethanol.

Formula Used: The formula to determine the mole fraction is said to be
\[mole{\rm{ }}fraction{\rm{ }}of{\rm{ }}A{\rm{ }}(\;\chi A\;){\rm{ }} = \;\frac{{No.{\rm{ }}of{\rm{ }}moles{\rm{ }}of{\rm{ }}A}}{{Total{\rm{ }}number{\rm{ }}of{\rm{ }}moles}}\]

Complete Step-by-step answer: A solution contains \[1\] mole of water and \[4\] mole of ethanol which is given in the question.

The equation format of the given information is as below,
\[{X_{water}}\] ​= Water’s mole fraction = 1
\[{X_{ethanol}}\] ​= Ethanol’s mole fraction = 4
Now, we have to determine the mole fraction of a substance
Mole fraction’s formula is said to be as follows:
\[{X_A} = \frac{{{n_A}}}{{{n_A} + {n_B}}}\]---- (1)
First, let us predict the mole fraction of an ethanol
Therefore, on substituting the value on the above formula we get
\[{x_{ethanol}} = \frac{4}{{1 + 4}}\]
On further simplification, we have
\[{x_{ethanol}} = \frac{4}{5}\]
Now, we have to write the above fraction in decimal form, we get
\[{x_{ethanol}} = 0.8\]
Now, let us determine the mole fraction of water.
Therefore, on substituting the value on the mole fraction formula (1), we obtain
\[{x_{water}} = \frac{1}{{1 + 4}}\]
On further simplification, we get
\[{x_{water}} = \frac{1}{5}\]
Now, we have to write the above fraction in decimal form, we get
\[{x_{water}} = 0.2\]
Therefore, the mole fraction of water and ethanol will be \[0.2\] Water + \[0.8\] ethanol

Hence, the option A is correct

Note: Students shouldn’t get confused about Molality and molarity. Molality and molarity is two different concepts. While Molarity (M) is defined as the number of moles of a solute added to a solution per litre of solution, Molality (m) is defined as the number of moles of a solute per kilogram of a solvent. Students should also keep in mind that the mole fractions of each component in the solution added up should equal one.