Question

A solution contains 36% water and 64% acetaldehyde $\left( {C{H_3}CHO} \right)$ by mass. The mole fraction of acetaldehyde is:
A) $0.42$
B) $0.2$
C) $4.2$
D) $2.1$

Answer 1

Mole fraction is a method of expressing the concentration of the components of a mixture or a solution calculated using the value of moles of each component present in the mixture or solution
Its value is independent of the temperature hence is widely used as a concentration expressing unit in solutions and mixtures.

Formula used:
${X_a} = \dfrac{{{n_a}}}{{{n_a} + {n_b}}}$
${X_b} = \dfrac{{{n_b}}}{{{n_a} + {n_b}}}$
Where ${X_a}$ is the mole fraction of component ‘a’ present in the mixture of ‘a’ and ‘b’
${X_b}$ Is the mole fraction of component ‘b’ present in the mixture of ‘a’ and ‘b’
While ${n_{a\,}}\,and\,{n_b}$ are the moles of component ‘a’ and component ‘b’
${X_a} + {X_b} = 1$ (Always)

Complete step by step solution:
In the given question a solution of water and acetaldehyde is given
Let the weight of solution be $100gm$
Then given water is $36\%$ present in the solution hence it is $36gm$
And acetaldehyde given as $64\%$ would be $64gm$
Now moles of a molecule is given by $n = \dfrac{{given\,weight}}{{Molecular\,weight}}$
Using this moles of acetaldehyde (also known as ethanal) will be
${n_a} = \dfrac{{64}}{{44}}$
${n_a} = 1.4545$
And moles of water will be
${n_b} = \dfrac{{36}}{{18}}$
${n_b} = 2$
As we know mole fraction is calculated as
${X_a} = \dfrac{{{n_a}}}{{{n_a} + {n_b}}}$
Using this mole fraction of acetaldehyde will be
${X_a} = \dfrac{{1.4545}}{{1.4545 + 2}}$
${X_a} = 0.42$
Hence option “A” is the correct solution for this question.

Additional Information:
-Mole fraction of a particular component in a mixture of at least two components will always be lesser than one
-Pressure due to an individual gas in a mixture of gases commonly known as partial pressure is directly proportional to the mole fraction of that gas

Note:
-Mole fraction being a ratio of number of moles is dimensionless.
-Also, Mole fraction and Molality are the only two concentration expression units whose value remains constant whatever be the changes in the surrounding temperature.