Question

The mole fraction of a solute in $2.5{\text{ m}}$ aqueous solution is:
A.$0.043$
B.$0.43$
C.$4.3$

Answer 1

Hint: To answer this question, you must recall the concept of molarity of a solution. Molality is a term used to denote the concentration of a solution. If we have a one molal solution, it means that $1{\text{ mole}}$ of solute is dissolved in $1{\text{ kg}}$ of solvent.
Formula used: ${\chi _{{\text{solute}}}} = \dfrac{{{{\text{n}}_{{\text{solute}}}}}}{{{{\text{n}}_{{\text{solute}}}} + {{\text{n}}_{{\text{solvent}}}}}}$
Where ${\chi _{{\text{solute}}}}$ is the mole fraction of the solute in the solution.
${{\text{n}}_{{\text{solute}}}}$ is the number of moles of solute
And, ${{\text{n}}_{{\text{solvent}}}}$ is the number of moles of solvent.

Complete step by step solution:
Mole fraction of a component in a solution is the ratio of the number of moles of the component to the total number of moles present in the solution. The sum of mole fractions of all the components in a system is equal to unity.
The mole fraction of the solute can be given by the formula,
$\Rightarrow$${\chi _{{\text{solute}}}} = \dfrac{{{{\text{n}}_{{\text{solute}}}}}}{{{{\text{n}}_{{\text{solute}}}} + {{\text{n}}_{{\text{solvent}}}}}}$
The molality of a solution can be given as,
$\Rightarrow$\[{\text{Molality(m)}} = \dfrac{{{\text{moles of solute (}}{{\text{n}}_{{\text{solute}}}}{\text{)}}}}{{{\text{mass of solvent(in kg)}}}}\]
We are given the molality of solution as$2.5{\text{ m}}$, thus we can say that $2.5{\text{ moles}}$of solute is present in $1{\text{ kg}}$ water.
The molar mass of water is known to be $18{\text{ g/mol}}$
So the number of moles of water in the solution is
$\Rightarrow$${n_{{\text{solvent}}}} = \dfrac{{1000}}{{18}} = 55.5{\text{ mol}}$
The mole fraction of the solute is
$\Rightarrow$${\chi _{{\text{solute}}}} = \dfrac{{2.5}}{{2.5 + 55.5}} = \dfrac{{2.5}}{{58}}$
$ \Rightarrow {\chi _{{\text{solute}}}} = 0.043$

Thus, the correct option is A.

Note:
Mole fraction is a unit less quantity. There can be confusion between molarity and molality. Both the terms are used to calculate concentration but are significantly different. Molarity uses the amount of solution while molality uses the amount of solute.