Question

In a binary solution, mole fraction of solute is found to be $0.4$. What could be the mole fraction of the solvent in the solution?
A.1
B.$0.4$
C.$0.6$
D.$0.3$

Answer 1

To answer this question, you should recall the formula for calculating mole fraction which involves the calculation of moles of solute and solvent. No. of moles can be calculated by dividing the given mass with the molecular mass of the component. Now use these values to arrive at the final answer.
Formula used:
Mole fraction = $\dfrac{{{{\text{X}}_{\text{A}}}}}{{{{\text{X}}_{\text{A}}}{\text{ + }}{{\text{X}}_{\text{B}}}}}$(from the above definition) where ${{\text{X}}_{\text{A}}}$is no. of moles of solute and ${{\text{X}}_{\text{B}}}$is the no. of moles of solvent

Complete step by step answer:
-We know the definition of mole fraction i.e. it is a way of expressing the concentration of a solution and can be calculated by dividing the number of molecules of a particular component in a mixture by the total number of moles in the given mixture. Now using the above definition let’s find the answer to this question.
-The components of a solution are solute and solvent, therefore we need to calculate the number of moles of these components to find the correct answer.
-Sum of mole fraction of solvent and solute or the total components in solution = 1
Thus, for the binary solution;
Mole fraction of solute + mole fraction of solvent = 1
Therefore mole fraction of solvent = $1{\text{ }} - {\text{ }}0.4{\text{ }} = {\text{ }}0.6$.

Hence, the correct option is option C.

Note:
Sometimes while calculating the mole fraction of a dilute binary solution, the moles of solvent are a lot higher than the moles of solute. Thus, the moles of solute are neglected while calculating the mole fraction. The formula of mole fraction of solute then becomes:
$\dfrac{{{{\text{X}}_{\text{A}}}}}{{{{\text{X}}_{\text{B}}}}}$ where ${{\text{X}}_{\text{A}}}$is no. of moles of solute and ${{\text{X}}_{\text{B}}}$is the no. of moles of solvent