Question

Estimate the mole fraction of the solute in a $1.00$ molal aqueous solution.

• A. $1.7700$
• B. $0.1770$
• C. $0.0177$
• D. $0.0344$

Answer 1

The correct option is C

$0.0177$

Explanation for correct option:

Option (C) $0.0177$

Step 1: Understand the term “Mole fraction”

The mole fraction of any component of a solution is defined as the ratio of the number of moles of that component present in the solution to the total number of moles of all the components of the solution.$\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{solute}=\frac{\mathrm{Moles}\mathrm{of}\mathrm{solute}}{\mathrm{Moles}\mathrm{of}\mathrm{solute}+\mathrm{Moles}\mathrm{of}\mathrm{solvent}}$

$\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{b}=\frac{{\mathrm{n}}_{\mathrm{b}}}{{\mathrm{n}}_{\mathrm{a}}+{\mathrm{n}}_{\mathrm{b}}}$

${\mathrm{n}}_{\mathrm{b}}$= number of moles of solute

${\mathrm{n}}_{\mathrm{a}}$ = Number of moles of solvent

Step 2: Determine moles of Solute and Water

To find the mole fraction of the solute in a $1.00$ molal aqueous solution, we need moles of solute and moles of solvent

It is given that there is 1 molal aqueous solution, which means that one mole of solute is dissolved in $1\mathrm{kg}$ of water.

Thus, the number of moles of solute is one

Number of moles of water$=\frac{1000}{18}=55.556$ ($\Rightarrow$$1\mathrm{kg}$ of water is there and molar mass of water is $18\mathrm{g}{\mathrm{mol}}^{-1}$)

Step 3: Find the mole fraction of the solute.

$\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{solute}=\frac{\mathrm{Moles}\mathrm{of}\mathrm{solute}}{\mathrm{Moles}\mathrm{of}\mathrm{solute}+\mathrm{Moles}\mathrm{of}\mathrm{solvent}}$

$\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{solute}=\frac{1}{1+55.556}$

$\mathrm{Mole}\mathrm{fraction}\mathrm{of}\mathrm{solute}=\frac{1}{56.556}=0.01768\approx 0.0177$

Thus, the mole fraction of the solute in a $1.00$ molal aqueous solution is $0.0177$. So, option (c) is correct.