Question

The mole fraction of a solute in a$100$ molal aqueous solution is _____$\times {10}^{-2}$ . (Round off to the Nearest Integer). [Given : Atomic masses : H : 1.0 u, O : 16.0 u].

Answer 1

Mole Fraction:

• The mole fraction of the solute is defined as the moles of the solute with respect to the total moles.
• $\mathrm{Mole}\mathrm{fraction}=\frac{\mathrm{Moles}\mathrm{of}\mathrm{solute}}{\mathrm{Total}\mathrm{moles}}$

Solution:

Further $100$ molal aqueous solution is given which means $100$ moles of solute is dissolved in $1Kg.$ of the solvent.

From here we can get

• The number of moles of the solute $=100$
• Weight of the solvent $=1kg$.

$\begin{array}{rcl}\mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{the}\mathrm{solvent}& =& \frac{\mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{solvent}}{\mathrm{Molecular}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{solvent}}\\ & =& \frac{1000}{18}\end{array}$

Now, apply the formula of the mole fraction written above

$\begin{array}{rcl}\mathrm{Mole}\mathrm{raction}& =& \frac{\mathrm{Moles}\mathrm{of}\mathrm{solute}}{\mathrm{Total}\mathrm{moles}}\\ & =& \frac{100}{(100+{\displaystyle \frac{1000}{18}})}\\ & =& \frac{100}{{\displaystyle \frac{1800+1000}{18}}}\\ & =& \frac{100}{{\displaystyle \frac{2800}{18}}}\\ & =& \frac{1800}{2800}\\ & =& 0.64\\ & =& 64\times {10}^{-2}\end{array}$

The mole fraction of a solute in a$100$ molal aqueous solution is $\begin{array}{rcl}& & 64\times {10}^{-2}\end{array}$.