Question

Molarity and Molality of a solution of a liquid ($\mathrm{Mol}\mathrm{Wt}=50\mathrm{g}$) in an aqueous solution are 9 and 10 respectively. what is the Density of the solution?

Answer 1

Step 1 Volume of the solution where one mole of a compound is present:

The molarity can be defined as the number of moles of solute per unit liter of the solution.

The molarity of a solution of a liquid in an aqueous solution is $9\mathrm{M}$.

That is, 9 moles of the compound are present in $1000\mathrm{ml}$ of solution.

Then 1 mole of the compound would be present in $\frac{1000}{9}=110\mathrm{ml}$

Step 2 Mass of the solvent required for one mole of solute:

The molality of a solution of that liquid in an aqueous solution is $10\mathrm{M}$.

10 moles of a compound are present in $1000g$ of solvent.

The molecular mass of solute is $50\mathrm{g}$.

Mass of solute $=10\times 50=500\mathrm{g}$

Mass of the solution is $1000+500=1500g$

Molality can be defined as the total moles of a solute contained in one kilogram of a solvent.

Therefore, the Mass of the solvent required for one mole of solute is $\frac{1500}{10}=150\mathrm{g}$.

Step 3 Density:

The density of a substance is the mass per unit volume.

$$\begin{gathered} \mathrm{Density}=\frac{\mathrm{Mass}}{\mathrm{Volume}} \\ \mathrm{Density}=\frac{150}{110} \\ \mathrm{Density}=1.35\mathrm{g}{\mathrm{mL}}^{-1} \end{gathered}$$

Therefore, the density of the solution is $1.35\mathrm{g}{\mathrm{mL}}^{-1}$