Question

How do you find the density of a solution if you know the identity of the solute and solvent, the amount that you combine of each, and their individual densities?

Answer 1

We can find the density of solution in each of the cases given in question by using the definition of density. Density is the ratio of mass of the solution and the volume of the solution. The solution consists of solute and solvent. Thus we can define density in terms of solute and solvent too.
$\Rightarrow {\text{ Density = }}\dfrac{{{\text{mass of solution}}}}{{{\text{volume of solution}}}}$

Complete Step By Step Answer:
The density of solution can be defined as the ratio of the mass of the solution and the volume of solution which can be represented as:
$\Rightarrow {\text{ Density = }}\dfrac{{{\text{mass of solution}}}}{{{\text{volume of solution}}}}$
Now we know that solution comprises of solute and solvent and thus equation can be deduced as:
$\Rightarrow {\text{ Density = }}\dfrac{{{\text{mas}}{{\text{s}}_{solute}}{\text{ + mas}}{{\text{s}}_{solvent}}}}{{{\text{volume of solution}}}}$
The mass of solute of solvent can be find by multiplying its molar mass $\left( M \right)$ by its number of moles $\left( n \right)$ and it can be deduced as:
$\Rightarrow {\text{ Density = }}\dfrac{{{n_{solute}} \times {{\text{M}}_{solute}}{\text{ + }}{n_{solvent}} \times {{\text{M}}_{solvent}}}}{{{\text{volume of solution}}}}$
Also when the total volume of solution is given by:
$V{\text{ = }}{n_{solute}} \times {V_{solute}}{\text{ + }}{n_{solvent}} \times {V_{solvent}}$
Therefore the density can also be found as:
$\Rightarrow {\text{ Density = }}\dfrac{{{n_{solute}} \times {{\text{M}}_{solute}}{\text{ + }}{n_{solvent}} \times {{\text{M}}_{solvent}}}}{{{n_{solute}} \times {V_{solute}}{\text{ + }}{n_{solvent}} \times {V_{solvent}}}}$
Therefore with the help of above conversions we can find the density of solution when we are given the identity of solute and solvent. Also we can find the density of solution when densities of solute and solvent are given too.

Note:
It must be noted that basic definition of density is the ratio of mass of solution and volume of solution, therefore its unit will be ${\text{g }}{{\text{L}}^{ - 1}}$ and it is represented by symbol $\rho$ . The moles of solute can be found by calculating the ratio of given mass of solute and molar mass of solute. The molar volume is calculated by multiplying the moles and the volume.