# 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?

May 24, 2017

You probably mean $\text{g/mL}$... Density is defined as:

$D = \text{mass solution"/"volume solution}$

$= \text{mass solute + mass solvent"/"volume solution}$

-= (m_"solute" + m_"solvent")/V_"soln"

= (n_"solute"M_"solute" + n_"solvent"M_"solvent")/V_"soln"

where the volume of the solution is not necessarily the volume of the solute plus solvent, but tends to be assumed so. $M$ is molar mass in $\text{g/mol}$ and $n$ is $\text{mol}$s.

The total volume is given by:

$V = {n}_{1} {\overline{V}}_{1} + {n}_{2} {\overline{V}}_{2}$,

where ${\overline{V}}_{i} = {V}_{i} / n$ is the molar volume of component $i$.

With one component in the solution with water, we have:

bb(D = (n_"solute"M_"solute" + n_"solvent"M_"solvent")/(n_"solute"barV_"solute" + n_"solvent"barV_"solvent")

The molar volume of water is known from its density at some temperature $T$ and $\text{1 atm}$ pressure. Simply do some unit conversion to get from $\text{g/mL}$ to $\text{mol/L}$, then reciprocate it.

So:

• By knowing the density of your solute at your temperature $T$ and $\text{1 atm}$ pressure, you can get ${\overline{V}}_{\text{solute}}$.
• By knowing the masses of both the solute and solvent individually before mixing the solution, as well as their molar masses, you can determine the total mass of the solution.
• Knowing their masses and their molar masses, you can also then determine the total volume of the solution.