# Density and solubility

Do all saturated solutions have the same density? Based on your data, which salt is more soluble?

\begin{align} &\ce{NaCl} & \pu{11.812 g/10 mL} \quad &\text{or} \quad \pu{1.181 g/mL} \\ &\ce{CaSO4} & \pu{9.783 g/10 mL} \quad &\text{or} \quad \pu{0.978 g/mL} \end{align}

I know the first part: all saturated solutions do not have the same density. For the second part I believe that solutions with higher density will be more soluble. So in this example $\ce{NaCl}$ will be more soluble that $\ce{CaSO4}$.

Would I be correct and my answer has to be based on density?

• Q: Are solutions with higher density more soluble. A: Yes, in general, but it does depend on the definition of "solubility." You could measure solubility as milligrams solute per milliliter of solution, or millimoles solute per milliliter of solution. The two different measures of solubility might give different results. For instance freezing point depression is more related to molar concentrations rather than gram concentrations. – MaxW Feb 19 '16 at 19:40

Let's think in terms of units. Density is mass per unit volume. Not only will different solutes have different masses dissolved into a unit volume, but the volume of the resulting solution will be different for different solutes.

When people say they can dissolve a unit of mass into a unit of volume (a common measure of solubility) they are not keeping track of the final volume of the resulting solution.

Here are the expressions for the density of the two saturated solutions (we should assume that the temperature and pressure are constant so that the density of the solvent itself is constant).

$\frac{m_{A,sat}}{V_{A,sat}} = \rho_{A,sat}$

$\frac{m_{B,sat}}{V_{B,sat}} = \rho_{B,sat}$

where $m$ and $V$ are masses and volumes, and $\rho$ is the density. $A$ and $B$ are the two solutes.

So if:

$\rho_{A,sat}{}\gt{} \rho_{B,sat}$

that could mean, in one limit where

$V_{A,sat} = V_{B,sat}$,

that

$m_{A,sat}{} \gt {}m_{B,sat}$.

Which is how I'm guessing you're thinking. If the volume change of solvation was similar for two solutes, one could trust that the density of the saturated solution with the (mass) solubility.

But there's another limit where there is a large difference in the volume change of solvation, between the two solutes. Then if:

$\rho_{A,sat}{}\gt{} \rho_{B,sat}$,

as before, and

$V_{A,sat}{} \lt{} V_{B,sat}$,

then it's possible that the unit mass dissolved in the two cases was equal,

$m_{A,sat} = m_{B,sat}$,

so that the two solubilities would be equal.

So no, with the above definitions of solubility and density, one cannot assume that the density of a saturated solution corresponds to the solubility.