Calculating the density of a saturated salt solution

Question

Is there a way to calculate the density of a saturated salt solution from the solubility limits or does it have to be experimentally determined?

First instinct, is to add the mass of the salt to mass of the water e.g. a solubility of $\pu{80 g}$ of salt in $\pu{100 mL}$ would have a solution density of $\pu{180 g/100 mL = 1.8 g/mL}$. However, it seems the salt should affect the volume of the solution. What additional information is needed or does this quantity just have to be empirically determined?

Answer 1

Often, solubility is given as mass per volume of solution (not solute). Nevertheless, unless you have the mass percentage (w) too, you are not able to calculate the density of the solution.

Answer 2

This is something you can calculate, provided you know the partial molar volumes of all the substances in your solution. But someone must have measured those at some point, and tabulated it for your conditions (or close enough that you can interpolate). You can probably estimate it closely enough, depending on your needs.

The experiment would be as simple as taking a known volume aliquot of your saturated solution and weighing it.

Answer 3

Your proposed method (adding the masses, but using the volume of the solvent) can work under certain circumstances; it is often a good first approximation for the times when it is not a good assumption.

For low solubility salts, you can safely assume that the volume of the solution is the same as the volume of the solvent. "Low" here is somewhat open for debate. As a general rule, I feel safer with this assumption for each order of magnitude below 1 molar / molal. So, I consider this method valid to one (or fewer) sigfigs for solutions near 1.0 molar; 0.1 M makes me feel "2 sig figs safe", etc. (Again, these are just guidelines, don't get hung up on specific numbers.) With a salt that can only dissolve fewer than 10 grams into 100g of water, this method is usually fine to 2 or 3 sig figs. A salt that dissolves less than 1.0g into 100g of water is now getting into the territory of measurement errors of accurately measuring the volume of the solution (in most high school or even some college labs).

Seawater runs about 3% salt to water by mass. Estimating it's density at 1.03 g/mL is pretty valid. In the example in the OP of 80g of salt in 100mL of water (giving a value of 1.8 g/mL) is a good first order approximation, but I would take that value with... a grain of salt.