# Prediction of volume of solid-liquid solution

How does the volume of a solid in liquid solution change compared to the volume of the pure volume of the solvent?

If suppose I make a solution with a solid as solute and a liquid as solvent, and for simplification I assume that the solute is completely soluble in the given amount of solvent, is there is any mathematical relation to predict the volume of the resulting solution?

Is it similar to liquid-liquid solutions which show positive and negative deviations?

Borek
Mentor

The only sure way is an experiment (or density tables - but they just mean experiment was done by someone else).

I didn't say they were :D

The only sure way is an experiment (or density tables - but they just mean experiment was done by someone else).
So no mathmatical expression? Note, I was talking specifically about solid-liquid solitions

Borek
Mentor
I didn't say they were :D
But what you are trying to calculate requires this as an assumption.

Volumes are additive for ideal gases only, which is a rather boring case.

So no mathmatical expression? Note, I was talking specifically about solid-liquid solitions
Doesn't matter if it is solid/solid, solid/liquid, liquid/liquid, you can expect all kinds of deviations.

But what you are trying to calculate requires this as an assumption.
It seems that there has been some miscommunication here. Let me make my case clearer.

If suppose I have 1L of pure water in a beaker and to it I add 10 grams of sugar which then completely dissolves. Now I measure the volume of the solution; will I observe a different volume? If yes, can I find out a relation between the change in volume and the say the weight of the sugar added?

Borek
Mentor
No miscommunication here.

Yes, the final volume will be different from the initial volume of water, but there is no way to calculate it (without density tables).

The most obvious approach calls for assumption that the final volume is a linear combination of volumes (volume additivity) - but there are deviations which make this approach useless. I seem to remember there are more elaborate schemes using partial volumes - but they don't work neither.

My Concentration and Solution Calculator has built in density tables and is flexible enough for such calculations. It tells me if you add 10 g of sucrose to 1L of water you will end with 1006 mL of 1.0021 g/mL solution (assuming 20°C).

The most obvious approach calls for assumption that the final volume is a linear combination of volumes (volume additivity) - but there are deviations which make this approach useless. I seem to remember there are more elaborate schemes using partial volumes - but they don't work neither.
I'm sorry if I sounded like it, but I didn't expect any linear relationship; I was simply asking if there was one.

Yes, the final volume will be different from the initial volume of water, but there is no way to calculate it (without density tables).
Oh ok got it. Thanks!!

It is possible to calculate in principle. However, this will require you to use Water Models, which is currently a pretty big area of computational chemistry.

The theory of solvation, even today, is not complete. That is because when you dissolve something, the molecules are surrounded by a semi-rigid shell of water called the solvation shell. Depending on the energetics of the solvation shell, you have either phase separation or you have solvation.