# Calculating total volume mixing NaCl and water

I'm (as a non chemist) trying to calculate the the volume of a NaCl solution. The problem is that I know the volume of water prior to mixing in NaCl, but I want to know the volume of the solution after.

If my little research is correct, I need to use partial molar volumes of NaCl to estimate the volume change in response to adding NaCl. I found a value of $\pu{16.61 cm3/mol}$ for NaCl (and some other literature values being similar). The initial volume of water is 12 liter, and the added mass of NaCl is 1000 g, or 17.11 moles. This results then in $\pu{284 cm3}$ increase in volume, and a total volume of 12.284 liter.

My question is to what degree the partial molar volumes are dependent on the concentration in the solution and the temperature of the solution? I would like to do these estimations of total volume for a range of temperatures from 2 degrees C to 30 degrees C, and with variable amount of NaCl concentrations. I was not able to find information on whether NaCl partial molar volumes are dependent on these factors, but it seems other aqueous mixtures are.

Thanks!

• Wouldn't it be easier to look up the (surely available) tabulated values for the density of salt solutions at different concentrations and work backwards from there? – TAR86 Nov 2 '17 at 18:34
• Thanks, I didn't think of that! I'll do a more careful calculation later, but a quick check on mobile gives a volume of 12.22 liter - so comparable to the partial molar volume method – rhkarls Nov 2 '17 at 21:21