Can I get a solution density from the solute mass and solvent volume?

I am adding 50 gm of sugar to 500 ml of water. How do I calculate the density of the sugar solution? (Is it) 50 gm/500ml or 50/(volume of water displaced by the sugar)?
Jennifer Schmahl

The density of the solution will be mass of solution divided by volume of solution.
  • 50 g/500 mL isn't correct because the volume of the solution isn't 500 mL.
  • 50 g/(volume of water displaced by the sugar) isn't correct because you're comparing a sugar mass to a water volume.

To determine the solution's density, weigh a precisely measured volume of your solution, and divide the mass of solution by the volume of solution.

You must measure the volume of solution to obtain the density. You can't calculate the density of the solution with just the data you've given above. You can get a crude estimate (e. g., if you assume the volume of the dissolved sugar is negligible compared to the volume of the water, the density is roughly (50 g sugar + 500 g water) / 500 mL solution. But the assumption isn't correct- try it yourself!) Even if you happened to know what the volume of the added sugar was, the volume of a solution is NOT the volume of the solute plus the volume of the solvent.

Author: Fred Senese senese@antoine.frostburg.edu



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