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Is there an equation or simple way to calculate the final density of a solution made from x grams of sugar and y liters of water?

And would it work in reverse? if we have y liters of water at z density or specific gravity, can we know how much sugar is in the solution?

I'd like to run an experiment for my nephews, something like This.

However, lacking any background in chemistry, the precise math is tough to nail down. It would be great to have some deeper understanding of how this works...

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    $\begingroup$ You might use something like this graph. A rule of thumb used in brewing is that 1% (w/v) increases 0.004 g/mL above the density of water (~1 g/ml), i.e., 12% (w/v) sucrose would be around 1.048 g/mL. This works fine for low concentrations. $\endgroup$ – Felipe S. S. Schneider May 21 '18 at 17:38
  • $\begingroup$ To do the experiment for your nephews, you don't really need to know the density, nor do any math. The more sucrose you have per unit volume of water, the more dense that solution will be. This is the same a making a density gradient in biochemistry lab. Just take your time and be careful while layering one solution atop the other. If you can find a pipet, that will make it a lot easier to do. $\endgroup$ – Dr. J. May 21 '18 at 17:51
  • $\begingroup$ Yeah, but it could be a nice opportunity to learn some nice things myself Dr J, so why not? Also Felipe, that was a lot to unpack and waaaaaay above my understanding of chemistry. Any chance to get the 'For dummies' version? $\endgroup$ – Mike Meyers May 21 '18 at 18:03
  • $\begingroup$ @MikeMeyers - The link that Felipe posted has curves for a lot of chemicals. You want the one for sucrose (table sugar). You can ignore the others. $\endgroup$ – MaxW Aug 20 '18 at 3:49
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Here an empirical approach:

1) A simple way to calculate density: mass/volume

mass = x g of sugar + (y L of water*1000 mL/L*1g/mL)

1 g/mL = water density

Then measure the total volume (total mL) of the mix:

density = (x g of sugar + (y L of water * 1000 mL/L * 1g/mL))/(total mL)

2) For the reverse calculation, you can determine density as a function of sugar content by preparing solutions with different sugar concentrations and use this to interpolate your specific density value to a sugar concentration.

You can also use preexisting tables or graphs as Felipe suggested

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