So I was working with a college student in her 2nd year of chemistry. We were attempting to find the molality (moles of solute per kilograms of solvent) of a solution when given the molarity (moles of solute per liter of solvent) and the density (grams per milliliter).
Here's the general process of how the problem is supposed to be done. You look at the molarity of the solution, and from that we can figure out the mass of the solute in that solution. And from there, you can calculate the mass of the solvent with basic subtraction, and BOOM! there's your molality.
And it turns out there's a wrong way to do the problem, which I discovered the hard way. Turns out, even when working with an aqueous solution (salt water, for instance), we cannot assume that water's density will remain roughly 1 kg/L. For the purposes of the problem we did this week, water's density was calculated to be roughly 750 g/L. That's not a density I'd expect to see in the natural world. Even at 80 degrees Centigrade, water's density is roughly 970 g/L.
Now, I'm trying to visualise how one might lower the density of water to that point. Perhaps larger molecules (like potassium iodide, or anything else with a high molar mass) would displace the much-smaller water molecules to the point where water's density would be seriously affected. That's the only way I can see it happening.
I may update with an experiment to test whether or not we can successfully lower the density of water by 25% or so. That might be a challenge.