Add a cup of water to two cups of sugar (or vice versa) in a saucepan and stir while heating slightly. All the sugar will dissolve.
The concept of the blivet, ten pounds of stuff in a five pound bag, has amused many generations of little boys. But dissolving sugar in a cup of water is very different from stuffing it into a one-cup sack, and one of the reasons is very simple: The sugar molecules can squeeze into empty spaces between the water molecules, so they are not really taking up any new space.
At the submicroscopic level, water isn’t a densely packed pile of molecular particles, like a pail of sand grains. It’s a somewhat open latticework of molecules that are held to one another end-to-end in tangled strings, rather than in a randomly oriented heap.
The holes in this open latticework of molecules can accommodate a large number of dissolved particles, not only sugar molecules, but a great many others. That’s one reason why water is such a good solvent a good dissolver of many substances.
Perhaps more convincing, however, is the fact that two cups of sugar is a lot less sugar than it may seem. Sugar molecules are much heavier and bulkier than water molecules, so there won’t be as many of them in a pound or in a cup.
Also, the sugar is in granulated form, rather than in the form of a liquid, and the grains don’t settle down into the cup as tightly as you might think. The surprising result is that a cup of sugar contains only about one twenty-fifth as many molecules as there are in a cup of water. That means that in your two-cups-of-sugar-in-one-cup-of-water solution, there is only one molecule of sugar for every twelve molecules of water. Not such a big deal, after all.
I can dissolve two cups of sugar in one cup of water. Don’t use confectioner’s sugar; it contains cornstarch that will gum things up.