## Sinking Ice Cubes

### 2006-07-12 13:41 - General

Want a surefire bet for your next cocktail party? ...Bet that you can magically make an ice cube sink.

The key to the trick is heavy ice. ... Hydrogen atoms always have one proton and one electron, but only one in every 6,400 has a neutron that nearly doubles the atom's mass. ... It's possible to isolate this heavy hydrogen, also known as deuterium (D), creating water that's about 10 percent heavier than normal.

They go on to explain that you can get a bottle of this heavy water from "your neighborhood isotope supplier" for enough to make a single ice cube cost $15. I immediately thought "That sounds really silly, it's cheap and easy to make water heavier!" And I dug up a page that confirms my initial reaction:

The density of pure water is one gram per cubic centimeter. If salt is dissolved in the water, the volume of water does not change, but the density of the solution increased because the density of salt is much greater than that of water.

So, density of water is 1.0g/mL and once frozen into ice is 0.92g/mL. That supports the 10% heavier water makes sinking ice theory. That page goes on to calculate that "The increase in volume of ice is about 9%." But, how much can we increase the density of water by adding salt?

Well, my research is scarce here. But, one student's work has gotten me mostly there:

A mole, or 6.023 x 10^{23}, of Na atoms weighs 22.997 g, and a mole of Cl^{-}atoms 35.457 g. Therefore, a cube containing (1/2)NaCl has a weight of 29.227 / 6.023 x 10^{23}g, and a volume of (0.279)^{3}nm = 2.172 x 10^{-23}cm^{3}. This gives a density of 2.23 g/cm^{3}.

That paper also mentioned that "This is the density of a 16% solution by weight, or 16 g salt dissolved in 84 g of water. 100 g of solution has a volume of 100/1.12 or 89 cc, so the solution expands slightly as salt is added." So, apparently the volume does increase, by around 6%.

Finally, the best number I could find said that "The solubility of Sodium Chloride NaCl in water is 35.9 g/100 ml".

So how about those numbers, density: water 1.0g/mL, ice: 0.92g/mL, salt: 2.23g/cc. From that density, and solubility of 35.9g per 100mL, 35.9g / 2.23g/cc = 16cc of salt will dissolve in 100mL of water.

So saltwater can be: 16cc * (2.23g/cc) + 100mL * (1.0g/mL) = 135.9g of mass, and assuming a volume increase of 6% from the salt plus 9% more from the freezing, that makes 115.5mL of volume. Then, 135.9g / 115.5mL = 1.17g/mL density. Guess what, that's more than water!

So, unless my calculations are off, some cheap saltwater ice cubes will sink just as well as "heavy water" ice cubes. And if so, expect pictures a few hours after I get home!

**Update: July 13th**