I was cooking potatoes earlier today, and remembered a story I once read about salt potatoes, which sound quite a bit more delicious than the merely baked potatoes before me.

Living in Grand Forks, North Dakota, finding potatoes is not such a difficult task (though “bite size” potatoes as described is still a tall order). Finding salt is generally easy for non-ancient Romans, as well.

But cooking can be so imprecise an art. What exactly does * “1 cup salt to 6 cups water”* mean anyway?

Published values indicate somewhere between 273 and 283 grams of standard table salt per cup. A US cup is 1/16 of a gallon, or 236.59 ml.

This means that the solution is about **3.3** or **3.4 molar**. That’s a value that should satisfy any kitchen scientist with a decent scale.

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There’s a second value that can serve as a check, though: * “12 ounces of salt for 5 pounds of potatoes”* in the traditional package of one purveyor of salt potatoes.

To start, “12 ounces” means **340 grams** of salt. “5 pounds” means **2.268 kg** of potatoes.

But we’re missing the volume of water needed! No fear, though– without resorting to something as inelegant as laboratory experiements, we can calculate the molarity of the solution with a couple key pieces of data, and a few justified assumptions!

If we assume there’s just enough water to cover the potatoes, and if we know the shape and size of a potato, we can calculate the gaps that the water would fill.

I found data on USDA potato sizes here: Size B potatoes have a diameter of 38 to 57 mm. So let’s model a potato of diameter **48mm**.

To illuminate the shape of a potato, I found this paper on Iranian potatoes. On average, the ratio of major to secondary to minor diameters is about 1:0.78:0.6. So our potatoes would measure **48 by 37.3 by 31.3.**

The volume of an ellipsoid is (4/3)(pi)abc (where a, b, and c are radii), so each of our potatoes clocks in at a volume of **29.3 ml**. The same paper gives the density of potatoes as about **1.08**, meaning we have roughly 2.10 liters of potatoes — about 71 of them– in our as-yet undefined amount of salt water.

Modelling the potatoes as perfect ellipsoids that are hexagonally packed, widest side down, in a cylindrical pot 26cm in internal diameter, with the gaps filled with water. A bit of experimenting around in Inkscape and we find that not less than three layers of potatoes will be needed to pack in 71 of them. The minimal height would be about 86 mm. so 8.6 cm of water in a 26 cm cylinder less 2.1 liters of potatoes gives us 2.46 liters of water. 340 grams of salt in this mixture gives us a **2.36 molar** solution! Hmmmm, that seems to be significantly less than 3.3…

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WAIT NOW! Perusing Wikipedia’s sources, we find that indeed, less salt is actually used in the 1:6 recipe (it’s coarse-grained kosher salt, much less dense than table salt). And we find some evidence that an alleged quality of salt potatoes — that a “higher boiling point” causes the potatoes to cook differently — is in serious doubt!

A saturated salt water solution boils at about 108 degrees. And at lesser concentrations, well, the difference is less stark. For a 2 to 3 molar solution as described in our recipes, the boiling point only goes up by about 1 to 1.5 degrees!

My best guess as to the “difference” tasted in the salt potato, aside from the healthy dose of salt? A decrease in water concentration inside the potato, caused by osmotic action. I also wouldn’t discount the possibility of side reactions in the cooking process, with all those sodium and chloride ions floating around.