### Boiling with salt

Getting back into chemistry after last week's fun little diversion into mechanics, I feel like doing some more math. I was looking for a recipe not long ago and ran across repeated mentions that one adds salt to water when boiling food in order to raise the temperature at which the water boils, thus cooking the food faster.

Boiling point elevation is a real thing, as is freezing point depression, and it's not hard to calculate.

The boiling point of pure water at sea level is 100oC. In order to calculate the change in temperature, we need the following equation:

$\Delta T = K_b m$

Purdue university has a convenient table of $$K_b$$ constants which states that for water, $$K_b$$ is 0.512.

In the equation above, $$m$$ is the molality of the solution, or moles of solute per kilogram of solvent.

For the purposes of cooking, let's say we're putting about 1g of salt into a pot containing 4kg of water. 1g of salt is a lot more than I learned to add to water when cooking, but we'll use that number anyway.

1g of salt at 58.5g/mol is 0.0171mol of NaCl. This makes the molality of our boiling water $${2 \times 0.0171 \over 4} = 0.00855\mathrm{mol/kg}$$.

Thus:

$\Delta T = K_b m = 0.512 \times 0.00855 = 0.00437\mathrm{^oC}$

So by adding 1g of salt to 4kg of water, we raise the sea level boiling point from 100oC to 100.004oC. This doesn't strike me as something that will make a significant difference to cooking times.

I'm curious: how much salt does it take to raise the boiling point by 1oC?

$m = {\Delta T \over K_b} = {1.0\mathrm{^oC} \over 0.512} = 1.95$

With a molality of 1.95, that means 3.9 moles of NaCl was added to our 4kg of water, or 228.5g of table salt. This is a lot of salt to be adding to your food, and would taste terrible. In fact, it's a full quarter of this box of salt:

...where what's in the spoon is closer to how much you'd actually put in the pot.

By contrast, the range of altitudes humans live at, from sea level to 3800m, causes water to boil at a full 13 degree range, from 100oC at sea level to 87oC at 3800m.