What is vodkas boiling point?

The easiest way to answer this would be to take some and boil it. Then measure with a thermometer. Of course, you would want to avoid open flames while doing that.

If you want to do it by theory, we can approximate it.
Vodka typically comes in 80 and 100 proof. 100 proof makes the math slightly easier, so I'll go with that.
100 proof is 50% by volume. So, you have 50 vol% ethanol and water. We need to get a mole ratio, so we will first approximate the mass of each by density.

Ethanol - 0.789 g/cm³
Water - 0.998 g/cm³

So, for 2 cm3 of liquid, we would have 1 cm3 each of E and W. That means we have .789 g of E and .998 g of W.
Next, we need moles of each. n = m/MW

Molecular Weight:
E - 46
W - 18

So, number of moles is:
E - .789 / 46 = .0172
W - .998 / 18 = .0554
total # moles = .0172 + .0554 = 0.0726

the mole percent of ethanol in the liquid would then be xE = .0172/.0726 = 24%.

Looking at a T-x-y chart for binary distillation between ethanol and water: (figure 2 at the link)

At 24 mol% E, the bubble point is roughly 82-83 degrees C.

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