Question

The ethanol content of alcoholic beverages is sometimes expressed in terms of “proof.” This term comes from a 17th century test for the alcohol content in whiskey. The whiskey was poured onto gunpowder and then set on fire. If the whiskey was too wet, the gunpowder would not ignite after the whiskey had burned off. However, if the whiskey had not been watered down, the gunpowder would ignite. A positive test required a minimum ethanol content of approximately 50% ethanol (by volume), which was called “100 proof.” Whiskey with 40% ethanol is “80 proof,” and so on. What is the approximate molar concentration of ethanol in 100 proof whiskey? The density of pure ethanol is 0.789 g mL-1. Report your answer to two significant figures. If the vapour pressure of water is 17.5 torr at 20°C, what is the water vapour pressure inside a bottle of 100 proof whiskey?

Answer 1

Whiskey

80 proof = 40%

100 proof = (40/80) x 100 % =50%

For 100 proof -

500 mL of ethanol in 1000 mL of solvent

= (500 x 0.789) g of ethanol in 1000 mL of solvent

= 394.5 g of ethanol in 1000 mL of solvent.

Now,

46 g of ethanol in 1000 mL of solvent = 1 M

394.5 g of ethanol in 1000 mL of solvent = (394.5/46) M = 8.5 M

Raoult's Law:

P_solvent = X_solventP^o_solvent

P_solvent is the vapor pressure of the solvent above the solution,

X_solvent is the mole fraction of the solvent in the solution, and
P^o_solvent is the vapor pressure of the pure solvent.

In 100 proof whiskey,

500 mL of water in 1000 mL of wisky

500 g of water in 1000 mL of wisky (taking density =1)

(500/18) moles of water in 1000 mL of wisky

27.77 moles of water in 1000 mL of wisky

Again, 8.5 moles of ethanol in 1000 mL of wisky.

Mole fraction of water = 27.77/(27.55+8.5) = 0.76.

Now, P_water = X_waterP^o_water

   = 0.76 x 17.5 torr

= 13.3 torr