You have 1 L of 100 proof (50% V/V) Scotch whisky (ethanol, #C_2H_5OH#). Calculate the molarity, the mole fraction, the molality of the ethanol and if the temperature drops to -10C could you still drink the whisky? Density of ethanol =0.79g/ml kf=-1.86C/m
!! LONG ANSWER !!
The first thing you need to do is determine exactly how much ethanol your 1-L sample contains.
Since you're dealing with a 50% v/v solution, you'll get 50 mL of ethanol for every 100 mL of solution, which means that you have
Use the density of ethanol to determine how many grams you have in the 1-L sample
Use ethanol's molar mass to determine how many moles you have
To get the mole fraction of ethanol, you need to determine how many moles of water you have in the 1-L sample.
Since you have 500 mL of ethanol in the 1-L bottle, you'll of course also have 500 mL of water. Use water's density and its molar mass to determine how many moles you have
The total number of moles present in the solution will be
The mole fraction of ethanol will be
Now you have to determine whether or not you can still drink the whiskey if the temperature of the sample is dropped to
To do that, you have to determine if the amount of alcohol present in the sample would lower the freezing point of water enough to allow for the solution to remain liquid at that temperature.
The equation for freezing point depression is
Since you're dealing with a non-electrolyte, the van't Hoff factor will be equal to 1.
So, your solution will have a freezing point of
Therefore, you can still drink the whiskey at
SIDE NOTE I've given all the answers with two sig figs, but I should have used 1 sig fig, since that is all you gave for the volume of the sample.