The "proof" of an alcoholic beverage is twice the volume percent of ethyl alcohol, C2H5OH in water. The density of ethyl alcohol is 0.789g/ml and that of water is 1.00g/ml. A bottle of 100 proof rum is left outside on a cold winter day.

a.) Will the rum freeze if the temperature drops to -18 degrees celsius?
b.) Rum is used in cooking and baking. At what temperature does 100 proof rum boil?

hint, 100 proof rum is 50% alcohol and 50% water.

a 1L bottle of 100 proof rum has (789/2) = 394.5g of alcohol and 500g of water.

To answer these questions, we need to understand the concept of proof, freezing point, and boiling point.

Proof: In the context of alcoholic beverages, proof is a measure of the alcohol content. It is double the volume percentage of ethyl alcohol (C2H5OH) in the solution. For example, 100 proof means the beverage contains 50% ethyl alcohol by volume.

Freezing Point: The freezing point of a liquid is the temperature at which it changes from a liquid to a solid state. Different liquids have different freezing points.

Boiling Point: The boiling point of a liquid is the temperature at which it changes from a liquid to a gaseous state. Again, different liquids have different boiling points.

Now, let's answer each question:

a) Will the rum freeze if the temperature drops to -18 degrees Celsius?

To determine if the rum will freeze, we need to compare the freezing point of the solution to the given temperature (-18°C).

The freezing point of a solution depends on the alcohol and water concentrations. Alcohol lowers the freezing point of water, which means the freezing point of the rum will be lower than that of water alone.

Since the rum is 100 proof, it contains 50% ethyl alcohol by volume. To calculate the freezing point of the rum, we can use colligative properties. However, since we don't have the molality or weight percentages, we'll make an estimation.

Assuming the density of the rum is the same as water (1.00 g/ml), we can calculate the approximate freezing point using the formula:

Freezing Point = (0.00 - (0.789 * 0.5)) * 100

Where 0.789 is the density of ethyl alcohol and 0.5 is the volume fraction of ethyl alcohol in the rum. Evaluating this expression, we get:

Freezing Point ≈ -39.45°C

Since the given temperature is -18°C, which is warmer than the estimated freezing point of the rum, it will not freeze.

b) At what temperature does 100 proof rum boil?

To determine the boiling point of 100 proof rum, we need to compare it to the boiling point of pure ethyl alcohol. Pure ethyl alcohol boils at approximately 78.4°C.

Since the boiling point of alcohol is affected by its concentration, 100 proof rum will have a slightly different boiling point.

However, since water has a higher boiling point than alcohol, the presence of water in the rum will increase the boiling point. Therefore, the boiling point of 100 proof rum will be higher than 78.4°C.

Exact calculation of the boiling point requires precise measurements, but we can estimate it. Assuming the density of the rum is 1.00 g/ml, we can use the formula:

Boiling Point = (0.00 + (0.789 * 0.5)) * 100

Where 0.789 is the density of ethyl alcohol and 0.5 is the volume fraction of ethyl alcohol in the rum. Evaluating this expression, we get:

Boiling Point ≈ 39.45°C

So, the estimated boiling point of 100 proof rum is approximately 39.45°C.