# GRE Subject Test: Chemistry : Colligative Properties

## Example Questions

### Example Question #5 : Physical Chemistry

What is the freezing point of a 2M solution of  in water?

Explanation:

First, we need to calculate the molality because that is what we use in our equation for freezing point depression. We can get that from the molarity without knowing exactly how many liters or grams we have. We just have to know what we have one mole per liter. The weight of water is one kilogram per liter, so this allows us to make this conversion.

The molality is 2m. The van't Hoff factor is 3, as we get one calcium ion and two chloride ions per molecule during dissociation.

We can now plug the values into the equation for freezing point depression.

This gives us our depression of .  The normal freezing point of pure water is , which means our new freezing point is .

### Example Question #1 : Colligative Properties

How much sodium chloride has been added to four liters of water if the freezing point of the solution is ?

Sodium chloride has a molar mass of .

Explanation:

We can determine how much sodium chloride was added to the water using the freezing point depression equation.

The normal freezing point of wtaer is 0 degrees Celsius, so we know that the temperature of the solution has changed by 2.5 degrees. Since sodium chloride will generate two ions per molecule in solution, the van't Hoff factor will be 2. Based on the density of water, we can determine that 4 liters of water weighs 4 kilograms.

### Example Question #6 : Physical Chemistry

Two moles of sodium chloride (NaCl) are added to 1kg of a mystery solvent. The addition of the NaCl caused an increase of 6K to the solvent's boiling point.

Based on this information, what is the boiling constant for the solvent?

Explanation:

In order to solve this problem, we can use the boiling point elevation equation: .

We know the temperature change, we can compute molality from the given information, and we know the van't Hoff factor (expected to be 2 in this scenario due to NaCl becoming 2 ions in solution). We can calculate the boiling point constant for the solvent.

### Example Question #1 : Colligative Properties

What is the boiling point of a solution composed of three liters of water and 50 grams of sodium chloride?

The molar mass of sodium chloride is .

Explanation:

We can use the boiling point elevation equation in order to determine the new boiling point once the salt has been added:

Since sodium chloride will form two ions for each molecule in solution, the value for the van't Hoff factor will be 2. In addition, the mass of the water in the solution will be 3 kilograms, which can be determined by using the density of water.

Since water boils at 100 degrees Celsius, this means that the final boiling point of the solution is 100.29 degrees Celsius.

### Example Question #1 : Colligative Properties

The vapor pressure of water at 25 degrees Celsius is 22.8mmHg. If three moles of a nonvolatile solute are added to twelve moles of water, what is the new vapor pressure of the solution?

A nonvolatile solute will not change the vapor pressure.

Explanation:

Since the solute is nonvolatile, it does not have an additive vapor pressure, but it will lower the vapor pressure due to taking up surface space in the solution. Using Raoult's law, we can determine the new vapor pressure of the solution:

Here,  is the molar fraction of the water, and  is the original vapor pressure of the water. Since 3 moles of solute were added, water now makes up 80% of the moles in the solution:

### Example Question #11 : Physical Chemistry

At 25 degrees Celsius, methanol has a vapor pressure of 95mmHg, and toluene has a vapor pressure of 300mmHg.

What is the vapor pressure of a solution that is 30% methanol and 70% toluene?

Assume that the solution is ideal.