Colligative Properties - MCAT Chemical and Physical Foundations of Biological Systems

The local atmospheric pressure at 13,000 feet is less than the pressure at sea level; therefore, it takes less heat to make the vapor pressure meet the local atmospheric pressure. Heat added to the system easily exits again as the water is converted to steam, leaving less heat in the water to cook the food. Food cooks more slowly as a result.

Adding solute to water will result in boiling point elevation due to the presence of more molecules. Change in temperature is given by the relation , where is a constant for the solvent, is the solution molality, and is the van't Hoff factor. In this example, the molalities are equal.

Since dissociates into and , , representing the two ions derived from each molecule. For glucose , as the molecule does not dissociate. Solution 1 will have a higher elevation in temperature due to the greater number of ions in solution.

Boiling point elevation is a colligative property, meaning that it depends on the relative number of solute particles in solution. The answer choice with the largest number of moles of particles will show the greatest boiling point elevation. The equation for boiling point elevation is:

Molality is equal to moles of solute per kilogram of solvent, meaning that it will be proportional to the moles of solute added. Each solute is added to equal amounts of water, allowing us to keep this value constant. Similarly, will be constant for all of the solutions. Overall, boiling point elevation will be proportional to the moles of solute multiplied by the van't Hoff factor.

Using this proportion, we can find the solute that will most impact the boiling point of water.

Since sodium chloride results in the greatest moles of ions in solution, it will yield the greatest boiling point elevation.

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.

In order to answer this problem, consider the equation for boiling point elevation: .

is a specific constant for the boiling substance, so it will not change between the solutions (they are all aqueous). Molality is designated as "m", and a high molality will result in a higher boiling point, however, the value we want to look at for this problem is , which is also known as the van't Hoff factor. The van't Hoff factor is the number of particles that a single solute will dissociate into when added to a solution. MgCl2 will dissociate into three particles: 1 Mg2+ cation and 2 Cl- anions. Since 2m of MgCl2 has the highest molality as well as the largest van't Hoff factor out of the options, it will result in the highest boiling point.

If there is ion pairing taking place in a solution, the van't Hoff factor will be slightly lower than predicted. As a result, the boiling point will not be as elevated as it would be if all of the ions were separated from each other. This conclusion can be draw from the given equation, . The number of particles in the solution does not affect the molality.

Based on the equation , we see that there are two factors that differ between the containers and can affect the elevation of the boiling point: molality and the van't Hoff factor ().

The sodium choride added to container 1 has a molality of 2, as well as a van't Hoff factor of 2. As a result, we are looking for a compound that has a larger combination of these two factors, which would cause a higher boiling point. 2m CaF2 has a molality of 2 and a van't Hoff factor of 3. Since this combination of factors in container 2 would be higher than the combination in container 1, we can conclude that this was the mystery compound added to the container with the higher boiling point.

Note that C6H12O6 is the formula for glucose, and will not ionize in solution.

Colligative properties are dependent only on the number of particles in a solution, and not their identity. Some examples of colligative properties are vapor pressure, boiling point, freezing point, and osmotic pressure.

There is a direct relationship between the boiling point elevation and the number of particles present in a solution. The more particles that are present in solution, the higher the boiling point elevation.

We are looking for the compound that will create the greatest number of ions when dissolved in solution.

Sodium chloride and magnesium sulfate will produce two ions per mole.

Magnesium chloride and barium chloride will produce three ions per mole.

Calcium hydroxide will also produce three ions per mole, but we are given two moles instead of one.

Calcium hydroxide will produce the greatest number of ions, thus creating the greatest increase in boiling point elevation.

We first need to find the boiling point elevation with the equation:

Ammonium phosphate has an van't Hoff value of four; each molecule dissociates into four ions in solution. To calculate the molality, we need to find moles of solute per kilogram of solution.

Next, use the molality, van't Hoff factor, and boiling point elevation constant to solve for the increase in boiling point.

Add this increase to the boiling point of pure water to find the boiling point of the solution.

Boiling point elevation depends on three variables: the boiling point elevation constant of the solvent, the van't Hoff factor of the solute, and the molality of the solution. In this question, molality is held constant.

First, calculate the van't Hoff for each compound.

Ultimately, we are looking for the greatest product of the boiling point elevation constant and van't Hoff factor (since molality is constant).

Magnesium phosphide has the greater van't Hoff factor and acetic acid has the greater boiling point elevation constant. A solution of magnesium phosphide in acetic acid will thus have the greatest boiling point elevation.

When a nonvolatile solute is added to a solvent, it will not contribute to the molecules which exert pressure on the container. It will, however, take up some of the surface area interacting with the air in the container. This reduces the number of solvent molecules that are able to break from their bonds and become gas molecules in the container. The reduction of vapor pressure is dependent on the percentage of solute molecules in the solution. Since 5% of the molecules in this solution come from the solute, the vapor pressure will be 95% of the pure solvent's vapor pressure.

Recall that the boiling point of a solution depends on the number of ions in the solution and the concentration of the solution. Increase in both of these factors will elevate the boiling point to higher temperatures. The equation describing this is given below.

where is change in boiling point, is the boiling point elevation constant, is the number of ions, and is the molality. Sodium chloride, or , will produce two ions in solution whereas calcium chloride, or , will produce three ions. If the concentrations were the same, the calcium chloride solution would have a higher boiling point; however, since we are not given the concentration we cannot determine the relative boiling points of the solution.

Recall that adding solutes to a solution increases the boiling point. This phenomenon is called the boiling point elevation. Knowing this information, we can eliminate two choices immediately. The equation to calculate the boiling point elevation is as follows.

where is change in boiling point, is the boiling point elevation constant, is the number of ions, and is the molality. The question gives us the concentration in molarity; therefore, we need to convert the concentration to molality.

Molarity =

Molality =

We need to find the mass of solvent in kilograms. The molarity is ; therefore, let’s assume we have of solute and of solution. The density of the solution is or . We can calculate the mass of the total solution using density.

mass of total solution =

We need the mass of the solvent only. To find this, we need to first calculate the mass of solute. The MW of potassium bromide is (this can be calculated by obtaining values from the periodic table). We have of solute; therefore, the mass of solute is

This means that the mass of solvent is equal to:

mass of solvent = total mass of solution - mass of solute = =

Molality of solution is

, or the number of ions, for is 2 (because will produce two ions in solution). Now we have all the information to calculate the boiling point elevation.

Therefore, boiling point increases by .

Freezing point depression is given by the equation .

i is the Vant Hoff Factor that tells us how many particles (often ions) a solid produces when dissolved in solution. m is the molality of the solution. kf is the freezing point constant.

The question gives us m as 3mol, kf as 1.9, and i is found to be 3 (2K+ and SO42- ). Whe then plug the values into the equation.

The key to understanding this problem is realizing that it is asking about freezing point depression, or colligative properties. The main factor that concerns freezing point depression is the number of particles in solution, rather than other features, such as size or weight. The more solute dissolved, the greater the freezing point depression will be, meaning that a colder temperature will be needed for a solution to freeze.

In our answer choices we are looking for the solute that is dissociate into the greatest number of ions, or has the highest van't Hoff factor. Magnesium chloride and calcium bromide both generate three moles of ions per mole of solute. The answer choice with magnesium chloride is more concentrated, however, making this the correct option.

Freezing point depression is a colligative property, meaning that it depends on the amount of particles present in solution. The more ions that a solute dissociates into, the larger the magnitude of freezing point depression. Here, we're looking for the smallest amount of depression, so we want to find the solute that dissociates into the fewest particles. The answer is glucose, which is not ionic and does not dissociate at all in solution.

This question asks us to consider what would happen to the freezing point (also known as the melting point) of the solution if a polar molecule were added, for exampl adding NaCl to water. More directly, this question is a freezing point elevation/depression problem. After we determine what would happen to the freezing point of the solution, we can predict the change in the slope of the line.

The formula for freezing point depression is given below.

kf is the cryoscopic constant that says how easily a solution freezes with a given change in temperature, m is the molality of the solution, and i is the Vant Hoff factor. (The Vant Hoff factor is the number of ion particles per individual molecule that has been added; i.e. for NaCl this is 2 because it will separate into exactly two ionic particles when dissociated).

Given that kf and b will be constants for a given solution, we know that adding a molecule will decrease the freezing point because i has some positive value. Now that we know the freezing point is depressed (lowered), how will the slope of the line change?

At the same pressure, a lower temperature will be required for the solution with the added polar molecule to freeze, thus the slope will be less negative (segment AD will look more flat on the graph).

Why does the added molecule have to be polar to have an effect? First, notice that we are told that the phase diagram is of a polar solution. Next, let’s look at the i factor. i only has a value if the added molecules can be dissolved in the original solution. If, for example, we added a nonpolar molecule, it could not be dissolved by the solution and will not contribute to depressing the freezing point. “Like-dissolves-like” also applies here; the freezing point will only change if the solution and molecule added are both polar or both nonpolar.

Freezing-point depression is a colligative property and is calculated with the formula:

The van't Hoff factor, , represents the number of particles a compound will dissociate into when dissolving in a solution. is the freezing-point depression constant, which is given in the question. is molality.

Using the equation, we can calculate the freezing point depression using the values from the question.

The standard freezing point of water is . With the freezing point depression, the solution will freeze at

Freezing-point depression is a colligative property and is calculated with the formula:

The van't Hoff factor, , represents the number of particles a compound will dissociate into when dissolving in a solution. is the freezing-point depression constant, which is given in the question. is molality.

Using the equation, we can calculate the freezing point depression using the values from the question.

The standard freezing point of water is . With the freezing point depression, the solution will freeze at .