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.

 

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.

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.

Colligative properties are defined as properties that depend entirely upon the ratio of the number of solute particles to the number of solvent particles. Only osmotic pressure and vapor pressure depression are examples of such phenomena. While color emission is a property of a solution, it depends on the chemical species involved, and not the number of particles.

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.

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.

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.

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.

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.

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.