Vapor Pressure Lowering (Raoult's Law): Videos & Practice Problems

Vapor pressure lowering is a phenomenon where the addition of a solute to a solvent reduces the vapor pressure of the resulting solution compared to the pure solvent. This effect is quantified by the formula:

P_solution=X_solvent⁢P°_solvent⁢i which accounts for the number of particles the solute dissociates into. It's important to note that the vapor pressure of the solution is always lower than that of the pure solvent due to the presence of the solute. Understanding this concept is crucial for calculations involving colligative properties and helps explain how solutes affect the physical properties of solutions.

Raoult's Law and Vapor Pressure

Raoult's law is essential for understanding vapor pressure lowering, which refers to the decrease in vapor pressure of a solvent when a solute is added. Vapor pressure is defined as the pressure exerted by a gas in equilibrium with its liquid phase at a specific temperature within a closed system. It is crucial to note that vapor pressure is the pressure exerted by the gas at the surface of the liquid, where both condensation and vaporization occur at equal rates.

The formula for calculating vapor pressure lowering is given by:

\[P_{\text{solution}} = \chi_{\text{solvent}} \times P^{\circ}_{\text{solvent}}\]

In this equation, \(P_{\text{solution}}\) represents the vapor pressure of the solution, \(\chi_{\text{solvent}}\) is the mole fraction of the solvent, and \(P^{\circ}_{\text{solvent}}\) is the vapor pressure of the pure solvent, denoted with a degree symbol to indicate its purity.

To calculate the mole fraction of the solvent, the formula can be expressed as:

\[\chi_{\text{solvent}} = \frac{n_{\text{solvent}}}{n_{\text{solvent}} + i \cdot n_{\text{solute}}}\]

Here, \(n_{\text{solvent}}\) is the number of moles of the solvent, \(n_{\text{solute}}\) is the number of moles of the solute, and \(i\) is the van 't Hoff factor, which accounts for the number of particles the solute dissociates into in solution. This factor is crucial in colligative properties, as it influences the overall effect of the solute on the solution's properties.

It is important to remember that the addition of a solute always results in a vapor pressure that is lower than that of the pure solvent, meaning:

\[P_{\text{solution}} < P^{\circ}_{\text{solvent}}\]

This principle is fundamental when performing calculations related to vapor pressure lowering, as it highlights the impact of solute addition on the vapor pressure of a solution.

Vapor Pressure Calculation Example

To calculate the vapor pressure of a solution containing cadmium nitrate and water, we first need to determine the number of moles of each component. The molecular weight of cadmium nitrate is 236.43 grams per mole. Given that we have 53.7 grams of cadmium nitrate, we can calculate the moles of cadmium nitrate as follows:

\[\text{Moles of Cadmium Nitrate} = \frac{53.7 \text{ grams}}{236.43 \text{ grams/mole}} \approx 0.22713 \text{ moles}\]

Next, we calculate the moles of water. The molecular weight of water is 18.016 grams per mole, and we have 155 grams of water:

\[\text{Moles of Water} = \frac{155 \text{ grams}}{18.016 \text{ grams/mole}} \approx 8.60346 \text{ moles}\]

Now, we can find the vapor pressure of the solution using Raoult's Law. The formula for the vapor pressure of the solution is:

\[P_{\text{solution}} = \left( \frac{n_{\text{solvent}}}{n_{\text{solvent}} + i \cdot n_{\text{solute}}} \right) \cdot P^0_{\text{solvent}}\]

In this case, the solvent is water, and the solute is cadmium nitrate. Cadmium nitrate dissociates into three ions in solution: one cadmium ion and two nitrate ions, giving us \(i = 3\). Therefore, we can substitute the values into the equation:

\[P_{\text{solution}} = \left( \frac{8.60346 \text{ moles}}{8.60346 \text{ moles} + 3 \cdot 0.22713 \text{ moles}} \right) \cdot 131.8 \text{ torr}\]

Calculating the denominator:

\[8.60346 + 3 \cdot 0.22713 \approx 8.60346 + 0.68139 \approx 9.28485 \text{ moles}\]

Now substituting back into the vapor pressure equation:

\[P_{\text{solution}} = \left( \frac{8.60346}{9.28485} \right) \cdot 131.8 \approx 122 \text{ torr}\]

Thus, the vapor pressure of the solution is approximately 122 torr, rounded to three significant figures, consistent with the significant figures of the given data (53.7 grams and 155 grams).

How many grams of glucose, C₆H₁₂O₆, must be added to 515.0 g of water to give a solution with a vapor pressure of 13.2 torr at 20.0ºC? The vapor pressure of pure water at 20.0ºC is 17.5 torr.

• A. 9.54 × 10² g
• B. 1.68 × 10³ g
• C. 5.29 g
• D. 9.31 g

Answer: (B)

Determine the vapor pressure lowering associated with 1.32 m C₆H₁₂O₆ solution (MW:180.156 g/mol) at 25°C. The vapor pressure of pure water at 25°C is 23.8 torr.

• A. 0.553 torr
• B. 27.6 torr
• C. 23.2 torr
• D. 0.976 torr

Answer: (C)

The vapor pressure of water at 100.0ºC is 0.720 atm. Determine the mass percent of iron (II) chloride, FeCl₂, needed to reduce its vapor pressure to 0.655 atm. (MW of FeCl₂ is 126.756 g/mol)

• A. 67.7%
• B. 18.9%
• C. 22.5%
• D. 58.3%

Answer: (B)

Here’s what students ask on this topic:

What is Raoult's law?

Raoult's Law is a principle in chemistry that relates the vapor pressure of a solution to the concentration of the solute. According to Raoult's Law, the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solvent. In other words, adding a non-volatile solute to a solvent decreases the solution's vapor pressure proportionally to the amount of solute added.

The law can be mathematically expressed as:

$P_{\text{solution}}=X_{\text{solvent}}\cdot P_{\text{0 solvent}}$

Here, Psolution is the vapor pressure of the solution, Xsolvent is the mole fraction of the solvent in the solution, and P0 solvent is the vapor pressure of the pure solvent.

Raoult's Law is particularly applicable to solutions where the interactions between molecules of different components are similar to the interactions between molecules of the same components, which is characteristic of ideal solutions. It is fundamental in the study of colligative properties, which are properties that depend on the ratio of solute to solvent particles, such as boiling point elevation and freezing point depression.

What is the equation for Raoult's law?

Raoult's Law describes the relationship between the vapor pressure of a solvent and the presence of a non-volatile solute in an ideal solution. The equation for Raoult's Law is expressed as:

$P=P_0\cdot X_1$

In this equation:

• $P$ represents the vapor pressure of the solution.
• $P_0$ is the vapor pressure of the pure solvent.
• $X_1$ is the mole fraction of the solvent in the solution.

The law states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solvent. It's important to note that Raoult's Law applies to ideal solutions, where the interactions between different particles are similar to those present in the pure substances, and it is most accurate for solutions with non-volatile solutes and volatile solvents.