Vapor Pressure Lowering (Raoult's Law) - Online Tutor, Practice Problems & Exam Prep

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.

Vapor Pressure Lowering Concept 1

Raoult’s law deals with vapor pressure lowering. Here we're going to say that vapor pressure is the pressure exerted by a gas that has an equilibrium with its liquid phase at a specific temperature within a closed system. Now here if we were to look at vapor pressure and Reynolds law, we're going to say here vapor pressure is the pressure exerted by a gas at the surface of a liquid. So remember, this orange portion represents the surface of the liquid. We have gases already dissolved within.

My solution and we have gases above it. Remember, under vapor pressure we have both condensation and vaporization happening at the same rate. The vapor pressure is just the pressure that results from that on the surface of the water. Now vapor pressure lowering comes with its own formula and that is the pressure of our solution equals the mole fraction of our solvent. And since it's the mole fraction of our solvent here that would be moles of solvent on top.

We're customizing mole fraction with solute on top with vapor pressure. It's not that it's solvent on top now divided by I. Remember, I is your Van Hoff factor and I is associated with our solute. So it would be I times our moles of solute plus moles of solvent. Now look at how it's written. The I and the moles of solute are what are multiplying each other, not the moles of solvent. Moles of solvent are off to the side. All right. And then here.

So that's the mole fraction of solvent times the pressure of our pure solvent. And to show that it's pure, we put that little degree above. So here this is our formula for vapor pressure lowering. Now if we look at all the variables, this equals the pressure after adding solute to solvent. So that would be the pressure of our solution because remember solute and solvent together equals a solution where we talked about I being the Van Hoff factor.

If you're not familiar with that variable, take a look back on some of my videos dealing with the colligative properties, this being one of them. In the colligative properties section we talk about the Van Hoff factor. Next we have mole fraction of our solvent which is XSOLV and then pressure of our pure solvent is pressure degree solvent here on the bottom. Now here we're going to say since adding solute lowers the vapor pressure, that means that the pressure of my solution is always less than the pressure of my pure solvent. So that's just a piece of information should always keep in mind when dealing with different calculations with vapor pressure lowering.

Vapor Pressure Lowering Example 1

Calculate the vapor pressure in Tor of a solution containing five 3.7 grams of cadmium nitrate, which has a molecular weight of 236.43 grams per mole in 155 grams of water at 30°C. Here we're told the vapor pressure of pure water at this temperature is 131.8 Taurus. All right. So first what we're going to do is we're going to calculate the moles of both cadmium nitrate as well as water.

So we have 53.7g of cadmium nitrate and we're told for everyone mole of cadmium nitrate we have 236.43g. So here when we plug that in, that's going to give me moles of 0.22713 moles of cadmium nitrate, and then we're going to do the same thing with water. We have 155 grams of water for everyone mole of water. Its mass is 18.016g, so that equals 8.60346 moles of water.

With that we can now figure out the pressure of our solution. So pressure of solution equals the moles of our solvent, so 8.60346 moles of water divided by I is the number of ions your solute will break up into in solution. Cadmium nitrate is ionic, so it breaks up into one cadmium ion +2 nitrate ions. So that's a total of 3 ions. So I = 3. So three times the moles of cadmium nitrate, which is 0.22713 moles plus the moles of water again, OK.

And then that's going to be multiplied by R 131.8 Tors. So when we do that, we're going to get, as our final answer, 122 tours for our solution here, our answer has three sig figs, because 53.7 is 3 sig figs and 155 also has three sig figs.

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

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

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%

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.