Boiling point and vapor pressure inverse relationship of addition

Colligative Properties

boiling point and vapor pressure inverse relationship of addition

Vapor Pressure Depression, Boiling Point Elevation and Freezing Point This equation, which is known as Raoult's law, is easy to understand. Adding a solute to a solvent doesn't change the way the melting point Raoult found that the vapor pressure of the solvent escaping from a solution is proportional to the mole. The boiling point decreases as the vapour pressure increases. The addition of solute dilutes the solvent molecules and makes it harder for them to escape into the The Relationship Between Boiling Point Elevation and Vapor Pressure It is directly proportional to the molal concentration of the solution.

And so at any given time, although the average is here, there's some molecules that have a very low kinetic energy. They're moving slowly or maybe they have-- well, let's just say they're moving slowly. And at any given time, you have some molecules that have a very high kinetic energy, maybe just because of the random bumps that it gets from other molecules.

It's accrued a lot of velocity or at least a lot of momentum. So the question arises, are any of these molecules fast enough?

boiling point and vapor pressure inverse relationship of addition

Do they have enough kinetic energy to escape? And so there is some kinetic energy. I'll draw some threshold here, where if you have more than that amount of kinetic energy, you actually have enough to escape if you are surface atom. Now, there could be a dude down here who has a ton of kinetic energy. But in order for him to escape, he'd have to bump through all these other liquid molecules on the way out, so it's a very-- in fact, he probably won't escape. It's the surface atoms that we care about because those are the ones that are interfacing directly with the pressure outside.

So let's say this is the gas outside. It's going to be much less dense. It doesn't have to be, but let's assume it is. These are the guys that kind of can escape into the air above it, if we assume that there's some air above it.

How are vapor pressure and boiling point related? | Socratic

So at any given time, there's some fraction of the particles or the molecules that can escape. So you're next question is, hey, well, doesn't that mean that they will be vaporized or they will turn into gas? And yes, it does. So at any given time, you have some molecules that are escaping. Those molecules-- what it's called is evaporation. This isn't a foreign concept to you. If you leave water outside, it will evaporate, even though outside, hopefully, in your place, is below the boiling temperature, or the normal boiling temperature of water.

The normal boiling point is just the boiling point at atmospheric pressure. If you just leave water out, over time, it will evaporate.

What happens is some of these molecules that have unusually high kinetic energy do escape. They do escape, and if you have your pot or pan outside or, even better, outside of your house, what happens is they escape, and then the wind blows. The wind will blow and then blow these guys away. And then a few more will escape, the wind blows and blows them all away. And a few more escape, and the wind blows and blows them all the way.

So over time, you'll end up with an empty pan that once held water. Now, the question is what happens if you have a closed system?

Why is there an inverse relationship between boiling point and vapor pressure?

Well, we've all done that experiment, either on purpose or inadvertently, leaving something outside and seeing that the water will evaporate. What happens in a closed system where there isn't wind to blow away? So let me just draw-- there you go. Let's say a closed system, and I have-- it doesn't have to be water, but I have some liquid down here. And there's some pressure from the air above it. Let's just say it was at atmospheric pressure. It doesn't have to be.

So there's some air and the air has some kinetic energy over here. So, of course, do the water molecules. And some of them start to evaporate. So some of the water molecules that are up here in the distribution, they have enough energy to escape, so they start hanging out with the air molecules, right? Now something interesting happens.

This is the distribution of the molecules in the liquid state. Well, there's also a distribution of the kinetic energies of the molecules in the gaseous state.

Just like different things are bumping into each other and gaining and losing kinetic energy down here, the same thing is happening up here. So maybe this guy has a lot of kinetic energy, but he bumps into stuff and he loses it.

boiling point and vapor pressure inverse relationship of addition

And then he'll come back down. So there's some set of molecules.

boiling point and vapor pressure inverse relationship of addition

I'll do it in another set of blue. These are still the water-- or whatever the fluid we're talking about-- that come back from the vapor state back into the liquid state. And so what happens is, there's always a bit of evaporation and there's always a bit of condensation because you always have this distribution of kinetic energies.

At any given moment in time, out of the vapor above the liquid, some of the vapor loses its kinetic energy and then it goes back into the liquid state. Some of the surface liquid gains kinetic energy by random bumps and whatever else and goes into the vapor state.

And the vapor state will continue to happen until you get to some type of equilibrium. And when you get that equilibrium, we're at some pressure up here.

So let me see, some pressure. And the pressure is caused by these vapor particles over here, and that pressure is called the vapor pressure. I want to make sure you understand this. So the vapor pressure is the pressure created, and this is at a given temperature for a given molecule, right? Every molecule or every type of substance will have a different vapor pressure at different temperatures, and obviously every different type of substance will also have different vapor pressures.

For a given temperature and a given molecule, it's the pressure at which you have a pressure created by the vapor molecules where you have an equilibrium. Where you have just as many things vaporizing as things going back into the liquid state. And we learned before that the more pressure you have, the harder it is to vaporize even more, right?

We learned in the phase state things that if you are at degrees at ultra-high pressure, and you were dealing with water, you would still be in the liquid state.

So the vapor creates some pressure and it'll keep happening, depending on how badly this liquid wants to evaporate. But it keeps vaporizing until the point that you have just as much-- I guess you could kind of view it as density up here, but I don't want to think-- you have just as many molecules here converting into this state as molecules here converting into this state.

So just to get an intuition of what vapor pressure is or how it goes with different molecules, molecules that really want to evaporate-- and so why would a molecule want to evaporate? It could have high kinetic energy, so this would be at a high temperature. It could have low intermolecular forces, right? It could be molecular.

Obviously, the noble gases have very low molecular forces, but in general, most hydrocarbons or gasoline or methane or all of these things, they really want to evaporate because they have much lower intermolecular forces than, say, water. Or they could just be light molecules. You could look at the physics lectures, but kinetic energy it's a function of mass and velocity. So you could have a pretty respectable kinetic energy because you have a high mass and a low velocity.

So if you have a light mass and the same kinetic energy, you're more likely to have a higher velocity.

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  • Vapor pressure
  • How are vapor pressure and boiling point related?

You could watch the kinetic energy videos for that. But something that wants to evaporate, a lot of its molecules-- let me do it in a different color. Something that wants to evaporate really bad, a lot more of its molecules will have to enter into this vapor state in order for the equilibrium to be reached. Let me do it all in the same color. So the pressure created by its evaporated molecules is going to be higher for it to get to that equilibrium state, so it has high vapor pressure.

And on the other side, if you're at a low temperature or you have strong intermolecular forces or you have a heavy molecule, then you're going to have a low vapor pressure. For example, iron has a very low vapor pressure because it's not vaporizing while-- let me think of something.

Carbon dioxide has a relatively much higher vapor pressure. Much more of carbon dioxide is going to evaporate when you have it. Well, I really shouldn't use that because you're going straight from the liquid to the solid state, but I think you get the idea. And something that has a high vapor pressure, that wants to evaporate really bad, we say it has a high volatility.

You've probably heard that word before. So, for example, gasoline has a higher-- it's more volatile than water, and that's why it evaporates, and it also has a higher vapor pressure. Because if you were to put it in a closed container, more gasoline at the same temperature and the same atmospheric pressure, will enter into the vapor state. And so that vapor state will generate more pressure to offset the natural inclination of the gasoline to want to escape than in the case with water.

By itself, the change in the triple point is not important. But it results in a change in the temperature at which the solution freezes or melts. To understand why, we have to look carefully at the line that separates the solid and liquid regions in the phase diagram.

This line is almost vertical because the melting point of a substance is not very sensitive to pressure. Adding a solute to a solvent doesn't change the way the melting point depends on pressure.

The line that separates the solid and liquid regions of the solution is therefore parallel to the line that serves the same function for the pure solvent. This line must pass through the triple point for the solution, however. The decrease in the triple point that occurs when a solute is dissolved in a solvent therefore decreases the melting point of the solution.

The figure above shows how the change in vapor pressure that occurs when a solute dissolves in a solvent leads to changes in the melting point and the boiling point of the solvent as well. Because the change in vapor pressure is a colligative property, which depends only on the relative number of solute and solvent particles, the changes in the boiling point and the melting point of the solvent are also colligative properties.

The best way to demonstrate the importance of colligative properties is to examine the consequences of Raoult's law. Raoult found that the vapor pressure of the solvent escaping from a solution is proportional to the mole fraction of the solvent. Only the change in the vapor pressure that occurs when a solute is added to the solvent can be included among the colligative properties of a solution.

Because pressure is a state function, the change in the vapor pressure of the solvent that occurs when a solute is added to the solvent can be defined as the difference between the vapor pressure of the pure solvent and the vapor pressure of the solvent escaping from the solution. As more solute is dissolved in the solvent, the vapor pressure of the solvent decreases, and the change in the vapor pressure of the solvent increases. Because changes in the boiling point of the solvent TBP that occur when a solute is added to a solvent result from changes in the vapor pressure of the solvent, the magnitude of the change in the boiling point is also proportional to the mole fraction of the solute.

The equation that describes the magnitude of the boiling point elevation that occurs when a solute is added to a solvent is therefore often written as follows.

A similar equation can be written to describe what happens to the freezing point or melting point of a solvent when a solute is added to the solvent. A negative sign is used in this equation to indicate that the freezing point of the solvent decreases when a solute is added.

Values of kf and kb as well as the freezing points and boiling points for a number of pure solvents are given in the tables below.