What is pv=nrt

And we can measure that in terms of number of moles. And so that's what this lowercase n is. So let's think about how these four things can relate to each other. So let's just always put volume on the left-hand side. How does volume relate to pressure? Well, what I imagine is, if I have a balloon like this and I have some gas in the balloon, if I try to decrease the volume by making it a smaller balloon without letting out any other air or without changing the temperature, so I'm not changing T and n, what's going to happen to the pressure?

Well, that gas is going to, per square inch or per square area, exert more and more force. It gets harder and harder for me to squeeze that balloon.

So as volume goes down, pressure goes up. Or likewise, if I were to make the container bigger, not changing, once again, the temperature or the number of moles I have inside of the container, it's going to lower the pressure. So it looks like volume and pressure move inversely with each other.

So what we could say is that volume is proportional to one over pressure, the inverse of pressure. Or you could say that pressure is proportional to the inverse of volume. This just means proportional to. Which means that volume would be equal to some constant divided by pressure in this case. Now how does volume relate to temperature? Well, if I start with my balloon example, and you could run this example if you don't believe me, if you take a balloon and you were to blow it up at room temperature, and then if you were to put it into the fridge, you should see what happens.

It's going to shrink. And you might say, "Why is it shrinking? They have lower individual kinetic energies. And so in order for them to exert the same pressure to offset atmospheric pressure on the outside, you are going to have a lower volume. And so volume you could say is proportional to temperature. Now how does volume compare to number of moles?

Well, think about it. If you blow air into a balloon, you're putting more moles into that balloon. And holding pressure and temperature constant, you are going to increase the volume. So volume is proportional to the number of moles. If you were to take air out, you're also going to decrease the volume, keeping pressure and temperature constant. So we can use these three relationships, and these are actually known as, this first one is known as Boyle's law, this is Charles' law, this is Avogadro's law.

But you can combine them to realize that volume is going to be proportional to the number of moles times the temperature divided by the pressure.

Divided by the pressure. Or another way to say it is, you could say that volume is going to be equal to some constant, that's what proportionality is just talking about, is gonna be equal to some constant, let's call it R, times all of this business, RnT over P.

Over P. Or another way to think about it is we can multiply both sides by P. And what will you get? We will get P times V, this might be looking somewhat familiar to some of you, is equal to, and I'll just change the order right over here, n, which is the number of moles, times some constant times T, our temperature measured in kelvin.

And this relationship right over here, PV is equal to nRT, is one of the most useful things in chemistry. And it's known as the ideal gas law.

And in future videos we're going to apply it over and over again to see how useful it is. A value for R will be given you if you need it, or you can look it up in a data source. The SI value for R is 8. Note: You may come across other values for this with different units.

A commonly used one in the past was The units tell you that the volume would be in cubic centimetres and the pressure in atmospheres. Unfortunately the units in the SI version aren't so obviously helpful. The temperature has to be in kelvin. Don't forget to add if you are given a temperature in degrees Celsius. Calculations using the ideal gas equation are included in my calculations book see the link at the very bottom of the page , and I can't repeat them here.

There are, however, a couple of calculations that I haven't done in the book which give a reasonable idea of how the ideal gas equation works. If you have done simple calculations from equations, you have probably used the molar volume of a gas. You may also have used a value of These figures are actually only true for an ideal gas, and we'll have a look at where they come from.

And finally, because we are interested in the volume in cubic decimetres, you have to remember to multiply this by to convert from cubic metres into cubic decimetres. And, of course, you could redo this calculation to find the volume of 1 mole of an ideal gas at room temperature and pressure - or any other temperature and pressure. The density of ethane is 1. Calculate the relative formula mass of ethane. The volume of 1 dm 3 has to be converted to cubic metres, by dividing by We have a volume of 0.

Now put all the numbers into the form of the ideal gas equation which lets you work with masses, and rearrange it to work out the mass of 1 mole. Now, if you add up the relative formula mass of ethane, C 2 H 6 using accurate values of relative atomic masses, you get an answer of Which is different from our answer - so what's wrong?

The density value I have used may not be correct. I did the sum again using a slightly different value quoted at a different temperature from another source. This time I got an answer of So the density values may not be entirely accurate, but they are both giving much the same sort of answer. Ethane isn't an ideal gas. Well, of course it isn't an ideal gas - there's no such thing! So although ethane isn't exactly behaving like an ideal gas, it isn't far off.

If this is the first set of questions you have done, please read the introductory page before you start. Kinetic Theory assumptions about ideal gases There is no such thing as an ideal gas, of course, but many gases behave approximately as if they were ideal at ordinary working temperatures and pressures.

The assumptions are: Gases are made up of molecules which are in constant random motion in straight lines. The molecules behave as rigid spheres. Pressure is due to collisions between the molecules and the walls of the container. The temperature of the gas is proportional to the average kinetic energy of the molecules. And then two absolutely key assumptions, because these are the two most important ways in which real gases differ from ideal gases: There are no or entirely negligible intermolecular forces between the gas molecules.

Exploring the various terms Pressure, p Pressure is measured in pascals, Pa - sometimes expressed as newtons per square metre, N m You would have to divide a volume in dm 3 by , or in cm 3 by a million. Number of moles, n This is easy, of course - it is just a number. You will most often use the ideal gas equation by first making the substitution to give: I don't recommend that you remember the ideal gas equation in this form, but you must be confident that you can convert it into this form.