okay in our last video we talked about gas pressure and we got on that subject by making some observations about the air that's inside of a balloon so I've got a red balloon and I'll give it a white string my balloon gets a string and then getting back to the the observations that we're talking about for example we said that pressure and the pressure inside the balloon was really a measure of the force attributed to all the gas particles colliding with the sides of the balloon walls so we've got our particles and they're colliding against the sides of our balloon and given that temperature is a measure of the energy of those particles motion we we said that increased temperature would mean increased pressure because if you think about it all those particles would be moving faster with greater temperature and and just like a speeding car would crash into a wall with more Force these these little particles once they get they they get bumping they exert more force and increase the pressure so written mathematically we would say that pressure and temperature are directly related as the temperature is increased so is the pressure now we also saw that as volume goes down the pressure goes up and again this makes sense because with less space to move around the particles will have more collisions with the wall so pressure will increase and again written mathematically this means that pressure is inversely related to volume so pressure is related to the inverse of volume because we see that as the volume is decreased the pressure is increased and then we also showed that increasing the number of moles of gas would increase the pressure because moles are just a measure of the number of particles so if we have more particles we have more collisions so again pressure is directly proportional to moles and N is the symbol for moles now based on these empirical observations which which means observations that we can actually see as opposed to just Theory we have the the composite formula if we put them together we see that pressure is directly related to the the moles and the temperature and inversely related to volume and so we have this composite formula p is directly related to NT over V and we can make this composite formula an equation if we add a constant we could call the constant anything but we'll call it R and that'll give us p is equal to R time and that's our constant time NT over V and so if we multiply both sides by V and do just a little bit of rearranging we're going to get a pretty important equation called the ideal gas equation which is PV is equal to nrt so PV equals nrt and we call this the ideal gas equation so ideal gas equation and if you're like me you're probably immediately curious about what that blue R is and don't worry I'm going to show you how we derive that in the next video but for now I just want you to enjoy how profound this equation is and and think about what we can do with it for example if we know the pressure and the volume and and we know the temperature we can use this formula to find the number of particles that are in the system and if we know the the number of particles and we know the volume and the temperature we can find the pressure and if we know the the number of particles and we know the volume and and we know the pressure then we'd be able to solve for the temperature and it's pretty incredible and and this is true for any ideal gas so the next kind of obvious question is what's an ideal gas well an ideal gas is one that obeys three conditions the first condition is that the molecules can't exhibit any intermolecular forces so no intermolecular intermolecular forces and we make this condition because um because if there were intermolecular forces it would interfere with our assumption that all of our kinetic energy is completely directed to the pressure so that's our first condition and and the second condition is that the molecules occupy no microscopic volume and other words the molecules are Point masses and have no volume and we make this condition because in our equation here moles and volume are directly related n is directly related to V but if our particles take up space then as they're added the containers volume would actually go down instead of going up but the particles are extremely tiny so kind of assuming their point masses isn't that far-fetched and it allows our equation to to make sense so this is an ideal gas no volume now the third condition is that all collisions are perfectly elastic so collisions are perfectly perfectly elastic because again we need to assume that none of our kinetic energy is loss in the collisions of these particles so we make these three conditions and and while no gases are actually ideal the ideal gas equation does get us some pretty close approximations and it helps us answer lots of questions especially those related to kind of the before and after conditions when when we're changing some of these values for a gas so next up I'm going to explain a little bit more about the ideal gas constant and we'll kind of dig into this r value and then we're going to move forward with some specifics about the ideal gas equation