By rearranging the ideal gas law, we can establish direct and inverse relationships between its variables. So here we have the ideal gas law formula which is PV=nRT. R is our gas constant. Because it's constant we don't have to relate it to the other variables. Next we have our variable chart and we'll see what effect happens to the other variables if pressure is increasing and volume is increasing. And then in our variable relationships, we'll take a look at different pairs of variables and see are they directly proportional or inversely proportional to one another?
All right. So first let's look at what happens when I increase pressure. Let's see what is the effect that it has on volume. Our equation is PV=nRT. We're not going to talk about nRT because we're looking strictly at the relationship between pressure and volume. Now to make them relate to one another, we're going to say that this is equal to a constant. Let's just say that it's one and we're going to bring the volume over to the other side. By doing that, we can see that the relationship is that pressure is equal to 1V. Pressure here is a numerator, Volume is a denominator. If you've watched my other videos in terms of direct and inverse relationships, realize that because they're on different levels, they're inversely proportional.
If volume is increasing and the top is staying constant, if volume is increasing, that means pressure would be decreasing. If volume is decreasing, pressure would be increasing. So coming back to our variables chart, we're going to say that the relationship is if we increase my pressure, that's going to decrease my volume because they have an inversely proportional relationship or opposite relationship. Now let's compare pressure and moles. OK, so pressure and moles ignore volume RT. So then this would just be pressure equals moles. They're both numerators, both on the same level. If I increase one, that's going to cause an increase in the other. So increasing pressure while keeping all the other variables out increases my moles. Since they're increasing or decreasing together, they are directly proportional.
Next, pressure equals temperature, right? Ignore volume, moles, and R because we're focusing only on pressure and temperature. Again, they're both numerators, so they both increase together, so they are directly proportional. All right, now that we've done that, let's look at volume, so volume. We're increasing volume, and we're trying to see what effect it has on my moles and my temperature here. So focus on only moles and volume. Ignore pressure, ignore RT. Volume in moles are on the same level with one another. They're both numerators, so increasing one would cause an increase in the other. Why? Because they are directly proportional.
And then finally volume equals temperature. At this point you've seen us do the other ones. Give yourself a second, pause the video if you want, and see what the relationship between volume and temperature would be. All right. Hopefully you've done that and realize that volume and temperature, both of them considered numerators, both on the same level. An increase in one will cause an increase in the other. Why? Because they too would be directly proportional. So these are the relationships that we can establish between the variables of the ideal gas law, and we can see that really only pressure and volume is where we would see an inverse relationship when doing these pairings of the variables. So keep this in mind if you're faced with any type of theoretical question where they're increasing or decreasing one variable and asking for the effect on another within the ideal gas law.
