Avogadro's Law

Avogadro's law talks about the relationship between the amount of gas in a gas sample and the volume of the gas sample, so what does that mean? First of all, a gas sample is just a fancy term that means a bunch of gas that we have anywhere. For example, this balloon has a lot of gas in it which is what keeps it inflated, so the gas here can be considered a sample of gas. This sample of gas the balloon has volume and occupies a certain amount of space that we can measure and there is also a certain amount of gas inside, but I talked about the relationship between these two things.

All I want to say is what happens when I change one of them, what happens with the other, so let's talk about this, let's imagine that I have my balloon and let's investigate. the relationship between these two bit variables, okay, here is a very quick drawing of the balloon, okay, let's talk about the relationship here, let's say I untie the knot at the end of the balloon and blow more air into it, which will increase the amount of gas that is in that balloon, so we will say that little n, the symbol that we use to indicate the amount of gas, the little n goes up, so the relationship what effect that change will have on the volume of the balloon, well, okay.

It's not exactly rocket science This is not exactly rocket science Let's make the volume of the balloon grow We increase the amount of air, the amount of gas inside the volume increases, so n increases and V also increases Okay, let's look at the opposite case. I untie it at the end of the balloon and let out a lot of gas, so in that case the little n will get smaller and what effect will that have on the balloon? volume of the balloon well, the balloon is going to shrink, it is going to occupy less and less volume and here is our little baby balloon, here the volume has gone down, so here there is a relationship when one of them goes up, the other goes up when one One of them goes down, the other goes down.

What is this type of relationship called? You may already know that this is what we call a direct relationship, it is when two variables move in the same direction and we can show this relationship with a graph here here on the X X I have the amount of gas that is in moles we will talk about that later , but this is how we measure the amount of gas in an amount of gas here and on the y axis I have volume as we increase the amount of gas, the volume increases Well, actually it turns out that if we double the amount of gas that is in a gas sample like a balloon, it also doubles the volume and the amount of space that gas sample takes up, so here's an avocado salad graph.

Well, now one thing is important. Keep in mind that when I was talking about the balloon I was changing only two things, right? The two things I was changing were the amount of gas, which was one of them, and the volume was the other. There are other things that I was not changing about that balloon, okay, while it was changing the amount of gas, it wasn't changing the temperature, okay, it's not like it was releasing gas and it was heating the balloon, you can't do that, the other thing is it wasn't changing. It wasn't changing the pressure, so it's not like I was inflating the balloon but then taking it to the top of Mount Kilimanjaro, where the air pressure is much lower than here at sea level, so it wasn't changing either. the pressure then we are talking about Avogadro's law the relationship between the amount of gas and the volume I can change any of them but I cannot change I cannot change the pressure or the temperature of that gas these are my constants these are my variables, it is okay, there's one thing I want to show you very quickly, and it's this device that we talked about a lot when we applied Avogadro's law, okay, you always see pictures of this in textbooks and stuff when we talk. about Avogadro's law so that's what I want to talk about for a minute and this is crazy okay it's a gas can that has a sliding lid and I made 100 I made a model of one out of a soda bottle , OK. and you can see how this works.

I have imagined that this is a container that contains gas and I have a pipe that goes in that I can add gas to and then you can see this top, imagine this top could slide up and down here, okay, so which one is the point of this? The reason we always see these guys and this is how they are usually drawn and we are talking about Avogadro's law is because they are a way of changing the volume of a gas sample without changing its pressure, this pipe here indicates something that could use to pump gas, so I imagine I pump gas here that would normally increase the pressure of a container, but not if the top can slide, instead the volume changes, so I add a little bit of gas and the top slides up and then I suck in some gas and the top falls back down instead of the pressure changing the top slides up and down, that's why you always see pictures of this type of thing, It's kind of a device that's a fancy gadget, but the point is simply that it's a gas canister with a sliding lid that can go up and down and that can change the volume of the canister as I change the amount of gas in it. here without changing a pressure is fine, so Avogadro's law is used a lot for mathematical problems and when we talk about mathematical problems with Avogadro's law, the form of the law that we generally use is n 1 divided by V 1 equals n 2 divided by V 2 this equation assumes that some type of change is occurring like the change I was talking about before.

I'm supposed to have an initial amount of gas, an initial volume which is before the change and then the amount of gas and the volume changes after I do something to it, okay? Let's solve this Avogadro's law by looking at a mathematical problem, so in a sample of gas, 50.0 grams of oxygen occupy 48 liters of volume keeping the pressure constant. Remember that this is important, not the law of God Rosa, the pressures must be constant, keeping the pressure constant. The amount of gas is changed until the volume is 79 liters. How many grams of gas are now in the container?

When I do problems like this, I find it very helpful to keep track of my variables by making a graph like this. my before and my after because we said there is a change, this little arrow takes place, we are moving from one to the other, let's clarify our variables before we insert something into this equation, so in a gas sample you take 50 grams. 40 liters, that's what we start with, okay, that means n1 I'm going to make those 50 point zero grams, that's that and the volume that says here that they take up 48 liters of volume, okay, so 48 liters is before of change, now here it is. the change keeping the pressure constant the amount of gas is changed until the volume is 79 liters ok that means my v2 will have a volume of 79 liters after the change and the question is how many grams of gas are now in the container After the change, I'm going to resolve n2, so now I have my variables clear.

I know what I'm going to solve and I know the others. Okay, now it's important to look at the units. There are two things to keep in mind when we apply Avogadro's law. This little n always has to be in correct moles. This is usually how we keep track of how much gas we have in a sample, so the amount of gas was given here. in grams, that's not going to work, we're going to have to convert it to moles and that's probably the biggest mistake people make when applying Avogadro's law: they don't remember to convert grams to moles, so hey, if you get a problem practice and you have n1 or n2 it's already in moles, you're all set, it's no big deal, you can skip this step, but if you have a practice problem like most of them, where the extremes are in grams, let's We have to convert it to moles, so we'll do that in a minute, the other thing is the v's, it doesn't matter what units the volume is in, as long as they're both in the same units, okay, so the leaders here, the leaders here they were established. if this was milliliters, milliliters, that would be fine too, but it wouldn't work if one was milliliters and the other was leading, okay, the units of volume don't matter as long as they're both the same, okay, so now I have my before and I have my after I'm going to change my fifty grams to moles and to do that I'm going to have to use the molar mass which tells us how much one mole of a gas weighs, so the molar mass for oxygen is 2 times 16 because each oxygen atom weighs 16 and then we do double that because there are two oxygens and we get 32.0 grams per mole.

Okay, now we want to go from grams, which is 50 point zero grams, and I want to multiply this by these grams per mole fraction in a way that cancels out the grams, so I'm actually going to want to flip this so that it has grams in the bottom so they cancel out, so I'm going to make a mole. divided by 32.0 grams, all I've done is turn this around. Now I have grams up here and grams down here, which means they cancel out. I will have moles left and the answer I get is one point six moles, so I can cross out my 50 grams and replace it with one point six moles.

Now I have my ends in moles. I got one of my ends and moles. I got both my volumes and my liters which is the same unit and now I'm ready to go. There are going to be two that I want to solve. I want to rearrange the equation to get n two by itself on one side of the equation, so to get n two by itself, I want to get rid of the V 2 that's in the denominator. Right now I'm going to multiply both sides of the equation by V two. Now I have V two on top of V two down here, which means they cancel and I'll be left with V 2 times n 1 divided by V 1. it's equal and some people like to have the variable that we're solving for on the left, so I'm going to change that real quick, but it doesn't make any difference, I'm just going to put it backwards here V 2 multiplied by N 1 divided by V 1 ok, now we're ready to take the variables that we've set here and plug them in to get n 2 equal a V 2 79 liters multiplied by n 11.6 moles divided by V 1, which is 48 liters and when I do that, the number I'll get is let me check here 2.6 and what my units will be.

The liters up here and the liters down here cancel out, so my final answer here is going to be two points. However, six moles are not done with the problem yet because my question here was asking how many grams of gas are now in a container, not how many moles of gas, so now I will have to take this number of moles and convert it back to grams, how am I going to do that? What I'm going to do is take the molar mass of oxygen again, which as we said before was thirty-two point zero grams per mole and I'm I'm going to take my mole number two point six moles and I want to multiply it by this conversion factor in a way Let me eliminate my moles so I can keep the conversion factor as it is now and I will have moles. in the top moles at the bottom, then two point six moles times thirty-two point zero grams divided by one mole now the mole at the top mole at the bottom cancel out and when I do the calculations two point six times thirty-two two I'm I'm going to get 83 grams, which I'm going to round to two significant figures because I have two sig figs here and three sig figs here.

I always use a smaller number, so I'll get 83 grams as my final answer. Avogadro's Law If you have questions about how to rearrange this law to solve for any of the other variables, I have made a video on that, check out my videos on rearranging gas equations. If you have any general questions about these gas laws, be sure to ask. Discover the gas laws, additional help, and an FAQ video that should clear up any other questions you have about this sort of thing.