# Avogadro's Principle

**Avogadro s Principle**, also known as Avogadro s Law, is one of the gas laws. **Avogadro s Principle** states that equal volume of mass at the same temperature and pressure contain the same number of molecules. This principle can be expressed in mathematical terms as *volume/amount of gas = proportionality constant.*

Alright. Avogadro did several experiments when dealing with the concept of the molar. Remember he is the one who came up with the number 6.02 times 10 to the twenty third. He also came up with several other things, one dealing with gas particles. Here's Avogadro's principle. And it states that equals volumes of gases at the same temperature and pressure contain equals number of particles. Alright. What does that mean? How can we break that down?

Okay. Let's say we have a container and we have one mole of I don't know. Let's say something small. Helium gas. Okay, and the temperature's 273 kelvin and one atmosphere or 101.3 kilo pascals or 760 milimetres mercury. These are all the same just different units of pressure. Okay, let's see with one mole of helium. We're going to say at these conditions, he found that one mole of this is actually 22.4 liters. But let's say we change it. Let's say we take out the small helium, put in something really really large. Let's say you put in something like iodine. Iodine's extremely large compared to helium.

Well, he also found at this conditions, matter of fact it's actually 22.4 liters also. How can that be? Well, it's because gas particles are atoms in general, are so so so small compared to the container that holds it that it doesn't matter if they're large or small. Relatively, they are all the same compared to the massiveness of the container that holds it. So let's talk about how why that's important and how they can move on.

We're going to call this volume the molar volume. It's a volume that one mole of any gas, don't forget, it doesn't matter whether it's a huge gas particle had tonnes and tonnes and tonnes of elements or if it's something that's very small such as helium. It doesn't matter. At these condition zero degree celsius, also known as 273 kelvin and what atmospheric pressure, we're going to call this condition STP which you might have heard of in class, standard temperature and pressure, that any gas at this conditions is going to be 22.4 liters. Anything, doesn't matter what it is.

What if I had two moles of that particular gas? Well, it would be 22.8 liters. what if I have half a mole of that particular gas? And I write, notice I didn't tell you what gas it was because it doesn't matter. It would be 11.2 liters. Okay. So how can we use this number when dealing with calculations? Okay. Let's do a problem. Let's calculate the volume that 4.5 kilograms of ethylene gas c2h4 will occupy at STP. Now, the only time I can ever use 22.4 liters is when my conditions are at STP. Otherwise you might have to calculate that particular volume using your gas laws that you've learned, that you might have learnt in class.

But I'd like to do, I'd like to do this problem. So we want to figure out the mo- how many moles of ethylene gas we have to figure out the molar volume. Well, we have 4.5 kilograms. I'm going to change that to grams, I don't like kilograms. So one kilogram is equal to 1000 grams. And see we have 4500 grams of ethylene, awesome. Okay. Let's then change these grams to moles. So we have 4500, 4500 grams and then my molar mass ethylene is 28. So we have 28 grams for every one mole. And so now I know that I have 160.71 moles of c2h4. Okay. So I look how many moles I have and at my conditions at STP, so what's my volume? Well, multiply by 22.4 liters because I know that it doesn't matter what gas it is. Any gas at STP is going to be 22.4 liters. So I'm going to say, okay. I'm going to multiply, I'm going to say in one mole of gas, we have 22.4 liters. I'm going to multiply these two together 160.71 times 22.4 liters. And I get 3600 liters-that's a lot-of ethylene gas at those conditions of STP.

So that is molar volume and it talks about how we can use this, we can use this volume in virtually everything as long as you're dealing with the conditions at STP.

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