# Combined Gas Law

The **Combined Gas Law** combines Charles Law, Boyle s Law and Gay Lussac s Law. The **Combined Gas Law** states that a *gas pressure x volume x temperature = constant*.

Alright. In class you should have learned about the three different gas laws. the first one being Boyle's law and it talks about the relationship between pressure and volume of a particular gas. The next one should be Charles law which talks about the volume and temperature of a particular gas. And the last one should be Gay Lussac's law which talks about the relationship between pressure and temperature of a particular gas. Okay. But what happens when you have pressure, volume and temperature all changing? Well, we're actually going to combine these gas laws to form one giant gas law called the combined gas law. Okay.

If you notice then these three gas laws the pressure and volume are always in the numerator. So we're going to keep them on the numerator. p1v1. And notice the temperature is in the denominator over t1. So all these things are just squished into one and then p2v2 over t2. Okay. So this is what we're going to call the combined gas law. So let's actually get an example and do one together.

Alright, so I have a problem up here that says a gas at 110 kilo pascals and 33 celsius fills a flexible container with an initial volume of two litres, okay? If the temperature is raised to 80 degrees celsius and the pressure is raised to 440 kilo pascals, what is the new volume? Okay. So notice we have three variables. We're talking about pressure, temperature and volume. Okay, so now we're going to employ this combined gas law dealing with all three of these variables. So we're going to look at our first, our first number 110 kilo pascals and that's going to, that is the unit of pressure. So we know that's p1. Our p1 is 110 kilo pascals, at 30 degree celsius. I don't like things with celsius so I'm going to change this to kelvin. So I'm going to add 273 to that which makes it 303 kelvin. That's our temperature. And my initial volume is two litres so I'm going to say v1=2 litres. Okay then I continue reading. If the temperature is raised at 80 degree celsius, again we want it in kelvin, so we're going to add 273 making it to 353. So our t2 is 353 kelvin and the pressure increased to 440 kilo pascals, the pressure p2 is equal to 440 kilo pascals which I'm very happy that I kept it in kilo pascals that I kept it in kilo pascals. I've got to make sure these units are the same because pressure can be measured in several different units. I'm going to make sure all units are the same. And what is the new volume? So our v2 is our variable, what we're trying to find. Okay.

So let's basically plug all these variable in into our combined gas law to figure out what the new volume would be. Okay. So I'm going to erase this and say our pressure one is 110 kilo pascals. Our volume one is two litres. Our temperature one is 303 kelvin. Our pressure two is 440 kilo pascals. We don't know our volume so we're just going to say v2 over 353 kelvin. Okay. When I'm looking for a variable I'm going to cross multiply these guys. So I'm going to say 353 times 110 times 2 and that should give me seven, 77660, if you put that in a calculator. So I just cross multiply these guys. And I cross multiply these guys 303 times 440 times v2 gives me 133320v2. Okay, so then I want to get my, I want to isolate my variable, so I'm going to divide 133320. 133320. And I find that my new volume is 0.58. 0.58 metres. And that is how you do the combined gas law.

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