# Combined Gas Law

these are the three guest loves we've looked at so far they each assume that some sort of change has happened and they tell us how to variables relate to each other before and after the change right so like Boyle's law here has pressure and volume we make some sort of change in pressure or in volume and that tells us how the other one is going to respond it was sex law pressure and temperature and Charles law volume and temperature two variables always let's say that had a problem

like this let's say that I had like a balloon okay and it was a certain volume I wanted to increase the amount of air pressure that's pushing on that balloon and I wanted to cool that balloon way down and then I wanted to ask the question what is the new volume gonna be okay we can't use any of these three laws here because there are three variables here new pressure new temperature I want to make a colder and that's gonna cause a new volume so PV and teeth are gonna be variables

there so for that we use the

## combined

gas law which is sort of a combination of all three of these laws and you can see if I put it together its p1 times v1 that looks a lot like Boyle's law divided by t1 equals p2 times v2 divided by t2 so it's like all of these three rules put together in one law so that I can look at how these three variables respond to each other I could use this## combined

gas law to solve a problem like this I have a balloon is filled with air at sea level which isone point zero Tsar ATM's of pressure twenty five point zero degrees Celsius it's time to iraq and thrown in a cold body of water i tied to the rock so that it sinks down in the water if I didn't do it just float on the surface so tied to a rock throw it into coal body of water and it sinks to the point where the pressure is 4 degrees Celsius it gets colder and the pressure is the lemon atm so there's much more pressure pushing on this balloon what will its new pressure be so

I'm going to use this

## combined

gas law to figure this out first let's look at the variables that we already have and the variables that we're going to need to solve for okay a forty liter balloon that is v1 is filled with air at sea level so sea level pressure is one point zero zero ATM and temperature is twenty five point zero degrees Celsius but remember we're going to have to convert that to Kelvin temperature because we're dealing with gas we'll do that in the netthough it's tied to a rock blob a lot it seems to the point where the temperature is four degrees Celsius so we have t2 although we'll have to convert it to a calvin temperature and the pressure is 11.00 atm so that means that we have p2 what we're going to be solving for is v2 what will its new volume be okay so the first thing that we're gonna have to do is we're gonna have to rearrange the

## combined

gas law here so that we can solve for v2 here we go VG's on this sideso we want to get a loan so the first thing I'm gonna do is I'm going to multiply both sides by t2 to get t2 out of the out of the denominator all right times t2 here times t2 here since the t2 is on the top here and on the bottom here it cancels out and I can rewrite this as t2 times p1 times v1 divided by t1 equals p2 times v2 now again I want to get this P 2 out of the numerator here so that I can get v2 by itself so I'm gonna divide both sides of the equation by p2 that means

these two P twos are going to cancel out and my final rewritten equation with v2 isolated all by itself is going to be t2 times p1 times v1 divided by t1 P 2 equals V 2 as we've said before if you get a little bit uncomfortable with the idea of V 2 being on its own on the right side I'll just rewrite this so that can be a little bit easier V 2 on the left if that makes you comfortable equals t2 times p1 times v1 divided by t1 times p2 but all I've done here is I've flipped it

around okay so let's go about solving this the first thing I'm going to want to do is take these two Celsius temperatures and convert them to kelvins all right so I have twenty five point zero degrees Celsius plus 273 is going to give me 298 Kelvin and the other temperature that I have to convert is forty point zero degrees Celsius plus 273 and that's going to give me two 77 Kelvin all right so now that I have these temperatures in the right units to solve for the equation let's

go ahead and put these variables so we have v2 equals t2 t2 is this equals to 77 Kelvin times p1 the initial pressure which is one point zero zero ATM times v1 the initial volume forty point two zero liters okay we're going to divide that by t1 again in Kelvin 298 Kelvin which is multiplied by P to the second pressure which is 11.00 atm so I'm going to do that math and my final answer rounded to three significant figures is going to be three point three eight now what are my units here

okay Kelvin / Kelvin those cancel out ATMs / ATMs cancel out and I'm left with liters here so my final answer is going to be three point three eight liters that's rounded to three sing in figures because there are three significant figures are the lowest number of significant figures that I have in my answer so my final answer three point three eight leaders if you have trouble doing other

## combined

gas law problems you don't know quite how to rearrange this equation because it can bea little bit tricky take a look at the rearranging gas equations video where I show how to multiply and divide the variables to isolate one by itself on a certain side of the equation