Combined Gas Law

These are the three guest loves we've seen so far, each assumes that some kind of change has occurred and tells us how the variables relate to each other before and after the change, so, like Boyle's law, here we have pressure and volume. make some type of change in pressure or volume and that tells us how the other is going to respond, it was the sexual law, pressure and temperature, and Charles's law, volume and temperature, two variables, always Let's say you had a problem like this, let's say I had like a balloon, okay and it had a certain volume.

I wanted to increase the amount of air pressure that pushes that balloon and I wanted to cool that balloon down and then I wanted to ask the question: what will the new volume be? 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 refrigerator and that will cause a new volume, so PV and teeth will be variable there, so that's what we use the combination for. gas law, which is kind of a combination of these three laws and you can see if I put them together it is p1 multiplied by v1 which looks a lot like Boyle's law divided by t1 is equal to p2 multiplied by v2 divided by t2, so it's like all these three rules put together into one law to be able to see how these three variables respond to each other.

You could use this

combined

gas law to solve a problem like this. I have a balloon filled with air at sea level, which is at point zero. Tsar ATM's pressure twenty five point zero degrees Celsius, it's time for Iraq and they threw it into a mass of cold water, I tied it to the rock so it would sink in the water, if it didn't it would just float on the surface, so was tied to A stone he throws it into a mass of water of coal and it sinks to the point where the pressure is 4 degrees Celsius, it cools and the pressure is the atmosphere of lemon, so there is much more pressure pushing this balloon, what will be its new pressure?

I'm going to use this

combined

gas law to solve this. First, let's look at the variables we already have and the variables we're going to need to solve. Well, a forty liter balloon that is v1 is full of air at sea level. so, the pressure at sea level is one point zero zero ATM and the temperature is twenty-five point zero degrees Celsius, but remember that we are going to have to convert that to Kelvin temperature because we are dealing with gas, we will do it in the network, although it is very tied to a mass of rock, it looks like the temperature is four degrees Celsius, so we have t2, although we will have to convert it to a Calvin temperature and the pressure is 11.00 atm, which means we have p2, what are we going to solve for v2, what will be its new volume?

So the first thing we're going to have to do is rearrange the combined gas law here so that we can solve for v2 here. we're going to VG this side, so we want to get a loan, so the first thing I'm going to do is multiply both sides by t2 to get t2 out of the denominator, multiplied by t2 here times t2 here. since t2 is at the top here and at 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 take this P 2 out of the numerator here so that I can get v2 by itself, so I'm going to divide both sides of the equation by p2, which means that these two P two will cancel and my final equation rewritten with v2 isolated by itself will be t2 times p1 times v1. divided by t1 P 2 equals V 2 as we've said before, if you're a little uncomfortable with the idea of ​​V 2 being just on the right side, I'll just rewrite this to make it a little easier V 2 on the left , if that makes you comfortable, it's equal to t2 times p1 times v1 divided by t1 times p2, but all I've done here is turn it around, okay, so let's figure this out, the first thing I'm going to want to do .

What you have to do is take these two Celsius temperatures and convert them to kelvins, so I have twenty-five point zero degrees Celsius plus 273, it will give me 298 Kelvin and the other temperature that I have to convert is forty point zero degrees Celsius plus 273. and that will give me two 77 Kelvin, so now that I have these temperatures in the correct units to solve the equation, let's go ahead and put these variables in so that we have v2 equal to t2 t2, this is equal to 77 Kelvin times p1. initial pressure which is a point zero zero ATM times v1 the initial volume forty point two zero liters, well, let's divide that by t1 again in Kelvin 298 Kelvin which is multiplied by P to the second pressure which is 11.00 atm, like this I'm going to do those calculations and my final answer rounded to three significant figures will be three point three eight.

What are my units here? Okay Kelvin / Kelvin, those ATMs are canceled / The ATMs are canceled and I have liters left here, so my final answer will be three point three eight liters which is rounded to three figures because there are three significant figures that are the lowest number of significant figures that I have in my answer, so my final answer three point three eight leaders if you are having trouble solving other combined gas law problems, you don't really know how to rearrange this equation because it can be a little complicated. Watch the video on rearranging gas equations where I show how to multiply and divide the variables to isolate one by itself. on a certain side of the equation