The Ideal Gas Law

in our exploration and described the behavior of gas is we come upon the ideal gas law. Now the ideal gas law formula relates the behavior of gas under varying conditions, off pressure volume, moles and temperature. So our ideal gas law formula is PV equals NRT. We see that it's in a purple box, which means that you need to memorize it. Your professor is going expect you to know this formula. It's gonna be involved in so many different types of ideas and calculations within this chapter. Now, if we take a closer look at it, we said that P equals pressure here. The units for pressure will be in atmospheres. Volume will be in leaders and equals the amount of gas in moles. Are is a gas constant. And here, when it comes to the ideal gas law, we tend to see it as 0.8 to 06 In the next section, we'll talk about the units involved with this gas constant, and then temperature year temperature will be in Kelvin's. So just remember to talk about the ideal behavior of gas is we use the ideal gas law. So click on the next video and let's take a look at an example question

here. We're told that a 500 million container at a pressure of 600 million liters of mercury, possesses 29.3 g nitrogen gas at 50 degrees Celsius. Here, we need to determine the correct units needed for the ideal gas law. So remember, the ideal gas law is PV equals n our teeth. So P stands for pressure. Remember, pressure needs to be in units of atmospheres. So here, we're gonna do a conversion. We're gonna go from 600 millimeters of Mercury into atmospheres millimeters of mercury, go here on the bottom, and then atmosphere go here on top. Remember, the relationship is that for every one atmosphere, it's 760 millimeters of mercury. Okay, so when we do that, we're gonna get a pressure off 0. atmospheres. All those 600 has won six figs. Let's just go with 36 fix here just so that we don't have just 360.8 as atmospheres. Next volume volume needs to be in leaders. So we have 500 mL. And remember, 11 mil e equals 10 to the negative three. So this would just come out as 500 leaders. Next we need moles. So moles is n remember. Nitrogen gas, nitrogen. It's natural or standard State is N two. It's one of our die atomic molecules. So we're told that we have 2029 0.3 g of end to We got to convert that into moles. So one mole of end to so there's two nitrogen. According to the periodic table, each one is 14. g. So multiplying that by two gives me 28.2 g for the combined weight in N o. An end to so grams here, cancel out and I'll have my moles here will put it as 1. moles of end to and then finally, we need our temperature. Ours are constant, so we don't have to worry about giving the correct units is 0. to 06 like we said earlier, So temperature here needs to be in Kelvin. Remember to go from Celsius to Kelvin, you're supposed to add to 73.15. Sometimes professors will just say plus 2, 73. But if you want to be as accurate as possible, you wanna put to 73.15. So when you add that, that's 3. 23.15 Kelvin. So here we have all of the units, um, that we need in the correct forms. So just remember, ideal gas law. And what is the correct unit that we need to utilize for each one of these variables?

As we said, the ideal gas law uses are, which is our gas constant, but realize that the gas constant are can have two different values, depending on the situation. Now the two terms you'll tend to see when it comes to the are constant is the first one we talked about earlier are being equal 2.8 to 06 will utilize this value when dealing with the ideal gas law, but our can also equal 8.314 This happens when we're dealing with speed, velocity or energy. So if a question is dealing with the speed of an object or a subatomic particle, or dealing with the energy of a reaction or solution through our converts to 8.314 now, the conversion factor between the are groups is that one leader times atmospheres equals one on one point 3 to 5. Jules. So we have our 0.8 to 06 year. We use the conversion factor. So remember we want to get rid of leaders times, atmospheres. So we put them on the bottom. So one leaders times atmosphere here on the bottom is one on 1.3 to 5 jewels here on top leaders. Times atmospheres cancel out, and that's how we end up with jewels at the end. When you plug this in, you get a long string of numbers as 8.314 to 95 jewels over most times K. But we just focus on the 8.314 portion. I know there's a seven there when you work it out completely, but to keep it simple, books will just listed as 8.314 So just keep in mind the gas constant can be two different numbers. And remember what the ideal gas law We use this value, and when dealing with speed, velocity or energy, we use this value of 8.314

here in this example question. It says how many moles of ammonia are contained in 25 liter tank at 190 degrees Celsius and 5.20 atmospheres. All right, so they're asking me to find moles of ammonia, so that would be my end Variable. They're giving me leaders. So that would be volume. They're giving me degrees Celsius, which is temperature, and they're giving me atmospheres, which is a unit for pressure. We can see that we have PV and Mt. So we have the ideal gas law to deal with and the variable that's missing, the one that we're looking for is moles. So all we have to do here is isolate moles. So divide both sides here by rt. And then we're gonna say here that moles equals P V over R T. Pressure is on writing atmosphere, So no need to convert. Then we're gonna have here volume which is already in leaders. So no need to convert. Then we have our our constant remember is 0.8 to And now that we know that we're using the ideal gas law, we have to use the units of leaders Times, atmospheres over moles times k temperature, Remember, has to be in Kelvin, so there is a little bit of converting here necessary. So we have 190 degrees Celsius. So add to 73.15 to that, and that will give us 4. 63.15. Calvin. So take those and plug it in 4. 63.15 Kelvin. So what cancels out atmospheres? Cancel out leaders, Cancel out Calvin's cancel out and you'll see that the only unit left are the moles that we need to find. So we're going to get initially 342050 moles. If we look back on the question, this has 366 to sig figs, three sig figs. We go with the least number of sick fix. So we're gonna put our answer asked 3.4 moles of ammonia. So this would be our final answer. So just realize, what variables are you being given? What's the missing variable? Just use your algebra skills toe. Isolate that one very variable and you'll get your answer at the end