explain why the pressure exerted by a gas does not depend on the type of the gas

Explain why the pressure exerted by a gas does not depend on the type of the gas

- In this video, we're going to introduceourselves come the idea the partial pressure due to ideal gases. And also the means to think about it is imagine some type of a container, and you don't just have actually onetype that gas in the container. You have much more than one form of gas. Therefore let's say you have actually gas onethat is in this white color. And also obviously, I'm notdrawing it to scale, and also I'm just illustration thosegas molecules moving around. You have actually gas 2 in this yellow color. You have gas three in this blue color. It transforms out that peoplehave been able to observe that the total pressure in this system and you could imagine that's gift exerted top top the within of the wall, or if you placed anything in this container, the pressure, the pressure perarea that would certainly be exerted on that thing is equal to the amount of the pressures contributedfrom each of this gases or the press that eachgas would certainly exert on its own. So this is going come be same to the partial pressure because of gas one add to the partial pressure because of gas 2 plus the partial pressuredue to gas three. And also this provides sense mathematically native the appropriate gas lawthat we have actually seen before. Remember, the best gas legislation tells us that pressure times volume isequal to the variety of moles time the best gas constanttimes the temperature. And also so if you to be tosolve for push here, simply divide both political parties by volume. You'd get pressure is same to nR time T over volume. And so we deserve to express bothsides the this equation that way. Our complete pressure, that wouldbe our total variety of moles. So let me write it this way, n complete times the ideal gas continuous times our temperature in kelvin divided by the volume of our container. And that's going to be same to, for this reason the pressure due to gas one, that's walk to be thenumber of mole of gas one, time the appropriate gas constanttimes the temperature, the temperature is not goingto be various for each gas, we're assuming they're allin the exact same environment, split by the volume. And once again, the volumeis walking to be the same. They're all in the samecontainer in this situation. And also then us would add that tothe variety of moles that gas two times the right gas constant,which when again is walk to it is in the very same for all of the gases, times the temperaturedivided through the volume. And then to that, we could include the numberof mole of gas 3 times the appropriate gas constant times the temperaturedivided through the volume. Now, ns just happen tohave 3 gases here, however you could plainly keep going and also keep adding moregases right into this container. But when you look at itmathematically prefer this, you have the right to see that the right-hand side, we can factor out the RT over V. And if you do that, youare walking to get n one to add n 2 plus n three, allow me close those parentheses, times RT, RT end V. And this appropriate over hereis the exact same point as our total variety of moles. If you to speak the number of moles the gas one to add the variety of moles of gas 2 plus the variety of moles that gas three, that's walk to provide youthe total number of moles the gas the you have in the container. So this makes sensemathematically and also logically. And also we have the right to use this mathematical ideas to answer other questions or to come up with otherways that thinking around it. Because that example, let's to speak that us knew that the total pressure in our container early out to every one of the gases is 4 atmospheres. And also let's speak we recognize thatthe total number of moles in the container is equal to eight moles. And also let's say we know that the number of moles the gas three is same to two moles. Can we use this details to number out what is walking to it is in the partialpressure because of gas three? stop this video, andtry come think about that. Well, one method you might think around it is the partial pressure due to gas 3 over the complete pressure, end the full pressureis going come be same to, if we simply look in ~ thispiece right over here, it's walking to it is in this. It's walk to it is in the numberof moles of gas three times the best gas consistent times the temperaturedivided by the volume. And also then the complete pressure, well, that's simply goingto be this expression. For this reason the total number of molestimes the right gas continuous times that same temperature, 'cause they're every inthe same environment, separated by that exact same volume. They're in the same container. And also you deserve to see very clearlythat the RT over V is in the numerator and the denominator, therefore they're going come cancel out. And we acquire this idea the the, I'll write it down here, the partial pressure as result of gas three over the complete pressure is equal to the number of moles the gas three divided by the total, total variety of moles. And also this amount right end here, this is known as the mole fraction. Let me simply write that down. It's a valuable concept. And you have the right to see the molefraction can help you figure out what the partial push is going come be. So because that this example, if wejust instead of the numbers, we recognize that the total pressure is four. We recognize that the totalnumber of moles is eight. We know that the moles, the number of moles that gas 3 is two. And also then we can just solve. Us get, permit me simply doit, write it over here, I'll compose it in one color, the the partial pressuredue to gas three over four is equal to two overeight, is equal to 1/4. And also so you have the right to just pattern complement this, or you have the right to multiply both sides by 4 to number out that the partialpressure due to gas 3 is going to be one.