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we have a situation here where we have a four meter cubed container let's say that's a balloon of some sort and instead of having just one type of molecule of gas in this container we have three molecules of gas we have some oxygen molecules some hydrogen molecule and some nitrogen molecule and what the problem tells us we have 2.1 total kilograms of gas and of that by mass 30 point four eight percent is oxygen two point eight six percent as hydrogen molecules and 66.67% is nitrogen now we need to figure out and it's all it's at standard temperature at least at zero degrees Celsius which we know is 273 Kelvin but we need to figure out what is the total pressure in the container or being exerted on the on the surface of the container and then this is the new concept we want to figure out the partial pressures of each of these gases essentially how much are each of these gases contributing to the total pressure and you could imagine if this is a container and each of these are the three types of gases some of the pressure is going to be from the blue maybe oxygen is the blue gas from the blue gas bumping into the walls some of the pressure is going to be from the hydrogen pumping of the wall maybe that's these yellow gases and some of the pressure is going to be from the nitrogen bumping into the walls I'd say that's the brown gas so the partial pressure is a partial you say the partial pressure due to nitrogen that's the pressure just due to the brown particles bumping into the walls so let's let's see if we can figure this out so the first thing to figure out the total pressure is we have to figure out the total moles of molecules we have so how and the easiest way I can figure out if figuring out the total number of moles let's figure out the moles of each of these molecules so if we have 2.1 kilograms of gas let me write this down if we have 2.1 so if we just dealing with if you want to know moles of nitrogen we have to let me do it in the nitrogen color moles of nitrogen we know that 66.67% of this two well we could say 2.1 kilograms or 2100 grams we know that that's nitrogen so let's do it in grams because when we talk about molecular mass it's always in grams it doesn't to be but it makes it a lot simpler to convert between atomic mass units and and mass in our world so this is two thirds so two thirds of 2,100 that's 1400 1400 grams of n2 now what's the molar mass of this nitrogen molecule well we know that the atomic mass of nitrogen is 14 so this molecule has two nitrogen's so it's atomic mass is 28 so one of these molecules will have a mass of 28 atomic mass units or one mole of n2 would have a mass of 28 grams so one mole is 28 grams we have 1400 grams so we have so or we say grams per mole so if we want to keep our units right so if we say 1400 total grams divided by 28 grams per moles for a mole so we have 50 moles 50 moles of n2 so we could write that right there 50 50 moles all right let's figure out I don't know let's do oxygen next so we do the same process over again 30% is oxygen so we take so let's do oxygen down here oh - so we take 30% and remember this percent these percentage that gave you these are the percentages of the total mass not the percentage of the moles so we have to figure out what the moles are so thirty point four eight percent of 2100 grams is equal to well the 640 grams and then how much what is the mass of one mole of gas of the oxygen gas of the oxygen gas molecule atomic the atomic mass of one oxygen atom is 16 you can look that up on the periodic table although you should probably be pretty familiar with it by now so the atomic mass of this molecule is 32 atomic mass units so one mole of o2 is going to be 32 grams we have 640 grams how many moles do we have 640 640 divided by 32 is equal to that's 20 we have 20 moles of oxygen let me write that down we have 20 moles now we just have to figure out the hydrogen this 2% of that 20 100 grams is 60 grams and then what's the molecular what's the molar mass of one hydrogen this is h2 so we know that the hydrogen atom by itself has a mass of 1 doesn't have a neutron and in most cases so the atomic mass of this is 2 or the molar mass of this is 2 grams so one mole of h2 is equal to 2 grams so one mole is 2 grams we have 60 grams so we have we clearly have 60 divided by 2 we have 30 moles 30 moles so this is interesting even though hydrogen was a super small fraction of the total mass of the gas that we have inside of the container we actually have more actual particles more actual molecules of hydrogen than we do of oxygen and that's because each molecule of hydrogen only only has an atomic mass of 2 atomic mass units while each molecule of oxygen is 32 because there's two oxygen atoms so already we're seeing we actually have more particles due to hydrogen than do the oxygen and the particles are what matter not the mass when we talk about part pressure and partial pressure so the first one thing we can think about is how many total moles of gas how many total particles do we have bouncing around 20 moles of oxygen 30 moles of hydrogen 50 moles of nitrogen gas add them up we have a hundred moles 100 moles of gas so if we want to figure out the total pressure first we can just we can just apply this 100 moles and let me erase this because I want to keep the problem statement there the whole time so let me erase this there you go there you go and I can raise some stuff that you're not seeing off the screen and now I'm ready so we have a hundred moles so we just do our PV is equal to n R T we're trying to solve for P P times 4 meters cubed 4 meters cubed is equal to n and is the number of moles we have a hundred moles is equal to 100 moles times R I'll put a blank there for our X we have to figure out which are we want to use times temperature remember we have to do it in Kelvin so it's zero degrees Celsius is 273 degrees Kelvin and then which are do we use so I always like to write my arse down here so we're dealing with meters cubed we're not dealing with liters so let's use this one 8.3145 meters cubed Pascal's per mole Kelvin eight-point so this is 8.3145 and it was and the unit's there actually maybe I should let me do this oh I wanted to want to that in yellow the unit's there I think I should keep these are in meters cubed Pascal's / moles Kelvin and then our temperature was 273 Kelvin now let's do a little dimensional analysis to make sure that we're doing things right these meters cancel out with those meters who divide both sides of the equation by meters these moles cancel with DS moles moles of the numerator moles of the denominator Kelvin in the numerator Kelvin in the denominator and all we're left with is Pascal's which is good because that is a unit of pressure so we get 4 so if we divide both sides equation by 4 we get P is equal to let's divide 100 by 4 25 times 8.3145 times 273 and the only unit we were left with was Pascal's which is nice because that's unit of pressure so let's do the math 25 times 8.3145 times 273 is equal to 56 thousand seven hundred and forty six fifty six thousand seven hundred and forty six Pascal's and that might seem like a crazy number but the Pascal is actually a very small amount of pressure it actually turns out that one hundred one thousand I think it's 325 Pascal's is equal to or one hundred one three and is equal to one atmosphere so if we want to figure out how many atmospheres this is we could just divide that by 100 and that that large number I think that's right let me look it up on this table is it 101 yep 101 325 so if we wanted to put this in it we could we could write this in kilo Pascal's that's fifty six point seven four six kilo Pascal's or if we wanted in atmospheres we just take 56 746 divided by 101 325 it equals 0.5 six 0.56 atmospheres so that's the total pressure being exerted from all of the gases I deleted that picture so this is a total pressure so our question is what's the partial pressure we could use either of these numbers they're just in different units what's the partial pressure of say nitrogen well even though 66 two-thirds of the mass is nitrogen only 50% of the actual particles are nitrogen so 50% of the pressure is due to the nitrogen particles remember we have to convert everything the mole because we only care about the number of particles so if you want to know the partial pressure the partial pressure due to the nitrogen molecules it's the 50 it's 50% of these so it's you know it's twenty eight thousand three hundred and now let's just say it's roughly 28-thousand well let me write it three hundred and was it 373 Pascal's that's not a that's a roughly or if you took half of this approximately twenty eight point four kilopascal or approximately 0.28 0.28 atmospheres and then finally if you want to figure out the partial pressure due to let me do in a different color the pressure due to the hydrogen atoms the partial pressure due to the hydrogen atoms hydrogen even though it's very small part of the mass it actually represents 30% of the molecules and it's the molecules that are bumping into things we don't care so much about the mass so 30% of the molecules 30% of the molecules and remember when we talk about kinetic energy if us something with a small mass is the same kinetic energy it's actually moving faster so when we talk about temperature that's average kinetic energy so maybe in this we could imagine that the hydrogen might be moving faster than say the nitrogen or the oxygen but we don't have to think about that too much right now but the partial pressure due to hydrogen is just 30% of any of these numbers pick one let's do it in atmospheres times 0.5 6 is equal to 0.3 times 0.5 6 is equal to 0.16 8 atmospheres and so the total pressure so the partial the total pressure should be equal to the pressure of each of the the partial pressures of each of the gases plus the partial pressure of oxygen plus the partial pressure of hydrogen and so this one we figured out was point two eight atmospheres the oxygen was point eleven one one one two atmospheres and this was 0.168 and if you add these together you will see indeed that they add two 0.56 atmospheres which