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AP.Chem:

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we're told that a 10 liter cylinder contains seven point six zero grams of argon in gas form and four point four zero grams of molecular nitrogen once again in gas form at 25 degrees Celsius calculate the partial pressure of each gas and the total pressure in the cylinder alright so pause this video and see if you can work through this on your own before we work through it together alright so you might imagine that the ideal gas law is applicable here and it's applicable whether we're just thinking about the partial pressures of each gas or the total so the ideal gas law tells us that pressure times volume is equal to the number of moles times the ideal gas constant times temperature and in this case we're trying to solve for pressure whether it's partial pressure or total pressure so to solve for pressure here we can just divide both sides by V and you get pressure is equal to the number of moles times the ideal gas constant times the temperature divided by the volume and so we can use this to figure out the partial pressure of each of these gases so we can say that the partial pressure of argon is going to be equal to the number of moles of argon times the ideal gas constant times the temperature both gases are the same temperature over here divided by the volume and then we can also say that the partial pressure of our molecular nitrogen is equal to the number of moles of our molecular nitrogen times the ideal gas constant times the temperature divided by the volume so we already know several of these things we can look up the ideal gas constant with the appropriate units over here they've given us the temperature at least in terms of degrees Celsius we'll have to convert that to Kelvin and they've also given us the volume so all we really have to do is figure out the number of moles of each of these and to figure out the number of moles they give us the mass we just have to think about molar mass so let's look up the molar mass of argon as well as the molar mass of molecular nitrogen so the molar mass of argon getting our periodic table of elements we look at argon right over here and it has an average atomic mass of 39.95 which also gives us our molar mass so a mole of argon will have a mass of 39.95 grams per mole and then if we want to figure out the same thing for our molecular nitrogen we look up nitrogen here we see an average atomic mass of 14 point zero one so we might be tempted to say that the molar mass of molecular nitrogen is 14 point zero one grams per mole but we have to remind ourselves that molecular nitrogen is made up of two nitrogen atoms so the molar mass is going to be twice this or twenty-eight point zero two grams per mole so this is equal to twenty eight point zero two grams per mole and then we can apply each of these equations so the partial pressure of argon let me give myself a little extra space here partial pressure of argon is going to be equal to the number of moles of argon well that's just going to be let me do this in another color so you can see this part of the calculation that's going to be the grams of argon so let me write that down seven point six zero grams times one over the molar mass so times one over 39.95 moles per gram and you can see that the units work out grams cancel with grams and this is just going to give you the number of moles of our argon and then we multiply that times our ideal gas constant and we have to pick which one to use in this case we're dealing with liters so both of these cases deal with that and the difference between these is how they deal with pressure the first is in terms of atmospheres the second is in terms of Torr so if we want our partial and total pressures in terms of tour we could use this second one so let's do that so in this case let's use this second ideal gas constant so that's going to be times sixty two point three six liter pour per mole Kelvin and then we need to multiply that times the temperature so 25 degrees Celsius in Kelvin we add 273 to that so that's 298 Kelvin and all of that is going to be divided by our volume which is 10.0 liters 10.0 liters and we can validate that the units work out we already talked about these grams cancelling out this mole cancels with this small this Kelvin cancels with that Kelvin and then this liters cancels with this leaders and we're just left with tour which is what we care about we are thinking about a pressure in this case a partial pressure we have seven point six zero divided by thirty nine point nine five times sixty two point three six times 298 divided by ten point zero is equal to this business and now we just have to think about our significant figures here so we have three here 4 here three here and three here so when we're multiplying and dividing we'll just go to the fewest number of significant figures we have so it's three so we'll want to go round to 354 Torr so the partial pressure of argon 354 tor and now we can do the same thing for the molecular nitrogen and let me get myself a little more space here so the partial pressure of our molecular nitrogen is going to be equal to I will do this in a different color as well when I figure out the number of moles that is going to be the mass of molecular nitrogen which is four point four zero grams times one over the molar mass so that's one over twenty-eight point zero two grams per mole and then that is going to be times our ideal gas constant so we can really just copy the rest of this right over here times sixty two point three six liter or per mole Kelvin times 298 Kelvin all of that is going to be over 10.0 liters and once again the units work out grams cancel with grams moles cancel with moles leaders with liters Kelvin with Kelvin and we're just left with tour and this gets us to four point four zero divided by twenty eight point zero two times sixty two point three six times 298 divided by ten point zero is equal to this and once again the lowest significant figures we have here are three so we'll rhine that we'll round this to two hundred and ninety two so this is equal to 292 tour and so we've figured out the partial pressure of each of these and if we want to figure out the total pressure the total pressure that's just going to be the sum of the partial pressures so it's going to be the partial pressure of the argon plus the partial pressure of the molecular nitrogen and so this is going to be let's see I think I can do this in my head 646 tour and we are done

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