Converting Between Moles and Liters of a Gas at STP

in this video we're going to learn how to convert back and forth between

moles

and

liters

of a gas at STP we'll do some problems like these and we'll look at some common mistakes here's our first question what is the volume and

liters

of 3.8

moles

of co2 gas at STP let's talk about some information is going to help us solve this problem first off what's STP well STP is an abbreviation for standard temperature and pressure and standard temperature and pressure are zero

degrees Celsius and 1 atm so whenever we're talking about something that takes place at STP it means that the temperature is zero degrees Celsius and the pressure is 1 atm here's another piece of information that's really helpful when we are at STP when we're at zero degrees Celsius from 1 atm one mole of any gas takes up twenty 2.4

liters

of volume ok twenty 2.4

liters

this is like a certain amount of space and this is how big 20 2.4

liters

is I made this box here ok so if

we're at STP and we filled this box up with gas or we had a balloon that was the size of this box and we filled it up with gas we would have one mole of gas here in these twenty 2.4

liters

okay so using this information let's just kind of think through this problem okay we have three point eight zero

moles

of co2 gas okay we know that it STP one mole of gas takes up twenty two point four

liters

okay so if we had one mole of gas we'd have twenty two point four

liters

that's how

much space would take up we don't have one mole we have three point eight zero

moles

so we want to multiply this by twenty two point four which is the amount of space that one mole takes up at STP okay this is sort of the method that we used to think through it now let's look at how we could solve this using conversion factors okay we're starting with three point eight zero

moles

and now we want to multiply this by a conversion factor that's going to get rid of

moles

and it's

going to take us two

liters

okay to do this we're going to want to take this information and write it as a conversion factor we could kind of sum up this information as an equation as an equivalence like this or say that one mole is equal to or is equivalent to twenty two point four

liters

okay and now we have something really conveniently let us write a conversion factor okay there are two possible conversion factors that we can write from an equation like this okay the first we'll put

this on top in this on the bottom okay and it's going to look like one mole on top over twenty 2.4

liters

on the bottom now the other conversion factor that we can write from this is the exact opposite it's just flipped okay so we do 20 2.4

liters

on the top and one mole on the bottom both of these are completely valid conversion factors we could use either one of them but in this problem we want to use a conversion factor that's going to get rid of

moles

from the top of this

equation so we are going to want to use a conversion factor that has

moles

on the bottom so for this particular problem we are going to be using this conversion factor okay so now we have

moles

on the top

moles

on the bottom they're going to cancel out and that's going to leave us with

liters

and the math that we're going to do is this times this divided by this and as you can see dividing by one doesn't really change something's value so all the math were doing is this times

this which is exactly the math that we came up with when we were just kind of thinking through the problem okay our final answer is going to be eighty one eighty five point one

liters

we round this to three significant figures because there are three significant figures here three significant figures here and this one here is part of a definition it's part of an equation like this so we don't worry about this one it has essentially an unlimited number of significant figures so we round

to three eighty five point one

liters

is how much how much space 3.8 0

moles

of co2 gas would take up at STP ok let's move on okay I'm going to do this problem and then I'm going to talk about some common mistakes ok how many

moles

are in 58.6

liters

of nitrogen gas and two at STP okay so again here's the information that we need at STP one mole of any gas takes up twenty 2.4

liters

of volume ok so if we had 20 2.4

liters

of nitrogen gas we'd have just one mole we have more

than 20 2.4

liters

so we're going to have more than one mole and what we want to do is we want to know essentially how many times twenty two point four goes into fifty eight point six so we're going to do fifty eight point six divided by twenty two point four we're going to find out how many times this goes in and it's going to tell us how many

moles

would fit into fifty eight point six

liters

okay now to do this with conversion factors we're going to start with 58.6

liters

and we are going to take this relationship and think about it sort of as an equation like this which is going to let us write these two conversion factors and we're going to want to choose the one that's going to get rid of

liters

which is on the top here so it's going to be the one here that has

liters

on the bottom move it over to here

liters

cancels out leaders cancels out it's going to leave us with

moles

and the math that we do is fifty eight point six times one divided by

twenty two point four which again as you can see here is the same math we do here we're just thinking it through right because this one doesn't really make a difference all we're really doing is fifty eight point six divided by twenty two point four the unit's cancel out and we get two point six two

moles

rounding to three significant figures because this one here doesn't count since it's part of this official definition two point six two

moles

okay now even if we're

getting the hang of this hold on for just a sec because I want to talk about two super common mistakes that a lot of people make and I really don't want you to make them okay here's the first super common mistake what is the volume in

liters

of ten point three

moles

of oxygen gas at 25 degrees Celsius and 2 ATM pressure ok well to solve this a lot of students would say well one mole of gas takes up twenty 2.4

liters

of volume and I have ten point three

moles

instead of one mole so

I'm going to do ten point three times twenty two point four and you can use conversion factors to do it like this okay now here's a trick this is totally wrong can you see why well it has to do with this thing here at STP one mole of gas takes up twenty two point four

liters

but remember STP is zero degrees Celsius and 1 atm okay 25 degrees Celsius and two ATM is not STP in this whole thing where one mole equals twenty two point four

liters

takes up twenty two point four

liters

of space

it only works at STP it only works at zero degrees Celsius and one ATM of pressure it doesn't work at other conditions say twenty five degrees Celsius and two ATM of pressure so we can't use this information to solve the problem unless we are at STP if you had to solve a problem like this you'd want to use the ideal gas law PV equals NRT because the ideal gas law works when you're not at STP I've got a whole bunch of videos on the ideal gas law check those out if you want to

learn more okay here's another really common mistake in it's super tricky sometimes teachers and textbooks you really love this one okay here's how it goes how many

moles

are in 29.4

liters

of liquid ethanol at STP okay and a student might solve this problem like this okay why isn't this right okay we're at STP so we can use one mole equals twenty 2.4

liters

and we can multiply that by this conversion factor but can you see the trick here we're talking about quit ethanol

okay and this idea of one mole equals twenty 2.4

liters

only works with gases okay so don't get tricked by this always double-check that you're working with a gas at STP not a liquid or a salt so if the problem is asking you about something that's a liquid or solid you can't use one mole takes up 22.4

liters

you have to solve it in a different way just basically don't get tricked by this don't get tripped up make sure that you're talking about gas at STP not something

that's a liquid or a solid now I'm going to do two more questions where we just do some some calculations between

moles

and

liters

if you want a little bit more practice what volume with 0.73 five

moles

of o2 gas occupy at one ATM of pressure and zero degrees Celsius okay so first of all we look at these conditions and we know we're at STP so we can use one mole equals twenty 2.4

liters

okay so if we had one mole of o2 gas it would take up twenty 2.4

liters

we have less than one mole

so this amount of gas is going to be taking up less than twenty 2.4

liters

but still to find out how much space this would take up we are going to want to take this amount of

moles

and multiply it by the amount of space that one mole would take up at STP this is kind of how we think through it and now to use a conversion factor we're going to start with zero point seven three five

moles

and we're going to multiply it by a conversion factor made from this relationship so here are our two

choices with this on top with this on the bottom and flipped we want to choose the one that's going to get rid of

moles

so puts it on the bottom put it right here

moles

cancels out

moles

cancels out leaves us with

liters

this times this divided by one is going to be sixteen point five

liters

which as we predicted is a little bit less than twenty two point four

liters

we're going to do one more 13 point zero

liters

of chlorine gas at STP contains how many

moles

okay we know we're at

STP so we can use this relationship if we had twenty 2.4

liters

of chlorine gas we'd have one mole we have less than twenty 2.4

liters

so we're gonna have less than one mole but basically want to find out how many times 22.4 goes in 213 so the math is going to be thirteen point zero divided by twenty two point four or with a conversion factor it's going to be 13.0

liters

times one of these conversion factors that we make from this relationship we're going to choose a one that

puts

liters

on the bottom so that they cancel out

liters

on top

liters

on the bottom cancels out it leads us with

moles

and we're going to do this times one divided by this the same math we did up here and our final answer is going to be zero point five eight zero

moles

which is less than one mole because 13.0

liters

is less than twenty two point four

liters

okay so that's how you convert back and forth between

moles

and

liters

of a gas at STP the two things you always want to keep in

mind is one we want to make sure that the the problem that you're working with actually says that you're at STP zero degrees Celsius and 1 atm if you're not a zero degrees Celsius and 1 atm you can't use this relationship between one mole and twenty 2.4

liters

the second thing that you want to keep in mind is that we have to be talking about a gas even if it's something that's at zero degrees Celsius and 1 atm if it's a liquid or a solid you can't use this

relationship so keep your eyes open double check those so don't get tripped up when you're doing these kind of problems