# Gas Pressure Conversions

a previous lesson we looked at how we can use units like millimeters of mercury or millimeters of water to measure gas

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but usually when we're measuring things there are many different units that we can use and support to understand how to inter convert them for example if I'm measuring length well I could use centimeters or I could use inches I could use feet yards or meters or miles so in this lesson which is very short we're going to look at a few common units formeasuring gas

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and then we're going to look at how we can use conversion factors to convert between them if you're a little rusty on conversion factors and significant figures it would help to go and look at those old lessons before you do this just to make sure that you have a firm foundation so some common gas### pressure

units you're already familiar with one of them and that's millimeters of mercury Miller millimeters of mercury is sometimes also referred to as tours andthis is an honour of the italian scientist tora celli who is the first to realize that you could use mercury in a glass tube to measure gas

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don't let this confuse you millimeters of mercury Torr it's the same it's a different name for the same thing another common gas### pressure

unit is the atmosphere and this seems a little bit tricky at first because atmosphere is also a physical thing the air surrounding the earth but it's also the name of a unit so we can have forexample two point seven atmospheres of

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it's just a unit like pounds or miles or inches or whatever and the third unit is called the kilopascal this is also named after a scientist Pascal who did a lot of work on force and### pressure

and so forth there are abbreviations for these millimeters of mercury and tours these are already abbreviated atmospheres we can abbreviate as atm in kilo Pascal is abbreviated as a lowercase K uppercase P and a lowercase a in order to do mathematicalconversion between these guys we have to have some sort of equation that explains how they all relate so here that is we can say that 760 millimeters of mercury or 760 torr that sort of a person equals 180 M which equals a hundred and 1.3 kilo Pascal's there are three different things in this equation but don't let it confuse you just as 760 millimeters of mercury equals 1 atm this also means that 760 millimeters of mercury equals 100 and 1.3 kilo Pascal's as we've done

previously an earlier conversion factor problems we're going to be using this equation to write conversion factors to go between these different units depending on which we want to start with or which we want to finish with so let's get a little hands-on experience with converting these guys working through this problem the

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inside of car tires 225 kilo Pascal's express this value in both ATM and millimeters of mercury we will do atmospheres first so as you remember fromconversion factors we always want to write conversion factors before we start the problem we're starting here with 225 kilo Pascal's and we're going to want to multiply that by something that's going to give us a new answer so we're converting from kilo Pascal's to atmospheres there are two conversion factors that we can write the first is going to be 1 atm is over and thus equals 100 and 1.3 kPa that's one conversion factor another conversion factor that we can write

is that same one but it's just flipped so we can write 101.3 kPa divided by 1 atm these guys are both perfectly good but which one do we want to use well remember that when we do a conversion factor what we want to do is we want to end up cancelling out the unit's the old units and ending up with new units we can only cancel out units if the unit is on the top on one side and is on the bottom on the other side so we're going to be using this conversion factor because kPa is obviously

on the top up here and it's on the bottom down here this is the one we're going to use so we're going to say 2 25 kPa times 180 m / 101 point 3 kPa since kPa is on the top here on the bottom here these guys are going to cancel out and we're going to go through and we're going to do our math remember the final math is going to be this times this divided by this and my final answer is going to be two point two two the reason why I round that to three significant figures is

there are three numbers here three digits here three significant figures four significant figures here there's one here but this is a this is a definition this is this a whole number so we don't worry about this we disregard this we take obviously the lesser of the two three or four and we choose one with three so our final answer has three significant figures now what are the final answers well kPa cancelled out so we're left with ATM's which means that our final answer is going

to be 2.2 to ATM 2.2 to ATM is our final answer if the method that I use to go through this canceling units and doing significant figures the end if this confuses you it's important to go back and look at the previous units that gave some information on this because I'm worried you'll be confused otherwise let's look at another example we did kPa 2 atmospheres now let's go from kPa to millimeters of mercury again we're going to start with 225 kilo Pascal's we're

going to be multiplying that by conversion factor as before there are two valid conversion factors that we could write the first is 760 millimeters of mercury over 100 and 1.3 kilo Pascal's that's one possible conversion factor or again we can flip it we can say that 100 and 1.3 kilo Pascal's is equal to and hence is written over 760 millimeters of mercury now again we want to choose a conversion factor that's going to this kPa cancelled out we can only cancel out the KPA if

it's on the top here it's in the bottom on the conversion factor which means that once again this is the conversion factor that we're going to use because kPa is on the bottom 225 kPa times 760 millimeters of mercury divided by 101 point three kPa now did we set it up right we did because KP is on the top here and on the bottom here which means they cancel out our final units the only ones that are left are going to be millimeters of mercury so I crank through I do this on a

calculator it's a little bit harder remember 225 times 760 the answer to that divided by a hundred and 1.3 kPa the final answer that I get there is one six nine zero millimeters of mercury obviously the answer that I get for this is much longer but there are only three significant figures in this number we don't worry about the significant figures in this because the smallest is three which means that I'm going to round this to one six nine zero millimeters of mercury and that's

my final answer so converting between these different gas

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units is not that difficult you just want to remember to choose the correct conversion factor so your old units cancel out and so you get your new unit this expression right here 760 millimeters of mercury equals blah blah blah blah blah blah blah is usually always going to be given to you by teachers that's going to show up on tests it's going to be in the textbook so it's probably not something that you need tomemorize only memorize it if your teacher says it's absolutely necessary otherwise it'll usually always be given