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- welcome to moomoomath and science in
- this video let's talk about some or
- solve some boyle's law example problems
- let's go over some abbreviations you may
- see atm is for atmosphere millimeters of
- mercury is for
- uh pressure tor is another name for
- pressure
- it's another name for millimeters of
- mercury and then liter is a volume
- measurement
- we'll use the formula p1
- times v1 equals p2 v2 now you could
- rewrite boyle's
- law remember boyle's law says that as
- pressure goes up volume goes down and
- the other way around so you could
- rewrite it pressure times volume is
- equal to k and k is a proportionality
- constant okay
- so
- a lot of times with boyle's law you're
- comparing things and so you have a
- before and after the before would be p1
- times v1 equals k and then the second or
- the afterwards would be p2 times p2 so
- what you can do since they're both set
- to k you can just set it to p1 times v1
- equals
- p2 times v2 so for all the problems
- we're getting ready to work you can use
- this formula then all you do is just
- plug and figure out the answer so let's
- get started with the very first one
- after that introduction
- okay so let's get started it says
- 2 liters remember that's volume of gas
- is at 740 millimeters of mercury so that
- is pressure what is the volume at 760
- milliliters of mercury so let's set this
- up we have p1
- times p2
- ah excuse me
- what am i doing
- p1
- times
- v1 is equal to
- p2 times v2 sorry about that a little
- problem there at the beginning so now
- what we need to do is identify what we
- have and then solve for the missing
- variable so we have 2 liters so that's a
- volume so i'm going to write
- 2
- liters okay
- and it says it's at
- 740
- millimeters of mercury so 740 m mhg
- okay equals you have a volume you're
- looking for volume but you have 760
- so you have another pressure reading 760
- times and we're looking that will be our
- x for volume okay so we have everything
- set up
- now all we do is we
- divide each side by 760
- okay
- and i'm writing my units of measure in
- there these cancel so that gives you x
- is equal to now what we do is solve this
- and i have my calculator here so i'm
- going to go 740
- times 2 and that equals
- 14
- 80.
- the pressure
- uh units cancel okay
- and so now all we have to do is divide
- the 1480 by 760.
- and
- that is fourteen eighty divided by seven
- sixty
- is equal to
- one
- nine four
- seven
- and our unit of measure is liters so the
- answer is 1.947
- liters okay so that's the first
- one
- let's look at our next problem
- but before we go to our next problem
- let's recap what we did
- we went ahead and wrote p1 740 2
- is the volume p2 is 760. the volume is
- missing we divided both sides by 760. we
- took 740 times 2 that's 1480
- and then we divided that by 760 and that
- gave us 1.947
- and the unit since it is asking for
- volume is
- liters so that's kind of a recap
- let's look at the next problem okay this
- one is very similar we have three liters
- of a gas is it the pressure of 740
- millimeters of mercury what is the
- volume at standard pressure well
- standard pressure is 760
- okay
- if you didn't know that so let's set it
- up we've got
- p1 times v1 equals p2
- times v2
- so now let's just plug in what we have
- we have a volume of 3 liters
- we have a pressure of 705
- mmhg
- i know that's a little messy and that
- equals two we're trying to find volume
- and we have a pressure of 760
- mmhgs okay
- so now what we do is we
- divide each side by 760 millimeters of
- mercury
- so i'm gonna do that
- okay and you'll see
- these cancel the units of measure cancel
- you're going to be left
- with liters now what i do is i take 740
- times 3
- 740 times 3
- equals
- two thousand two hundred and twenty
- okay and i'm going to divide that by
- seven hundred and sixty and that gives
- me an answer of
- two point
- nine
- two
- one
- what is my unit of measure it is liters
- it is volume but now let's see if this
- makes sense let's see if it is indeed an
- inverse relationship
- well
- the standard
- is greater than the 740 so pressure is
- going up and yes volume did go down just
- a little bit let's look at the next
- problem please
- okay a gas occupies 12.3 liters at a
- pressure of 40
- millimeters of mercury what is the
- volume when the pressure is increased to
- 60 okay
- so let's set this up
- p1 times v1 equals
- p2
- v2 remember this works also if you're
- looking for pressure you just plug in
- what you have you have
- 12.3
- liters
- okay
- you have a pressure of
- 40 and i'm just going to put hg for
- mercury and that is equal to
- you have a pressure of 60
- and you are trying to find what the
- volume is okay
- so now we divide each side by 60.
- okay
- units cancel you're left with
- liters
- these cancel out i take 40 times 12.3
- and that equals
- 492
- over 60
- and 492 times 60
- is equal to
- 8.2
- what is my unit of measure it's looking
- for
- volume and volume is liters okay
- now let's see if this makes sense
- the pressure is increasing and the
- volume is going down to 8.2 let's work
- one more final problem okay here's our
- problem final problem if a gas is at 25
- degrees celsius and it occupies 360
- liters at pressure
- of one
- atmosphere
- what would be its volume at a pressure
- of 2.5 atmospheres okay one the 25
- centimeters you don't really need that
- that just tells you what the temperature
- is it's not going to go in the formula
- p1 times v1 is equal to p2 times
- v2 so again we just kind of plug in what
- we have well we have a volume of 3.6
- liters
- okay and then we have a pressure of 1
- atmosphere
- and that is going to be equal to
- a pressure of 2.5
- atmosphere atm i need to write atm here
- okay
- times and we're trying to find volume
- okay so now what we do is we just divide
- through by 2.5 atms
- okay
- these units cancel
- these cancel
- i take one times 3.6 i think i can do
- that math in my head divided by 2.5
- and that is going to give us
- can't do it that math that quick in my
- head
- 2.5 that gives us
- 1.44 and what is the unit of measure it
- is liters
- let's check to see if this makes sense
- they it went from 3.6
- to 2.5
- so it actually went down so pressure
- went down
- so that means volume has to go up and
- the volume went from 1 to 1.44 so that
- makes sense i hope this helps and
- remember kindness multiplies kindness be
- kind to someone today
-
welcome to moomoomath and science in
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