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Ch 8.2 - Ideal Gas Law | General Chemistry | YouTubeToText
YouTube Transcript: Ch 8.2 - Ideal Gas Law
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Video Summary
Summary
Core Theme
This content explains the fundamental relationships between pressure, volume, temperature, and the amount of a gas, culminating in the derivation and application of the Ideal Gas Law (PV=nRT).
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the topic of this video is on relating
the pressure volume amount and
temperature of gases ultimately um
talking about the ideal gas law the
learning objectives are on your screen
so you can go ahead and pause the video
now to write those down I'm going to
first before jumping into the ideal gas
law just introduce some some
observations about gas the behavior of
gases under different conditions and um
many of these laws have names so the
first one is I guess sometimes known as
amonton's law although I this this is
honestly the first time I've seen it
written as amonton's law um uh but uh
the more common one at least in my own
experience is that of um uh the
scientist uh Joseph Louie gay
lasak and so sometimes or oftentimes uh
in my own experience I've seen it
written as gay lao's
law and really what this is doing is
exploring the relationship between
pressure and temperature at constant
volume all right and um so if we think
about a fixed volume container we can
think about like um some sort of rigid
vessel uh like we have in the figure
here in this R rigid vessel we have some
some container with the gas in it we can
heat that gas in a water bath and and uh
sort of monitor what's happening to the
pressure with this pressure gauge as a
function of temperature and what we see
is that when we increase the temperature
of the gas the pressure increases this
is intuitive and this is actually you
know you might if you have a pressure C
cooker an instant pot insta pot in your
kitchen um that's exactly what's
happening it doesn't oftentimes uh at
least mine doesn't have a pressure gauge
on it but certainly the pressure goes up
uh quite a bit when you heat this rigid
vessel so um you can also plot this
relationship here um and if we explore
pressure on the y- axis as a function of
temperature you see that there's a
linear relationship when temperature
goes up so too does pressure so
mathematically what we would say with
this type of relationship with this
positive slope um when we plot one
variable against the other is that
pressure is proportional to
temperature when temperature goes up so
too does pressure if we want to write
this as as a mathematical expression we
could say pressure is equal to
temperature I left a little space here
on purpose because we can't just leave
it as pressure equals temperature that's
clearly not the case they are different
units and um but they do they are
related to one another um so what we can
say here just for the time being is that
there's must be some constant K uh that
that's related to the the the slope
there right um of that of that linear
plot and so this is our relationship so
K is just some constant we don't need to
Define that right now this is just a
relationship pressure is directly
proportional to temperature
the next law that we can talk about is
referred to as Charles's Law
Law
Charles's Law this is relating um this
is exploring what happens uh uh between
um volume and temperature so exploring
that relationship when you actually have
constant pressure this could be some
type of vessel where it's not a rigid
vessel but it can expand to make sure
that the pressure is always constant you
could think about an imaginary balloon
that can expand to Infinity where the
pressure won't start increasing when
once you stretch out the material too
far you could also think about a piston
that um allows the the the volume to
fluctuate but it's it's it's set such
that um it will always adjust the volume
so that the pressure does not um
change um so if we look at the plot here
um in Charles's Law exploring volume and
temperature where volume as a function
of temperature um in this plot we see
again similar to uh amonton's law or gay
laak's law that there is a direct
relationship here that is when
temperature increases so too does the uh
volume right if we go from 100 to 200
Kelvin we see that we go from some lower
volume up to a higher volume this makes
sense if you heat up a piston that it's
allowed to have the the the sort of the
a variable um volume it would expand
right if you heat up a balloon um it
will expand but of course the pressure
will at some point increase um because
the material will no longer expansion
but we're talking under this particular
controlled case of constant of constant
pressure um so what we can say here is
similar to the first scenario um these
are directly proportional to one another
so we can write v um uh is proportional
to T and if we want to write this as an
mathematical expression uh we would say
that V is equal to some constant
lowercase k multiplied by T V is not
equal to T they are different um
variables but they are related to one
another and they're directly
proportional in that
relationship the next law that we can
look at is called Bo's law boils
law Bo
boils law and boils law explores the
relationship between volume and pressure
this time at
constant temperature the example given
for boils law is a syringe where we can
take this syringe plunger that is the
inner part of the overall device that
I'm circling in red this is the plunger
and we can either push that plunger into
the barrel of the syringe or we can pull
that plunger out of the barrel of the
syringe and in this particular case um
all we're doing is measuring the
pressure this would not be a very good
syringe for doing anything of uh like
biomedical importance but it's good for
looking at um pressure changes um in boils
boils
law so uh what we can say here is that
if we look um over in this plot where
we're we're looking at the effect of um
or the uh uh pressure as a function of
volume we have a little bit different
Behavior now actually very different
behavior from what we've seen in the
other laws um essentially what's
happening is that the um when we
increase the volume okay so we pull that
plunger out we actually see that the pressure
pressure
drops okay conversely okay if we think
about what happens when you shove that
plunger into the barrel of the syringe
let's say we go from 20 uh a volume of
20 Millers and we uh reduce that volume
by half by shoving the syringe down so
it's only 10 Millers of space of
available to the gas again at constant
temperature what happens is we see that
this pressure goes up from about 10 here
to 20 in this plot this is a very
different relationship than before so so
what's happening is when volume
decreases pressure increases when
pressure decreases volume increases that
is an inversely proportional
relationship not only that but as
written um here it's not linear so what
we can say is what if we plot the
inverse of pressure if this is an
inverse relationship we plot inverse
pressure as a function of volume we get
a linear relationship where we increase
the volume here from like let's say 10
to 20 and we see an increase in the
inverse pressure so what does that mean
it means that if we want to write out
boils law as a uh sort of the expression
here um the the relationship is that
pressure is inversely proportional to
volume so we write one over v um and
then as a mathematical expression we
could write P equals um K some constant
K times 1 over V or just you know some
constant K Over
V again um uh p is not exactly equal to
1 over B but they are proportional to
one another there's an inverse
relationship there
okay the uh last law before we get into
the ideal gas law um is going to be uh avagadro's
avagadro's
law and you're wonder you might be
wondering like avagadro as an avagadro's
number yes uh and so avagadro's law
explores um the quantity of gas and um
volume so n here is not principal
quantum number anymore um it is actually
going to stand for a mo quantity okay so
moles so moles of gas and its
relationship with volume and this is
going to be at constant pressure and
temperature I don't have a plot to show
you for this um but it's very intuitive
if you think about when you're inflating
a balloon let's say with um a noble gas
like helium um the more helium you add
the bigger the balloon gets the more
volume is required for that uh for
increasing amounts of gas
so you could imagine then that um that's
a direct relationship the more gas the
more moles of the gas you put into um a
container the larger the volume that gas
wants to occupy if we allow constant
pressure and temperature so um what that
means is that we would predict that uh
volume is directly proportional to n the
mole amount of gas or we could write
volume is equal to some constant K
multiplied by
n when you combine all of these laws
that we uh uh have discussed when you
combine these you uh we we come up with
law the ideal gas law when everything is
combined is p v equals
nrt this equation uh encompasses all of
the relationships we've discussed so far
in those individual laws those individual
individual
observations you already know pressure
volume mole amount and temperature the
let's just call this some constant thing
that I was doing throughout all of the
other laws is now coales into a singular
constant that we use in the ideal gas
law that is capital r this is the ideal gas
constant and depending on the units it
comes in different you can use different
values for it the two most common that
we will see is um r equal
0.08206 the units here and these are
very important that you keep track of
the units liter atmospheres per mole
Kelvin uh you can also sometimes see
ideal gas constant I mean there are many
versions of the ideal gas constant but
um another one is 8.314
8.314
kilopascal liters or liter kilopascals
uh per mole
Calin okay so what you clearly uh uh
what's what should be hopefully um uh uh
registering now is that your units of
all the other variables or your units of
the other variables will depend on which
ideal gas constant you use so be very
mindful of which ideal gas constant you
use because you have to make sure that
the units cancel out appropriately so
why don't we go ahead and um do a
practice problem Oh I want to say one
more thing for the ideal gas law any gas
that um obeys this relationship is
called an ideal gas so any
gas that
obeys uh this
this
relationship and by this relationship I
mean the ideal gas law um is called an
ideal gas so it's often times the case
that um in in most contexts we just
assume ideal behavior of gases even if
they have nonideal behavior um in some
experiments let's do a quick
example um so what we're going to do is
uh oops actually I have it over here I
forgot about that okay so using the
ideal gas law methane CH4 is being
considered for use as an alternative
Automotive fuel to replace gasoline one
gallon of gasoline could be replaced by
655 G of methane what is the volume of
this much methane at 25° C and 20 and 70
for 745 T so uh if we remember the ideal
gas law here PV equals
nrt um what we can do here is actually
uh uh solve we want to solve for volume
so the final expression that we will
P but we have to be uh let's pick what
ideal gas constant we want to use uh I'm
going to use r equal 0.08206
0.08206
ler atmospheres per mole
Kelvin so that means that we need um
units of uh uh atmospheres moles and
Calvin in all the other um variables so
to begin we can convert that 655 gram uh
methane quantity using the molar mass of methane
methane
16.04 G per 1 Mo will give us 4
4.8 moles of methane so we have moles
that's good um you'll notice though that
it gave us temperature in degrees
celsius but we need it in kelvin um so
temperature is going to be equal to 25°
C but we can convert uh celsus to Kelvin
273 so this gives us a value of
298 Kelvin and pressure was given to us
in um
T 7 45 T but we need atmospheres again I
know that because atmospheres appears in
our ideal gas constant units so we can
use this uh conversion factor 760 t uh
is equivalent to one atmosphere this
gives us
0.980 atmospheres so now if we plug
everything in volume is equal to
40.8 moles multiplied by here R again is
0.08206 liter
atmospheres over mole Kelvin our
temperature is
298 Kelvin all over a pressure of
0.980 atmospheres so Kelvin will cancel
out here and here moles will cancel out
here and here atmospheres cancel out top
and bottom we're left with units of
liters that's great because we want the
volume and that's going to be in liters
so this gives us 1.02 * 103r l so that's
how to use the ideal gas law finally
what I want to mention is um uh some
conditions that are often times used
with these types of problems it's called standard
standard
temperature and pressure so oftentimes
we do experiments where we keep the
temperature and pressure uh constant or
we we have a well- defined uh uh meaning
for these so this is oftentimes um
called STP for standard temperature and
pressure so you might see something
referred to
a problem at STP the temperature at STP is
is
273.15 Kelvin exactly and the
pressure is equal to one atmospheres one
atmosphere exactly at
STP um so this now in the molar Highway
uh I've been telling you know uh my
section to we have not covered ideal gas
law yet you cannot convert between moles
and a volume yet uh prior to chapter 8
because we did not talk about the ideal
gas law but now in the molar Highway uh
uh conversions when you see where you
can convert from a mole of some some
gaseous substance to the volume of that substance
substance
directly um that's going to be under the
assumption of standard temperature and
pressure and under standard temperature
and pressure at
STP one mole of
gas um equals or it occupies a volume of
22.4 L that 22.4 L is called the standard
standard molar
molar
volume and so the the beauty of the
ideal gas law and um uh is that if a gas
behaves ideally it doesn't matter what
the identity is it doesn't matter if
it's helium if we have four grams of
helium if we have 17 grams of ammonia or
if you have 32 grams of o2 one Mo if
it's one mole of an ideal gas will
occupy 22.4 lers uh uh at STP regardless
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