Avogadro's Hypoth - Redox Reactions Video Lecture | Physical Chemistry

Avogadro's law talks about the
relationship between the amount of gas
that's in a gas sample and the volume of
the gas sample so what does that mean
well first of all a gas sample is just a
fancy term that means a bunch of gas we
have anywhere so for example this
balloon has a whole bunch of gas in it
that is what's keeping it inflated so
the gas in here can be considered a gas
sample this gas sample the balloon has
both volume it takes up a certain amount
of space that we could measure and
there's also a certain amount of gas
inside but I talked about the
relationship between these two things
all I mean is what happens when I change
one of them what happens to the other so
let's talk about this let's let's
imagine that I have my balloon and
investigate the relationship between
these two bit variables okay here is a
real quick drawing of the balloon okay
so talk about the relationship here
let's say that I untie the knot at the
end of the balloon and I blow more air
into it that is going to increase the
amount of gas that's in that balloon so
we'll say that little n the symbol that
we use to indicate the amount of gas
little n goes up so the relationship
what effect is that change going to have
on the volume of the balloon well okay
this isn't exactly rocket science this
isn't exactly rocket science it's going
to make the volume of the balloon get
bigger we increase the amount of air the
amount of gas that's inside the volume
goes up so n goes up and V goes up as
well
okay let's look at the opposite case I
untie that out at the end of the balloon
and I let a whole bunch of gas out so in
that case little n is going to get
smaller and what effect is that going to
have on the balloon on the volume of the
balloon well the balloon is going to
shrink it's going to take up less and
less volume and here's our baby little
balloon here the volume has gone gone
down so here's a relationship when one
of them goes up the other goes up when
one of them goes down the other goes
down what's this kind of a relationship
called you may already know this is what
we call a direct relationship it's when
two variables move in the same direction
and we can show this relationship with a
graph here here on the X X I have the
amount of gas which is in moles we'll
talk about that later but that's how we
measure the amount of gas in something
amount of gas here and on the y axis I
have volume as we increase the amount of
gas the volume goes up as well and it
actually turns out if we double the
amount of gas that's in a gas sample
like a balloon it also doubles the
volume the amount of space that that gas
sample takes up so here's a graph of
avocado slaw okay now one thing is
important to keep in mind and that's
that when I was talking about the
balloon I was changing only two things
right the two things I were changing was
the amount of gas that was one of them
and the volume was the other there are
other things that I was not changing
about that balloon okay while I was
changing the amount of gas I was not
changing the temperature okay it's not
like I was letting out gas and I was
heating up the balloon you can't do that
the other thing that I wasn't changing
is I wasn't changing the pressure so
it's not like I was blowing up the
balloon but then taking it up to the top
of Mount Kilimanjaro where the air
pressure is much less than it is here
down at sea level so I was also not
changing the pressure so we're talking
about Avogadro's law the relationship
between the amount of gas and the volume
I can change either one of those but I
can't change I cannot change the
pressure or the temperature of that gas
these are my constants these are my
variables okay there's one thing that I
want to show you really quickly okay and
that is this device that we talk about a
lot when we're doing Avogadro's law okay
you always see pictures of
this when in textbooks and stuff when
we're talking about Avogadro's law so
that's just what I want to talk about
for a minute and this is this is a crazy
thing okay
it's a canister of gas that has a
sliding top and I made 100 I made a
model of one out of a soda bottle
okay and you can kind of see how this
works that I have imagined that this is
a canister that holds gas and I got a
pipe that goes in that I can add gas
into and then you can see this top
imagine that this top could slide up and
down in here okay so what's the point of
this the reason we always see these guys
and this is how usually how they're
drawn and we're talking about Avogadro's
law is because they're a way to change
the volume of a sample of gas without
changing its pressure this pipe here
indicates something that I could use to
pump gas and so imagine that I pump gas
in here that would normally raise the
pressure of a container but not if the
top can slide instead the volume change
so I add a little gas in here and the
top slides up and then I suck a little
gas out and the top falls back down
instead of the pressure changing the top
slides up and down so that's why you
always see pictures of this kind of an
apparatus it's kind of a device that's a
fancy whereat apparatus but the point of
it is just that it's a canister of gas
with a slidable top that can go up and
down that can change the volume of the
canister as I change the amount of gas
that's in here without changing a
pressure
okay so Avogadro's law is used a lot for
math problems and when we talk about
math problems with Avogadro's law the
form of the law that we usually use is n
1 divided by V 1 equals n 2 divided by V
2 this equation assumes that some sort
of change is taking place like the
change I was talking about earlier it
assumes that I have an initial amount of
gas
an initial volume that's before the
change and then the amount of gas and
the volume change after I do something
to it
okay so let's work through this
Avogadro's law by looking at a math
problem so in a sample of gas 50.0 grams
of oxygen gas take up 48 liters of
volume keeping the pressure constant
remember that's important not God Rose
law pressures got to be constant keeping
the pressure constant the amount of gas
is changed until the volume is 79 liters
how many grams of gas are now in the
container when I'm doing problems like
this I find it really helpful to keep
track of my variables by making a chart
like this I've got my before and I got
my after because we said there's a
change it takes place this little arrow
we're moving from one to the other let's
get our variables straight before we
plug anything into this equation so in a
sample of gas 50 grams take up 40 liters
that's what we start with okay
so that means that n1 I'm going to make
that 50 point zero grams that's that and
the volume it says here that they take
up 48 liters of volume okay so 48 liters
is before the change now here's the
change keeping the pressure constant the
amount of gas is changed until the
volume is 79 liters okay so that means
that my v2 is going to be 79 liters the
volume after the change and the question
is how many grams of gas are now in the
container after the change so it's going
to be n2 that I'm going to be solving
for so now I got my variables straight I
know what I'm going to be solving for
and I know the other guys okay now it's
important to look at units there are two
things to keep in mind when we're doing
Avogadro's law this little n always has
to be in
okay moles is usually how we keep track
of the amount of gas we have in a sample
so mole the amount of gas here was given
it in grams that's not going to work
we're going to have to convert it to
moles and it's probably the biggest
mistake that people make when they're
doing Avogadro's law they don't remember
to convert grams into moles so hey if
you get a practice problem and you're n1
or n2 is already in moles you're all set
no big deal you can skip this step but
if you get a practice problem like most
of them are where the ends are in grams
we're going to have to convert it to
moles so we'll do that in a minute the
other thing is the v's it doesn't matter
what units the volume is in as long as
they are both in the same units okay so
leaders here leaders here were set if
this was milliliters milliliters that
would also be okay but it wouldn't work
if one was milliliters and the other was
leaders okay so volume units don't
matter as long as they're both the same
okay so now I've got my before and I've
got my after I'm gonna change my fifty
grams into moles and in order to do that
I'm gonna have to use the molar mass
which tells us how much one mole of a
gas weighs okay so the molar mass for
oxygen is 2 times 16 because each oxygen
atom weighs 16 and then we do two times
that because there are two oxygens and
we get 32.0 grams per mole okay so now
we want to go from grams which is 50
point zero grams and I want to multiply
this by this grams per mole fraction in
a way that's going to cancel out grams
so I'm actually going to want to flip
this so that I have grams on the bottom
so they cancel out okay
so I'm going to do one mole divided by
32.0 grams all I've done is flip this
now I have grams up here and grams down
here that means they cancel out I'm
going to be left with moles and the
answer that I get there is one point six
moles so I can cross out my 50 grams and
replace it with one point six moles now
I got my ends in moles I got one of my
ends and moles I got both my volumes and
liters which is the same unit and now
I'm ready to go so it's going to be n
two that I want to solve for I want to
rearrange the equation to get n two by
itself on one side of the equation so to
get n two by itself I want to get rid of
the V 2 that's in the denominator right
now so I'm going to multiply both sides
of the equation by V two now I have V
two above V two down here which means
they cancel out and I'm going to be left
with V 2 times n 1 divided by V 1 equals
and to some people like having the
variable that we're solving for on the
left so I'm just going to switch that
real fast but it doesn't make a
difference I'm just going to put it in
reverse here V 2 times N 1 divided by V
1 ok now we're ready to take our
variables that we've laid out here and
and plug them in so I've got n 2 equals
V 2 79 liters times n 11.6 moles divided
by V 1 which is 48 liters and when I do
that the number that I get is going to
be let me check here 2.6 and what are my
units going to be well liters up here
liters down there cancel out so my final
answer here is going to be two point six
moles not quite done with a problem yet
though because my question here asked me
how many grams of gas are now in a
container not how many moles of gas so
now I'm going to have to take this mole
number and convert it back into grams
how am I going to do that
well what I'm going to want to do is I'm
going to want to take the molar mass of
oxygen again which as we said earlier
was thirty two point zero grams per mole
and I'm going to take my mole number two
point six moles and I want to multiply
it by this conversion factor in a way
that's going to get rid of my moles so I
can keep the conversion factor just as
it is right now and I'll have moles on
the top moles on the bottom so two point
six moles times thirty-two point zero
grams divided by one mole now mole on
top mole on the bottom they cancel out
and when I do the math two point six
times thirty-two I'm going to get 83
grams which I'm going to round to two
significant figures because I have two
sig figs here and three sig figs here I
always go with a smaller number so I am
going to get 83 grams as my final answer
okay so that's Avogadro's law if you
have questions on how to rearrange this
law to solve for any of the other
variables I've done a video on that
check out my rearranging gas equations
videos if you have any questions in
general about these gas laws be sure to
check out the gas laws extra help and
frequently asked question video which
should clear up any other questions that
you have with this sort of stuff