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in today's video we're going to be
focusing on this equation
which links the volume of a gas in
decimeters cubed
to how many moles of that gas we have
it's actually a really simple equation
because it doesn't matter which type of
gas you have
like whether you have chlorine or water
vapor or oxygen
all you have to do is multiply the
number of moles that you have
by the number 24
and that will give you the volume that
the gas takes up
measured in decimeters cubed
for example if we had 3.5 moles of
chlorine gas
then we would just do 3.5
times 24
to find that it took up 84 decimeters
cubed
we can also use the equation the other
way around
for example if we had 60 decimeters
cubed of oxygen
and we wanted to know how many moles
that was
we'd just rearrange the equation
to volume over 24 equals moles
and then do 60 divided by 24
which gives us 2.5 moles of oxygen
it can get a bit trickier if we're not
given the moles
for example if we had 27 grams of water
vapor
how would we find its volume
well we can see from our equation that
to find the volume we first need to find
the moles
so we're going to have to use this other
equation first
which links mass
moles and relative formula mass
already know that the mass is 27 grams
so we just need the mr
which for water which is h2o
would be 16 for the oxygen
plus 2 times 1 for the hydrogens
so eighteen
then we can divide the mass of 27 grams
by the mr of 18
to find that we must have 1.5 moles of
water vapor
then lastly all we need to do is go back
to our original equation
take our 1.5 moles
and multiply it by 24
to find that the water vapor would have
a volume of 36 decimeters cubed
another thing you might be asked to do
in the exam
is to find the volume of a product when
you're given the volume of a reactant
for example in this equation here
what volume of ammonia would be produced
if we reacted 18 decimeters cubed of
nitrogen with excess hydrogen
the first thing to notice is that the
hydrogen is in excess
which means that the nitrogen must be
the limiting reagent
and so the quantity of ammonia produced
is going to depend entirely on how much
nitrogen we have
next the normal thing to do in this sort
of question would be to find out how
many moles of nitrogen we have
so we take our volume of 18 decimeters
cubed
and divide it by 24
which tells us that we have
0.75 moles of nitrogen
and then we can use the molar ratio to
find out how many moles of ammonia that
will form
remember we find the molar ratio by
comparing these big numbers in front of
the chemical symbols
so an imaginary one for nitrogen because
when there's no number it just means
there's an unwritten one
and a two for ammonia
so the ratio is one to two
which tells us that for every mole of
nitrogen we have
we're going to make two moles of ammonia
so as we have 0.75 moles of nitrogen
we must have 0.75 times 2 moles of
ammonia
so 1.5 moles of ammonia
then finally we just go back to our
original equation
and multiply the 1.5 moles of ammonia by
24
to find that we'll make 36 decimeters
cubed of ammonia
now this whole idea of finding the moles
and then using molar ratios
is what you would normally have to do in
a question like this
however if you're only converting
between gas volumes like we are here
then you don't actually have to do any
of this stuff
all you need to do is look at the modal
ratio
which is one to two
and so you can multiply the original
volume of nitrogen which is 18
decimeters cubed
by two
to find that you'd make 36 decimeters
cubed of ammonia
and the reason we can do this is because
if we have twice as many moles of a gas
it's going to take up twice the volume
to see the zim practice let's change the
question a bit
if we start with four decimeters cubed
of nitrogen
how much hydrogen would it react with
because we're only converting gas
volumes we can just look at the molar
ratio between nitrogen and hydrogen
which is one two three
so then we just take the nitrogen's
volume of four decimeters cubed
and multiply it by 3
to find that it would react with 12
decimeters cubed of hydrogen
the very last thing i want to mention
is that this equation with the number 24
only works for gases at room temperature
and pressure
if we change the temperature or the
pressure
then it would change the number
as gases occupy different volumes at
different temperatures or pressures
but in the exams this equation with the
number 24 is the only one that you'll
need to use
anyway that's everything for this video
so hope you found it useful and we'll
see you again soon
