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S1.5.3 Molar volume of a gas
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this is msjcam in this video i'll be
looking at the molar volume of a gas
the molar volume of a gas is the volume
occupied by one mole of an ideal gas
the molar volume must be stated at
specific conditions
in this video i'll be using the
conditions of stp
these are a temperature of 273 kelvin
and a pressure of 100 000 pascals
here we can see these values plugged
into the ideal gas equation
which has been rearranged to calculate
for volume
as we can see this gives us a volume of
0.0227 meters
cubed the molar volume can be determined
by dividing the volume by the amount in moles
moles
in this equation we have a volume of
0.0227 meters
cubed which is the volume occupied by
one mole of an ideal gas
so this gives us the molar volume of an
ideal gas
under conditions of stp which is
0.0227 meters cubed per mole
or 22.7 decimeters cubed
per mole in the previous slide we
defined the molar volume of a gas as the
volume occupied by one mole of an ideal gas
gas
under conditions of stp under these conditions
conditions
real gases such as oxygen hydrogen and chlorine
chlorine
behave almost the same as ideal gases
for example one mole of oxygen gas under
conditions of stp
will occupy a volume of 22.7 decimeters cubed
cubed
the same is true for one mole of
hydrogen gas
and one mole of chlorine gas
so we can now say that under conditions
of stp one mole of
any gas be it an ideal gas or a real gas
occupies a volume of 0.0227 meters cubed
which is more commonly given as 22.7
decimeters cubed
next we'll look at equations that can be
used to calculate either the volume
or the amount in moles of a gas
the first equation we look at is used to
calculate volume
to calculate the volume of a gas
multiply the amount of moles
by the molar volume an easy way to remember
remember
this equation is v equals n multiplied by
by
22.7 note that this equation will give
you the volume
in decimeters cubed the next equation is
used to calculate the amount in moles
to calculate the amount of moles divide
the volume
by the molar volume once again an easy
way to remember this equation
is n equals v divided by 22.7
in the first example we'll calculate the
volume in decimeters cubed
occupied by 0.250 moles of nitrogen gas
at stp the equation that we'll use is volume
volume
equals amount in moles multiplied by the
molar volume of a gas
so the volume is equal to 0.250
multiplied by 22.7 and this gives a
volume of 5.68 decimeters cubed
note that the unit of volume in the
answer is the same as that in the question
question
which is decimeters cubed the next
example is calculate the volume in
centimeters cubed occupied by
0.00619 moles of carbon dioxide
at stp so first we'll calculate the
volume in decimeters cubed and then
convert to
centimeters cubed to do this we multiply
the amount in moles
by the molar volume and this gives us 0.14
0.14
decimeters cubed because the question is
asking for the volume in centimeters cubed
cubed
the final step is to convert from
decimeters cubed to
centimeters cubed one decimeter cubed
is equal to 1000 centimeters cubed so we
multiply this volume in decimeters cubed
by one thousand and this gives a volume
of 141
centimeters cubed of carbon dioxide
in the next example we'll calculate the
amount of moles of nitrogen in a 0.742
decimeter cubed sample so we'll use this
equation which is
n equals v divided by 22.7
the volume of nitrogen is 0.742
decimeters cubed
which we then divide by the molar volume
of a gas at stp
and this gives us an amount of nitrogen
of 0.0327 moles
in the next example we'll calculate the
amount of moles of ch4 which is methane
in a 2.36 centimeter cube sample at
stp the first step in this calculation
is to convert the volume from
centimeters cubed to
decimeters cubed so 2.36 centimeters
cubed is equal to 2.36 times 10 to the
negative 3 decimeters cubed
we can then use the same equation as in
the previous slide which is
n equals v divided by 22.7
so as we just calculated the volume of
ch4 is 2.36 times 10 to the negative
three decimeters cubed
which we then divide by the molar volume
of a gas at stp
which gives us an amount of methane of 1.04
1.04
times 10 to the negative 4 moles
in the last example we'll determine the
volume of hydrogen in centimeters cubed
produced at stp when 2 grams of
magnesium is reacted with excess
hydrochloric acid
so here we have the balanced equation
for the reaction
magnesium reacts with hydrochloric acid
to produce
magnesium chloride and hydrogen gas
the first step is to determine the
amount in moles of magnesium
to do this we divide the mass of
magnesium by the molar mass
which gives us 0.0823 moles
we then use the balanced equation to
determine the ratio
of magnesium to hydrogen so from the
balanced equation we can see it's a 1 to
1 ratio
so this means that 0.0823 moles of magnesium
magnesium
will produce the same amount which is
0.0823 moles of
hydrogen so in the previous slide we
determine the amount of moles of hydrogen
hydrogen
that will be produced in the reaction
next we'll convert the amount in moles
to volume
we'll use the equation volume equals
amount in moles
multiplied by 22.7 so that's
0.0823 multiplied by 22.7
which gives a volume of 1.87 decimeters
cubed in the final step we'll convert
from decimeters cubed to centimeters cubed
cubed
so 1.87 decimeters cubed is equal to
1.87 times 10 to the 3
centimeters cubed so this is the volume
of hydrogen gas
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