Hey it’s professor Dave, let’s discuss the molar gas volume.
There are number of assumptions we can make about ideal gases.
We know the all the gas laws that dictate the relationship between pressure, volume,
temperature, and moles, and since we make the assumption that all ideal gases will behave
the same way, regardless of the identity of the gas, we can also say something about the
volume occupied by one mole of any ideal gas at standard temperature and pressure.
As it happens, one mole of any ideal gas at zero celsius and one atmosphere, or STP, will
occupy precisely 22.4 liters.
This value can easily be derived using the ideal gas law.
We simply plug in one atmosphere, one mole, and 273 kelvin, and this is the volume that
we get.
Doesn’t matter if it’s oxygen, nitrogen, hydrogen, argon, or any other ideal gas, this
is the molar gas volume at STP.
At higher temperatures this value would be larger, and at lower temperatures this value
would smaller, as we know from Charles’s law.
If the exterior pressure were different, this would also have an effect on the volume, as
we can assume based on Boyle’s law.
But the volume will typically be the same regardless of the identity of the gas.
This has a wide range of applications.
First, it makes calculations regarding moles and volume quite simple.
If we want to find out the volume occupied by two moles of oxygen at STP, we won’t
need to use the ideal gas law, we can just do dimensional analysis.
Two moles times 22.4 liters per mole gives us 44.8 liters.
We can convert volumes of ideal gas into molar values precisely the same way.
Just bear in mind that this only works at STP.
For any other conditions, the values must be plugged into the ideal gas law.
Beyond simplifications of this variety, we can use molar gas volume to identify unknown
gases.
If we know that any ideal gas will occupy 22.4 liters for every mole of gas, then if
we measure the density of the gas, in grams per liter, we can solve for the molar mass
of the gas.
This should be a big clue in identifying any unknown gas.
For example, let’s say you have some sample of gas, and you measure its mass as 1.79 grams,
and it occupies precisely 2.5 liters.
That means that the gas has a density of 0.716 grams per liter.
Now we can apply what we know about the molar gas volume.
What would the mass of this gas therefore be if the volume was 22.4 liters?
Let’s multiple by 22.4 and we get 16 grams for every 22.4 liters.
We also know that one mole of any gas will occupy 22.4 liters, so for this particular
gas, 16 grams must be equivalent to one mole.
That means that the molar mass of this gas is 16 grams per mole.
If we think about some common gases, like these ones listed here, we may find that methane
is the only one that matches.
It would be a good idea to do further experiments to be sure of this identification, but without
a doubt, calculating the molar mass of a substance dramatically narrows down the possibilities.
So beyond all of the laws and equations we have learned that pertain to ideal gases,
we can add one more bit of information, and that’s the molar gas volume.
Let’s check comprehension.