Professor Dave here, let’s talk about Dalton’s law.
We’ve learned a lot about ideal gases and some of the laws that describe their behavior,
but up until now we have been examining the relationships between the variables that pertain
to an individual sample of gas.
But a lot of samples of gas involve mixtures of different substances, so we will want to
learn about how these gaseous mixtures behave as well.
If we take two different gases and mix them together, will there be any new properties
that can be observed?
What will be the total pressure?
It is the case that as long as these gases do not react with one another, the pressure
that each gas exerts in a mixture of gases is specific to the amount of that particular
gas that is present, and we will call the pressure of that particular gas, its partial
pressure.
In order to find the total pressure of the vessel, we will simply add up the partial
pressures.
This is stated in Dalton’s law.
When you think about it, it makes perfect sense, since pressure is just the force exerted
as particles strike the sides of the container.
So the pressure from all the particles of one gas plus the pressure from all the particles
of another gas should add up to be the total pressure for all the particles, assuming we
are treating these as ideal gases where their identities are irrelevant.
We can also make statements about the partial pressure of each individual gas as they relate
to something called the mole fraction of that gas, which is a measure of the number of moles
of a substance compared to the total moles of matter present, and the partial pressure
of a gas within a mixture will be equal to the mole fraction of that gas times the total
pressure.
So if there were 0.25 moles of a particular gas out of one mole of total gas particles,
that would mean a mole fraction of 0.25, and if the total pressure of the sample was 800
torr, the partial pressure of the gas in question would be 200 torr.
Again, this makes sense on the molecular level when we consider individual collisions occurring
between the particles and the sides of the contained, and the fraction of these collisions
that is represented by any individual substance.
To see this demonstrated, let’s say we capture a sample of earth’s atmosphere at sea level.
We know that there will be several different gases in the sample, as the atmosphere is
comprised of nitrogen, oxygen, and argon, in roughly these quantities, plus trace amounts
of a bunch of other things, and the sample as a whole exerts a pressure equal to atmospheric
pressure, or one atmosphere.
But what contribution to this total is provided by each component of the gas?
Recall that Dalton’s law says that the sum of the partial pressures of the component
gases in a mixture will be equal to the total pressure.
That means that if we pretend the atmosphere is comprised of only these three gases, the
partial pressure of nitrogen plus the partial pressure of oxygen plus the partial pressure
of argon will add up to atmospheric pressure.
But how do we calculate the partial pressure of each gas?
Well again, the partial pressure of a gas is related to the mole fraction of the gas,
or the fraction of the mixture that gas represents by number of particles.
This means we can take these percentages and divide them by a hundred in order to express
them as mole fractions, and then we can multiply each mole fraction by the total pressure to
get the partial pressure of each substance.
So it’s quite simple to calculate the partial pressure of each gas in our sample, and we
can see that these do add up to a total of one atmosphere, just as the individual percentages
add up to 100%.
We can do trickier calculations as well, by including other gas laws.
Let’s say we have quantities in moles of a few different gases, and we place them into
a vessel of known volume and at a known temperature.
We could then use the ideal gas law to solve for the total pressure, and then if we calculate
the mole fraction of each gas, we could combine this information to find the partial pressure
of each gas.
So Dalton’s law is quite intuitive when you think about it, but it allows us to do
important calculations regarding the partial pressures of individual gases within a mixture.
Let’s check comprehension.