Dalton’s Law and Partial Pressures


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.




Comments
  1. How does sparging work, when the partial pressure of each dissolved gas is independent of the partial pressure of the sparging gas?

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