In this video we're gonna look at partial pressures. We're gonna use Dalton's law to
calculate partial pressures and total pressures. We're also going to look at mole fractions.
Dalton's law of partial pressures: the total pressure exerted by a mixture of gases is
the sum of the partial pressures of the component gases. So if we have a container with several
different gases in it the total pressure exerted by the mixture will be the sum of the partial
pressures of each of those gases. If we had two ideal gases, A and B, Dalton's law could
be expressed as P total equals partial pressure of A plus partial pressure of B. You'll often
see Dalton's Law expressed in this way. But if we think about the ideal gas law we can
also express it as the number of moles. So therefore we can express it as pressure total
equals number of moles of A times RT over V plus number of moles of gas B RT over V
or we can convert that into pressure total equals the number of moles of gas A plus the
number of moles of gas B times RT over V. As you can see here we're expressing the pressure
total by the sum of the number of moles of the gases. This means that we can now express
it in terms of mole fraction. If we look at the mole fraction the mole fraction of A given
by X subscript A is the number of moles of A over the total moles or nA over nT. If we
relate this to partial pressures and total pressure we can see that PA PT over nA times
RT over V over nT times RT over V. We can show as you can see here RT then cancels giving
us nA over nT and we know that A over nT is the mole fraction for A so therefore PA over
PT is related to XA. We can then convert that into the formula PA equals small fraction
A times the pressure for the total. Okay let's use these two expression and work two different
problems. First problem what is the partial pressure of each gas if 1.65 moles of propane
C3H8 and 0.920 moles of carbon dioxide are placed in a 30 L container at 25°C? What
is the total pressure? So if we analyze the question here it's giving us some information
but it's actually asking us two things. One we're gonna get the partial pressures for
each the propane and the CO2 and it has a second question. What is the total pressure?
So we're also going to have to calculate the total pressure. We know that it gives the
number of moles of propane and CO2 and it gives us the volume and the temperature. We
can calculate the pressure by using PV equals nRT. If we convert PV equals nRT to get pressure
by itself we'll see that we get nRT over V. For partial pressure for propane we just need
to plug in our values. So 1.650 moles times the constant R times 293.15 Kelvin which is
the conversion of 25°C to Kelvin divided by 30.0 L. We do that calculation. We look
at our significant figures and we see that our answer here is gonna be the partial pressure
of propane is equal to 1.32 atm. We can do the same calculation using P equals nRT over
V for the partial pressure of CO2. Here we have the partial pressure of CO2 plug in our
values 0.920 moles times the constant R times 293.15 Kelvin which is the conversion of 25°C
divided by 30 L. That gives us the partial pressure of CO2 of 0.738 atm. So we've answered
the first question with partial pressures. Now we have to do total pressures. Remember
there's two ways to do this. One way we can look at partial total is equal to the partial
pressures of propane plus the partial pressure of CO2. We already calculated these so we
just have to plug them in. So the total pressure is going to be 1.32 atm plus 0.738 atm. Add
those together remember our significant figures and we come out with the total pressure equals
2.06 atm. At this point we've answered our problem but we can check it by using the other
expression for pressure total where we relate it to the number of moles. So we can take
the values directly out of the question 1.650 moles plus the number of moles for CO2 0.92
moles and we can put that in the formula number of moles of propane plus number of moles of
CO2 times RT over V. We plug all those values in. We do our calculation. Again following
significant figures and we come up with a pressure total of 2.06 atm. Now let's look
at calculating the ratio of moles of a gas from the partial pressures and total pressure.
For that value we're going to look at this problem what is the moles fraction of CO2
and a mixture of gases with a partial pressure of CO2 of 1.75 atm and a nitrogen of 0.425
atm. So in this case we're given the partial pressures so we can remember that the mole
fraction of CO2 which is what the question is asking for is going to be the partial pressure
of CO2 over the total pressure. We have the partial pressures of those both CO2 and Nitrogen
but not the total pressure. We can calculate the total pressure by adding the two partial
pressures so P total equals partial pressure of CO2 plus the partial pressure of nitrogen.
We can look those values up. Partial pressure CO2 is 1.75 atm from the question, partial
pressures of nitrogen is 0.425 atm from the question. We put those into the formula add
those together and we get a total pressure of 2.18 atm. Now we have both the values we
need to calculate the mole fraction. So we take the mole fraction that's the partial
pressure of CO2 over the total pressure so 1.75 atm over 2.18 atm. Do our calculation
and we come up with the mole fraction of CO2 is 0.80. Notice in this case that we do not
have any units because partial pressure of CO2 is in atmospheres and the total pressure's
in atmospheres so those cancel leaving us a unit-less quantity. Practice partial pressures,
calculating total pressure, and mole fractions. Practice and become confident.