# Partial Pressure & Vapor Pressure

Pi = Ptotal = P*
Since our system contains a pure substance at equilibrium, the vapor pressure of species i, P*(Tsat), equal to the total pressure and therefore :
Pi = (yi) (Ptotal) = Ptotal
For a pure substance there is only one species and, therefore, the vapor mole fraction is one (yi = 1). So, the partial pressure of species i is equal to the total pressure :
= the partial pressure of species i
= the vapor phase mole fraction of species i
= the total pressure

## Partial Pressure

:
The FRACTION of the total pressure in a gas phase due to the presence of one particular substance.
In an ideal gas mixture :
Ptotal V = ntotal R T
Pi V = ni R T
Pi = (yi) (Ptotal)
Where :

Pi

yi

Ptotal

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### Ch 2, Lesson D, Page 2 - Partial Pressure & Vapor Pressure

• Right up-front, you need to know that partial pressure is ONLY defined for gas phases.  So what does partial pressure mean ?
• The partial pressure of each species in a gas phase is the FRACTION of the total pressure due to that species.  If we REMOVED all of the other substances from the vessel and then measured the pressure remaining, we would be measuring the partial pressure of the remaining species.
• The symbol for partial pressure is a P with a subscript.  The generic subscript is “i.”  We might use P sub H2O for the partial pressure of water.  See how it works ?
• Now, let’s consider the case in which the gas phase is an ideal gas.  PV=nRT, right ?
• Well, the ideal gas law would also apply after we removed all of the other species from the can, right ?  So Pi V = ni R T.
• Now, just take the ratio of these two equations and notice that nii over ntotal is called the mole fraction of species i.  In the gas phase, we use the symbol yi to represent this mole fraction.
• The result is that the partial pressure of species “i” is equal to the mole fraction of species “i” in the gas phase times the total pressure.
• This makes sense since the mole fraction of species “i” is just the fraction of the molecules that are species “i.”
• Now lets get back to the can of water shown on the previous page.
• Since we have pure water in our can, the partial pressure of water is EQUAL to the total pressure.  Is this clear ?  The mole fraction of water in the vapor phase is 1.  It is pure water.  Now do you see why it is so important that we know that there is no AIR in the can ?  If there were air in the can, the mole fraction of water in the gas phase would be less than ONE !
• OK, so if we have a pure substance in VLE, what is the temperature within the system ?  It must be the saturation temperature that corresponds to the pressure in the system.
• But we also learned in the previous lesson that for a pure substance at vapor-liquid equilibrium, the total pressure must be equal to the vapor pressure.  That is, Ptotal = P*(Tsat).
• So, as we see in the last equation, because the substance is pure, yi = 1 and the partial pressure and the vapor pressure at Tsat and the total pressure are all equal !
• This makes for a nice simple way to measure the vapor pressure of a pure substance.  We can just submerge our can full of a pure substance in a constant temperature bath and read the vapor pressure from an ordinary pressure gauge !
• Now, lets see what happens if we let a little bit of air into our system.