One of the nice features of the ideal
gas law is that it applies both to pure gases and gas mixtures. If you
have a mixture of two gases, A and B
- Ptot = ntotRT / V
= (nA + nB)*RT / V = PA + PB
The terms
- PA = nART / V
- PB = nBRT / V
are called the partial pressures of
gases A and B, respectively. The partial pressure of the gas can be
computed from the ideal gas law in many gases, or from the mole
fraction of the gas and the total pressure.
The sum of the partial pressures of the
gases in a mixture is the total pressure of the gas:
- Ptot = PA + PB
+PC + ...
This relationship was first noted in the early
1800's by the English scientist John Dalton, and is sometimes known as Dalton's
Law of Partial Pressures.
Example: You have 1.00 grams of
hydrogen gas and 1.00 grams of oxygen gas confined in a 1.00 liter flask
at 25oC. What is the pressure in the flask?
Solution: Dalton's law tells us that
the pressure in the flask is the sum of the partial pressures. We can use
the ideal gas law to get the pressures of hydrogen and oxygen:
- Hydrogen: 1.00 g/ 2.02 g/mole = 0.496
moles of hydrogen
- PH2 = nRT / V
- PH2 = 0.496 moles
* 0.0821 (L*atm/mol*K)*298 K/1.00 L
- PH2 = 12.1 atm
Oxygen: 1.00 g/ 32.0 g/mole = 0.0313 moles of oxygen
- PO2 = nRT / V
- PO2 = 0.0313 moles
* 0.0821 (L*atm/mol*K)*298 K/1.00 L
- PO2 = 0.765 atm
The total pressure in the flask is just the
sum of the two partial pressures
- Ptot = PH2+
PO2
- Ptot = 12.1 + 0.765
- Ptot = 12.9 atm
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