John Dalton conculded that each gas in a mixture of unreactive gases acts,as far as its pressure is concerned, as though it were the only gas in the mixture.
According the the Dalton,each gas exerts the same pressure in the flask that it would exert if it were the only gas in the flask.
According to the Dalton's law the pressure the sum of the partial pressure of all different gases in a mixture is equal to the total pressure of the mixture.
If you let P be the total pressure and Pa,Pb,Pc..... be the partial pressures of the component gases in a mixture,the law of partial pressure can be written as:
Beacuse the ideal gas law applies to all gases, you might expect it to apply to gas mixtures.For a mixture of two gases A and B, the total pressure is given by the expression
Ptot= n tot RT/V = (nA+nB) RT/V
seperating the two terms on the right,
Ptot = nA RT/V + nB RT/V
terms nA RT/V and nB RT/V are according to the ideal gas law, the pressures that gas A and B would exert if they were alone.These quantiies are referred to as partial pressure , PA and PB .
PA = partial pressure A = nA RT/V
PB = partial pressure B = nB RT/V
so, Ptot = PA + PB
Partial pressure and mole fraction:
The composition of a gas mixture is often described in terms of mole fractions of the component gases.The mole fraction of a component gas is the fraction of moles of that component in the total moles of gas mixture.
PA= nA RT/V
Ptot= n tot RT/V
Dividing PA by Ptot gives
PA/Ptot = nA/ntot
The fraction nA/ntot is referred to as the mole fraction of A in the mixture. It is the fraction of the total number of moles that is accounted for by gas A.Using XA to represent the mole fraction of A:
PA= XA Ptot
in other words:
Partial pressure = mole fraction x total pressure
Lets see an example:
When one mole of methane, CH4 is heated with four moles of oxygen,the following reaction occurs:
CH4 + 2O2 ---------> CO2 (g) + 2H2O (g)
assuming all of the methane is converted to CO2 and H2O, what are the mole fraction of O2,CO2 and H2O in the resulting mixture? If the total pressure of the mixture is 1.26 atm .What are the partial pressures?
Strategy ; First calculate the number of moles of each gas (remember that oxygen is in excess).Then determine the mole fractions and finally the partial pressures.
Solution: Since, all the methane is consumed,
nCH4 = o ; nCO2 =1.00 ; nH2O = 2.00 ; nO2 = 4.00 -2.00 = 2.00
The total number of moles is 1.00+2.00 +2.00 = 5.00
X CO2 = 1.00/5.00 = 0.200 ; XH2O = 2.00/5.00 = 0.400 ; XO2 = 2.00/5.00 = 0.400
PCO2 = 0.200 x 1.26 atm = 0.252 atm
PH2O = 0.400 x 1.26 atm = 0.504 atm
PO2 = 0.400 x 1.26 atm = 0.504 atm