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Dalton's Law of Partial Pressure

 

 

Dalton’s Law states that "The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone."

Ptotal = P1 + P2 + . . . Pn

  • Pt is the total pressure of a sample which contains a mixture of gases
  • P1, P2, P3, etc. are the partial pressures (in the same units) of the gases in the mixture

However, there is an unavoidable problem. The gas saturates with water vapor and now the total pressure inside the bottle is the sum of two pressures - the gas itself and the added water vapor.

WE DO NOT WANT THE WATER VAPOR PRESSURE.

So we get rid of it by subtraction.

Pdry gas = Ptotal - Pwater vapor

This means we must get the water vapor pressure from somewhere.

We get it from a table because the water vapor pressure depends only on the temperature, NOT how big the container is or the pressure of the other gas.

Temp (oC) Vapor Pressure (mmHg) Temp (oC) Vapor Pressure (mmHg)
-10 2.15 40 55.3
0 4.58 60 149.4
5 6.54 80 355.1
10 9.21 95 634
11 9.84 96 658
12 10.52 97 682
13 11.23 98 707
14 11.99 99 733
15 12.79 100 760
20 17.54 101 788
25 23.76 110 1074.6
30 31.8 120 1489
37 47.07 200 11659

Regents Questions

Example 1   A sample of hydrogen gas is collected over water at 14.0 oC.  The pressure of the resultant mixture is 113.0 kPa.  What is the pressure that is exerted by the dry hydrogen alone?

Pdry gas=113.0 kPa(760mmHg/101.3 kPa)=847.8mmHg

Pwater vapor= From Table=11.99mmHg

Ptotal=?

Pdry gas = Ptotal - Pwater vapor

Pdry gas = 847.8mmHg - 11.99mmHg

Pdry gas =835.8mmHg

Example 2 A mixture of oxygen, hydrogen and nitrogen gases exerts a total pressure of 278 kPa.  If the partial pressures of the oxygen and the hydrogen are 112 kPa and 101 kPa respectively, what would be the partial pressure exerted by the nitrogen.

PO2=112 kPa

PN2= ?

PH2=101 kPa 

Ptotal=278 kPa

 

Ptotal = PO2 + PN2 + PH2

278 kPa = 112 kPa + 101 kPa + Pnitrogen

Pnitrogen = 278 kPa - (112 kPa + 101 kPa)

Pnitrogen = 65 kPa

 

Questions

Highlight to Reveal Answers

3. A mixture of neon and argon gases exerts a total pressure of 2.39 atm.   The partial pressure of the neon alone is 1.84 atm, what is the partial pressure of the argon? Ptotal = PNe + PAr 

2.39atm=1.4 atm +PAr 

PAr =0.55atm

4. A 450 cm3 sample of hydrogen is collect over water at 12oC.   The pressure of the hydrogen and water vapor mixture is 78.5 kPa.  What is the partial pressure of the dry hydrogen gas?  PH2=78.5kPa(760 mmHg/101.3kPa)=589mmHg

Ptotal = PH2 + PH2O

Ptotal = 589mmHg + 10.52mmHg =  600.mmHg    

5. 888 cm3 of oxygen are collected over water with a temperature of 25 oC.  The total pressure of the gases is 55.8 kPa.  What is the partial pressure of the dry gas? Ptotal =55.8kPa(760 mmHg/101.3kPa)=419mmHg

Ptotal = PH2 + PH2O

419mmHg= PO2 + 23.76mmHg

PO2 = 395mmHg

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