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
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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?
