Dalton's Law - Law of Partial Pressures

Dalton’s law of partial pressures states:

“The total pressure P of a gas mixture is the sum of the partial pressures of all the gases in the mixture”

P_TOTAL = P₁ + P₂ + P₃ +...+ P_n         (1)

where P_TOTAL the total pressure of the gas mixture, P₁ the partial pressure of gas 1, P₂ the partial pressure of gas 2, P_n the partial pressure of gas n.

Another version of Dalton’s law states:

“The partial pressure p_i of one component in a mixture of gases is equal to its concentration expressed in mole fraction x_i times the total pressure P_TOTAL”.

P_i = x_{i *} P_TOTAL         (2) 

Mole fraction, x_i, is an important measure of concentration in mixtures such as molarity, molality and normality. The mole fraction of the i th component in a mixture of substances is defined as the number of moles (n_i) of the substance divided by the total number of moles (n_n) of all substances:

x_i = n_i / n₁ + n₂ +…+ n_n = n_i / Σn_n       (3)

Equation (2), partial pressure of a gas in a mixture as a function of the total pressure of the mixture P_TOTAL ,  is derived from the ideal gas law as follows:

P_i = n_i * (RT/V) = (n_i/n) * n * (RT/V) = x_i * P_TOTAL       (4)

Dalton’s law is used in calculations involving the collection of a gas over water, as in the displacement of water by oxygen gas. In this situation there is a gas mixture that consists of O_2(g) and water vapor H₂O_(g). The total pressure in this case is atmospheric pressure (1 atm = 760 mmHg) and the partial pressure of the water vapor at this temperature is found in tables. Simple subtraction gives the partial pressure of oxygen.

 

Example I.1

A sample of methane gas was collected over water at 35 ℃. The sample was found to have a total pressure of 757 mmHg. Calculate the partial pressure of methane  gas in the sample. It is given that the vapour pressure of water at 35 ℃ is  41mmHg.

Given	T = 35℃, PTOTAL = 757 mmHg, PH2O = 41 mmHg
Asked for	PCH4 = ?

Using Dalton’s law:

P_TOTAL = P₁ + P₂ + P₃ +...+ P_n

In our case:   P_TOTAL = P_CH4 + P_H2O. The only unknown is P_CH4. Solving for P_CH4:

P_CH4 = P_TOTAL - P_H2O = 757 mmHg – 41 mmHg = 716 mmHg

Please see also another example in the video below: 

 

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Relevant Posts

Properties of Solutions - Henry’s Law - Effect of Pressure on Solubility

Solutions and Concentration

Gas Laws - Ideal Gas Law

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References

1. M. Clugston, R. Flemming., “Advanced Chemistry”, Oxford University Press, 2000
2. S. Zumdahl, "Chemical Principles", 6th Edition, Houghton Mifflin Company, 2007
   
   

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Key Terms

partial pressures, Dalton's law, mole fraction, ideal gas law, Dalton's law formula

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