Dalton’s Law – Law of Partial Pressures | Chemistry Net

# Dalton’s Law – Law of Partial Pressures

Dalton's law - Law of partial pressures

# 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

PTOTAL = P1 + P2 + P3 +...+ Pn         (1)

where PTOTAL the total pressure of the gas mixture, P1 the partial pressure of gas 1, P2 the partial pressure of gas 2, Pn the partial pressure of gas n.

Another version of Dalton’s law states:

The partial pressure pi of one component in a mixture of gases is equal to its concentration expressed in mole fraction xi times the total pressure PTOTAL”.

Pi = xi * PTOTAL         (2)

Mole fraction, xi, 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 (ni) of the substance divided by the total number of moles (nn) of all substances:

xi = ni / n1 + n2 +…+ nn = ni / Σnn       (3)

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

Pi = ni * (RT/V) = (ni/n) * n * (RT/V) = xi * PTOTAL       (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 O2(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:

PTOTAL = P1 + P2 + P3 +...+ Pn

In our case:   PTOTAL = PCH4 + PH2O. The only unknown is PCH4. Solving for PCH4:

PCH4 = PTOTAL - PH2O = 757 mmHg – 41 mmHg = 716 mmHg

Relevant Posts

References

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

Key Terms

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