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} = P_{1} + P_{2} + P_{3} +...+ P_{n} (1)
where P_{TOTAL} the total pressure of the gas mixture, P_{1 }the partial pressure of gas 1, P_{2} 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} / n_{1} + n_{2} +…+ 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 H_{2}O_{(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℃, P_{TOTAL }= 757 mmHg, P_{H2O} = 41 mmHg |
Asked for |
P_{CH4} = ? |
Using Dalton’s law:
P_{TOTAL} = P_{1} + P_{2} + P_{3} +...+ 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:
Relevant Posts
References
- M. Clugston, R. Flemming., “Advanced Chemistry”, Oxford University Press, 2000
- 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
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