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Dalton’s law of Partial Pressure was proposed by English chemist John Dalton in 1802. He extensively studied the mixtures of non-reactive gases enclosed in a vessel and states that the total pressure exerted by the mixture of non-reactive gases is qualt to the sum of partial pressures exerted by individual gases when kept at a particular temperature and volume.
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Partial Pressure
The gas molecules in an enclosed vessel always exert some kinetic pressure on the walls due to the collision of molecules. Therefore, the force per unit area is the pressure exerted by the gas inside the vessel.
In other words, partial pressure is the pressure exerted by individual gas molecules on the walls of the vessel. For example, if a vessel contains Hydrogen, Helium and Oxygen molecules, then the pressure exerted by the Oxygen molecule individually will be the partial pressure of Oxygen.
Similarly, the pressure exerted by Helium individually will be its partial pressure and the pressure exerted by Hydrogen individually will be its partial pressure.
The partial pressure of the gas is represented by the symbol P with the symbol of the gas in the subscript. For example, PO2 represents partial pressure of oxygen.
Dalton’s Law of Partial Pressure
According to Dalton’s law of partial pressure, total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture. Dalton’s law is perfectly true for ideal gas mixture. In ideal gas, molecules are very far from each other so they do not react. The mixture of real gases also follows Dalton’s law with slight variation.
To understand Dalton’s Law, consider a vessel filled with non-reactive gases like Helium (He), Oxygen(O2) and Hydrogen(H) which are kept at constant temperature and constant volume. In such a scenario, all three gases will exert some pressure on the walls of the vessel. Therefore the total pressure will be equivalent to the sum of all the partial pressures exerted by He, O2 and H molecules.
Ptotal = PHe + PO2 + PH
This is the expression for Dalton’s Law of partial pressure. In any closed vessel, when two or more non reacting gases are kept at a constant temperature and volume, the total pressure exerted by the mixture will be equivalent to the sum of the partial pressures exerted by individual gases.
Generally, the total pressure is represented by:
Ptotal = P1+P2+P3+…(at constant T and V)
Where Ptotal is the total pressure exerted by the mixture, P1 is the pressure exerted by the first gas, P2 is the pressure exerted by the second gas, P3 is the pressure exerted by the third gas and T is the temperature and V is the volume.
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Dalton’s Law of Partial Pressure: Mole Fraction
Mole fraction is the ratio of the number of moles of one gas component in the mixture and the total number of moles of all the components of a mixture. It is represented by xi.
The sum of mole fraction of all the components is always 1.
In mathematical terms, mole fraction is given as:
xi = ni/ ntotal
Where, xi is mole fraction
ni = number of moles of an individual gas component in the mixture
ntotal = total number of moles of all the component of a mixture
Relation between Mole Fraction and Partial Pressure
The relation between mole fraction and partial pressure can be explained through the following equations:
If three gases at a temperature T enclosed in volume V exert pressures P1, P2 and P3, then
From the ideal gas equation, we have
P1 = n1RT/V , P2 = n2RT/V and P3 = n3RT/V
Where, n1,n2 and n3 are the number of moles of these gases.
The total pressure from Dalton’s Law of Partial pressures will be,
Ptotal = P1 + P2 + P3
Ptotal = total pressure exerted by the mixture of gases.
P1, P2, P3are partial pressures of individual gases.
On applying the ideal gas equation,
P1 = n1RT/V , P2 = n2RT/V and P3 = n3RT/V
PTotal = P1 + P2 + P3
PTotal = n1RT/V + n2RT/V + n3RT/V
PTotal = (n1 + n2 + n3)RT/V
P1/PTotal = n1/(n1 + n2 + n3)
P1/PTotal = n1/n
n = n1 + n2 + n3
n1/n = x1
P1/PTotal = x1
P1 = x1 PTotal
Similarly,
P2 = x2 PTotal
P3 = x3 PTotal
Similarly for ith gas
Pi = xi PTotal
Here, Pi = partial pressure of ith gas
xi = mole fraction of ith gas
The given equation can be used to determine the pressure exerted by individual gases in a mixture if the total pressure is known.
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Important Questions Based on Dalton’s Law of Partial Pressures
Ques.1: Calculate the pressure of a mixture containing 1 atm He, 3 atm Ne, 5 atm C6 H14 and 0.7atm UF6. (2 Marks)
Answer: According to Dalton’s Law of Partial Pressures:
Ptotal = P1 + P2 + P3 + P4
Ptotal = PHe + PNe + PC6 H14 + PUF6
Ptotal = 1+3+5+0.7
Ptotal = 8.7 atm
Ques.2: A neon-dioxygen mixture contains 70.6 g dioxygen and 167.5 g neon. If the pressure of the mixture of gases in the cylinder is 35 bar. What is the partial pressure of dioxygen and neon in the mixture? (2 Marks)
Answer: Number of moles of dioxygen = 70.6g/32gmol-1 = 2.21 mol
Number of moles of neon = 167.5g/20gmol-1 = 8.375 mol
Mole fraction of dioxygen = 2.21/2.21+ 8.375
Mole fraction of dioxygen= 2.21/10.585
Mole fraction of dioxygen= 0.21
Mole fraction of neon = 8.375/2.21+8.375
Mole fraction of neon = 0.79
The mole fraction of neon can also be calculated as = 1-0.21
= 0.79
Partial pressure of a gas = mole fraction x total pressure
Therefore,
Partial pressure of Oxygen = 0.21 x 35
Partial pressure of Oxygen = 9.45 bar
Partial pressure of Neon = 0.79 x 35
Partial pressure of Neon = 27.65 bar
Ques.3: A container of volume 10.00 litre is evacuated and held at a constant temperature. In this container, 2.00 litre of oxygen gas at an original pressure of 202.6 kPa and 3.00 litre of neon gas at an original pressure of 303.9 kPa is injected at the same temperature. What will be the pressure created inside this container? (3 Marks)
Answer: The partial pressure exerted on the container by each gas will be less than the total pressure.
As temperature and number of moles of each gas in unchanged, the new partial pressure of each gas can be calculated by using Boyle’s Law
P1V1 = P2V2
Oxygen:
202.6 x 2.00 = P(O2) x 10.00
P(O2) = 40.5 kPa
Neon:
303.9 x 3.00 = P(Ne) x 10.00
P(Ne) = 91.2 kPa
Total pressure = sum of partial pressures
Total pressure = 40.5 + 91.2 = 131.7 kPa
Ques.4: In a container, 48g of Methane (CH4) and 16g of Helium (He) is kept at a temperature of 27 degrees and volume 2 L. Find mole fraction and partial pressure of each gas and total pressure. (3 Marks)
Answer: No. of moles of Methane = Mass/ Molar mass
No. of moles of Methane = 48/16= 3
Similarly, No. of moles of Helium = 16/4 = 4
Now, Mole fraction of Methane = Moles of Methane/ Total no. Of Moles
Mole fraction of Methane = 3/7
Similarly, Mole fraction of Helium = 4/7
Now, we know
Ptotal x V = (n1+ n2) RT
Ptotal x 2 = 7 x 0.082 x 300
Ptotal = 172.2/2
Ptotal = 86.1
To calculate partial pressure on Methane
P(CH4)= Ptotal x Mole fraction of methane
P(CH4)= 86.1 x 3/7
P(CH4)= 36.9 Pa
To calculate partial pressure on Helium,
P(He) =Ptotal x Mole fraction of Helium
P(He) = 86.1 x 4/7
P(He) = 49.2 Pa
Ques.5: State and explain Dalton’s law of partial pressures. Can we apply Dalton’s law of partial pressures to a mixture of carbon monoxide and oxygen? (3 Marks)
Answer: Dalton’s Law of Partial Pressure states that, when two or more non-reacting gases are enclosed in a vessel, the total pressure of the gaseous mixture is equal to the sum of the partial pressures that each gas will exert when enclosed separately in the same vessel at constant temperature.
P= P1 + P2 + P3
Where, P is the total pressure of the three gases A, B, and C enclosed in a container. P1, P2 and P3 are the partial pressures of the three gases when enclosed separately in the same vessel at a given temperature one by one.
No, the law cannot be applied to a mixture of carbon monoxide and oxygen. Carbon monoxide and oxygen readily combine to form carbon dioxide. The law can be applied only to the non-reacting gases.
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