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Dalton's Law

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What is Dalton’s Law?

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Dalton’s law of partial pressure first published by John Dalton in the year 1802 states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each individual gas present in the mixture. Eg: the total pressure exerted in a mixture of two gases is equal to the sum of the individual partial pressures exerted by each of the gas. In simple words, it can be stated that it is a mixture of two or more non-reacting gases, the total pressure is equal to the sum of the partial pressures of the non-reacting gases. In this topic, we have discussed what is dalton's law, let us state dalton's law of partial pressure with some examples. Let us suppose we have two mixture of gases A and B, so Dalton's gas law states that the total pressure exerted by a mixture of two gases A and B is equal to the sum of the individual partial pressures exerted by both gas A and gas B as shown below:

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Dalton's Law Formula

For a mixture containing n number of gases the total pressure can be given as:

p\[_{total}\] = \[\sum_{i=1}^{n}\] p\[_{i}\]

Or simply it can be written as:

p\[_{total}\] = p\[_{1}\] + p\[_{2}\] + p\[_{3}\] + p\[_{4}\] + p\[_{5}\] .... + p\[_{n}\]

Where Ptotal denotes total pressure exerted by the mixture of gases

and p1, p2,…, pn denotes the partial pressures of the gases 1, 2,…, ‘n’ in the mixture.


Expressing Partial Pressures in Terms of Mole Fraction

The mole fraction of a specific gas in a mixture of gases can be defined as the ratio of the partial pressure of that gas to the total pressure exerted by the gaseous mixture. This mole fraction is used to calculate the total number of moles of a constituent gas when the total number of moles in the mixture is known. Also, the volume occupied by a specific gas in a mixture can be calculated with the mole fraction formula with the help of the given equation.

X\[_{i}\] = P\[_{i}\] / P\[_{total}\] = V\[_{i}\] / V\[_{total}\] = n\[_{i}\] / n\[_{total}\]

Here X\[_{i}\] denotes the mole fraction of a gas ‘i’ in a mixture of ‘n’ gases, ‘n’ denotes the number of moles, ‘P’ denotes the pressure, and ‘V’ denotes the volume of the mixture.


Use of Dalton's law

Dalton's law can be used to calculate the mixtures of gases and the pressure and volume of each gas.

Presently many industries use sophisticated software for calculating these parameters. Still, Dalton’s and Avogadro’s laws are the basis of all these technologies.


Dalton's Law of Partial Pressure Explanation by an Example

If there is a mixture of nitrogen gas, helium gas, and argon gas we have to measure the pressure and it was assessed in 2 atm. Further, the specialist also confirmed that the pressure of nitrogen in the mixture is 0.8 atm and the pressure of helium is 0.5 atm. Calculate the pressure of argon gas in the given mixture?

Solution: In order to calculate the pressure we can use Dalton’s law formula given as:

p\[_{total}\] = p\[_{1}\] + p\[_{2}\] + p\[_{3}\] + p\[_{4}\] + p\[_{5}\] .... + p\[_{n}\]

Now we put all the given value in it and rearrange the formula:

p\[_{total}\] = p\[_{nitrogen}\] + p\[_{helium}\] + p\[_{argon}\] 

p\[_{total}\] = p\[_{nitrogen}\] - p\[_{helium}\] = p\[_{argon}\] 

p\[_{argon}\] = 2atm - 0.8atm - 0.5atm

p\[_{argon}\] = 0.7atm


Conclusion 

In this article, we have discussed Dalton's law of partial pressure definition and the Uses of Dalton’s law, We have also learned how to express Partial pressure in terms of mole fraction along with an example. To understand this topic more clearly try to solve maximum numerical.

FAQ (Frequently Asked Questions)

Question: Define Dalton's Law of Partial Pressure.

Answer: The dalton's law of partial pressure states that when there is a mixture of inactive gases (there is no reaction between them), the total pressure applied is equal to the sum of the partial pressure of each gas.

Question: If there are Three Gases Argon, Nitrogen, and Hydrogen Mixed in a Container of 700 mL. In Addition, the Pressure of Nitrogen is 221 torr, Hydrogen is 750 torr, and Argon is 655 torr. Calculate the Total Pressure in the Container.

Answer: We know that the total pressure can be given as the sum of the partial pressure of each gas. So, adding the total pressure we get

P total = P nitrogen + P hydrogen + P argon 

P total = 221torr + 750torr + 655torr

P total = 1626torr

Question: In a Given Sample Mixture of Hydrogen Gas and Oxygen Gas, Both Exert a Total Pressure of 2.5 atm on the Walls of its Container. If the Partial Pressure of Hydrogen is 2 atm, Find the Mole Fraction of Oxygen in the Mixture.

Answer: Given,  Phydrogen = 2 atm, Ptotal = 2.5 atm

Applying Dalton’s law formula, Ptotal = Phydrogen + Poxygen

Therefore, Poxygen = 0.5 atm

Now, the mole fraction of oxygen, Xoxygen = (Poxygen / Ptotal) = 0.5/2.5 = 0.33

Therefore, the mole fraction of oxygen in the mixture is 0.02.