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# Dalton’s Law of Partial Pressure- Statement, Formula, Practice problems and FAQs

Breathing is difficult for the people who ascend to high altitudes. As they climb higher, oxygen's partial pressure decreases as total atmospheric pressure decreases in accordance with Dalton's law of partial pressure. Oxygen has a difficult time making it into the bloodstream when the partial pressure of the gas decreases. Hypoxia, a serious medical problem potentially resulting in death, can occur when this happens. In the year 1801, John Dalton related the partial pressure of each gas with the total pressure of the gas at a constant temperature and volume using an ideal gas equation and formulated a law known as Dalton’s law of partial pressure.

• Statement of Dalton’s law
• Mathematical Representation of Dalton’s law
• Practice Problems

## Statement of Dalton’s law

According to Dalton’s law of partial pressure for two or more non-reacting gases, the sum of partial pressure of each gas is equal to the total pressure of the gas at a constant temperature and volume.

From the above image, it can be seen that;

PTotal=PO2+PN2

Partial pressure of a gas is defined as the pressure exerted by the gas in a mixture of gases if it occupies the same volume and is at the same temperature as the mixture when other gases are removed from the container.

## Mathematical representation of Dalton’s law

Let us consider,

Volume of the gas A = V

Temperature of the gas A = T

Partial Pressure of gas A = PA

No. of moles of gas A = nA

Using the ideal gas equation PV=nRT, we get;

PAV=nART

Volume of the gas B = V

Temperature of the gas B = T

Partial Pressure of gas B = PB

No. of moles of gas B = nB

Using the ideal gas equation PV=nRT, we get;

PBV=nBRT

Now, when all these gases are added to another container having the same volume (V) and at the same temperature (T). Consider;

Pressure of the mixture of gases (A) & (B) = PT

No. of moles of a mixture of gases A & B = (nA+nB)=nT

Using the ideal gas equation PV=nRT for the mixture of gases, we get;

PT V=nTRT

By adding equations (i) & (ii) , we get;

From equations (i), (ii) & (iii), we get;

PA+PB=PT

## Partial pressures in terms of mole fraction

Mole fraction of a gas in a mixture is represented by the ratio of a number of moles of a particular gas to the total number of moles of a mixture of gases.

It is generally represented by (X).

Using the ideal gas equation PV=nRT for gas "A", we get,

PAV=nART

Using the ideal gas equation PV=nRT for gas “B", we get,

PBV=nBRT

Using the ideal gas equation PV=nRT for the mixture of gases, we get,

PT V=nTRT

Dividing equation "(v)" by "(vii)", we get;

Now, dividing equation "(vi)" by "(vii)", we get;

Therefore, the partial pressure of the gas in a mixture of gases is equal to the total pressure of the gas multiplied by the mole fraction of that gas. .

## Practice problems

Q 1. If 0.5 mol of gas A is mixed with 0.25 mol of gas B in a container of volume 11.2 L at a temperature of 300 K. The total pressure exerted by the mixture of gases A and B would be: (Assume both gas A and B are non-reacting in nature and behave ideally)

1. 2.52 atm
2. 1.099 atm
3. 1.648 atm
4. 2.326 atm

According to the given data for gas A,

Volume of the gas A = 11.2 L

Temperature of the gas A = 300 K

Let the partial pressure of gas A = PA

No. of moles of gas A = 0.5mol

Using the ideal gas equation PV=nRT for gas A, we get;

PA11.2 L=0.5 mol0.0821 atm L mol-1K-1300 K

PA=1.099 atm

According to the given data for gas B,

Volume of the gas B = 11.2 L

Temperature of the gas B = 300 K

Let the partial pressure of gas B = PB

No. of moles of gas B = 0.25mol

Using the ideal gas equation PV=nRT for gas B we get,

PB11.2 L=0.25 mol0.0821 atm L mol-1K-1300 K

PB=0.549 atm

Using Dalton’s law of partial pressure;

Total pressure = PA+PB

Total pressure of the gas=1.099+0.549 =1.648 atm

Q 2. If equal mass of O2 and CH4 are mixed in an empty container such that total pressure exerted by the mixture of O2 and CH4 is 1.6 atm at 300 K . The partial pressure of O2 gas in the mixture is:

(Assume that O2 and CH4 are non-reactive at a given temperature and behave ideally)

1. 0.43 atm
2. 0.533 atm
3. 0.40 atm
4. 0.33 atm

According to the given data,

Let the mass of O2(g) & CH4 = x gm (∵ Equal mass to be taken of O2 and CH4)

Total pressure exerted by O2 and CH4 = 1.6 atm

Temperature of the mixture = 300 K

Using Dalton’s law of partial pressure;

Partial pressure of a gas = Total pressure of mixture of gases mole fraction of a gas in the mixture

Q 3. If 0.5 mol of an ideal gas A exerting a partial pressure of 1.5 atm in a mixture where0.5 mol of another ideal gas B is present in a container at a temperature of 273 K. The total pressure exerted by a mixture of gas A and B is:

(Assume the gases to be non-reactive)

1. 2.5 atm
2. 1 atm
3. 3 atm
4. 2 atm

According to the given data,

No. of moles of gas A = No. of moles of ideal gas B =0.5 mol

Pressure exerted by an ideal gas A = 1.5 atm

Using Dalton’s law of partial pressure;

Partial pressure of a gas = Total pressure of mixture of gases mole fraction of a gas in the mixture

Q 4.  Select the correct option for which dalton’s law of partial pressure is not applicable at room temperature. (Assume that gases are present at room temperature and gases to behave ideally)

1. H2 and N2
2. NH3 and HCl
3. Ar and O2
4. NH3 and H2

Solution : As we know Dalton’s law of partial pressure is valid only in the case of non-reacting gases at a given temperature. NH3 and HCl will react with each other at room temperature to form NH4Cl . So, Dalton’s law of partial pressure can not be applied on the mixture of NH3 and HCl gases.

Q 1. Why Dalton’s law of partial pressure is not valid for reacting gases?
If two or more gases react together it results in the formation of a new product and the number of moles of the product formed depends upon different factors like stoichiometric coefficient and limiting reagent. Therefore Dalton’s law of partial pressure cannot be applied directly in such a case of reacting gases.

Q 2. What is the importance of Dalton’s law of partial pressure?
Dalton’s law of partial pressure helps us to determine the total pressure exerted by the gas molecules present in a mixture when the partial pressure of each gas is known. It also helps us to calculate the partial pressure of each gas molecule in the mixture in terms of total pressure and the number of moles of each gas present in the mixture.

Q 3. What is the limitation of Dalton’s law of partial pressure?
Answer: Dalton’s law of partial pressure is valid for those gases that behave ideally. Therefore this law holds good at low pressure and high temperature because under these conditions a gas can behave ideally.

Q 4. What are the factors on which the partial pressure of a gas depends in a mixture of gases?
According to Dalton’s law, the partial pressure of a gas depends on the mole fraction of the gas component, total pressure of all the gases present in the container, volume of the container and temperature of the gas.

Related topics

 Charles's Law Boyle’s Law Avogadro’s Law Gay Lussac's law Ideal Gas Equation Real Gas

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