Dalton’s Law of Partial Pressure Formula & calculation

Let’s Explore Dalton’s Law of Partial Pressure!

Dalton’s Law of Partial Pressure Formula & calculation

Dalton’s Law of partial pressure is explained along with a basic idea of the partial pressure, dalton’s law, explanation, mathematical derivations, examples.

Let’s explore Dalton’s Law!

Dalton’s Law of Partial Pressure

Let’s try to understand Dalton’s Law of Partial Pressure! We love to ride a bicycle since our childhood and when tyre pressure reduced, we simply use to go to a mechanic to maintain required pressure both the tyres.

What mechanic do there?

They use one pressure measurement device like a barometer and check the air pressure. If the tyre is having less pressure, they maintain the required pressure with the help of a blower.

daltons law partial pressure basics
Dalton’s law partial pressure basics

Here comes pressure as well as partial pressure! let’s try to understand it before Dalton’s law of partial pressure!

Partial Pressure Formula & Calculation

What is Partial Pressure?

The pressure is a macroscopic property which is created by the action of a large number of gas molecules due to their Collison each other or with the wall of the tyre. The total pressure is increased within the tyre due to more collisions between them and in the same way, the pressure of individual molecule is also increased.

This pressure of individual gas is partial pressure.

Partial Pressure Definition

Partial pressure is defined as the pressure exerted by an individual gas in a mixture. 

Partial Pressure Formula

Let’s try to understand the formula of partial pressure. 

Suppose, there are 5 types of gasses in a vessel, a, b, c, d & e.

  • Pa = Partial pressure of gas a
  • Pb = Partial pressure of gas b
  • Pc = Partial pressure of gas c
  • Pd = Partial pressure of gas d
  • Pe = Partial pressure of gas e
partial pressure formula
Partial Pressure Formula

Therefore, the total pressure is the summation of the partial pressure of all gasses, 

Ptotal = Pa+Pb+Pc+Pd+Pe

Partial Pressure Calculation

We can have a partial pressure calculation for better understanding.

Calculation Inputs

A vessel consists of two gasses, Nitrogen and Oxygen.

The partial pressure of Nitrogen is 3 atm

The partial pressure of Oxygen is 1.5 atm

Find Out the Partial Pressure

What is the total pressure inside the vessel?

Solution

PN2  = Partial pressure of N2 = 3.0 atm

PO2 = Partial pressure of O2 = 1.5 atm

Total pressure inside the vessel, Ptotal,

Ptotal = PN2 + PO2

Ptotal = 0.8 + 0.3

Ptotal = 1.1 atm

The total pressure inside the vessel is 1.1 atm.

Dalton’s Law

Statement of Dalton’s Law

Any gas can dissolve, or diffuse, or react based on their partial pressures. Dalton has introduced a new relationship between total pressure and partial pressure and the same is known as Dalton’s Law.

Dalton’s Laws are as follows:

  • Rule -1: The total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture.
  • Rule-2: The partial pressure of each gas is the pressure at which each gas would exert if it occupied alone the volume at the same temperature.

Explanation of Dalton’s Law

Rule-1 Explanation

Let us consider, three types of different gasses like oxygen, nitrogen and helium are kept in three different containers and each container is having specific pressure i.e. partial pressure.

Partial pressure of Oxygen                     = Po2

Partial pressure of Nitrogen                    = PN2

Partial pressure of Helium                      = PHe

daltons law partial pressure
Dalton’s law partial pressure

Now, as per Dalton’s law, if we mix all three gasses in one container, the pressure of mixture will be the sum of all partial pressure.

Total pressure,                          P = Po2 + PN2 + PHe

The total pressure of a mixture of gases is made up by the sum of the partial pressures of the components in the mixture – also known from Gibbs’-Dalton’s Law of Partial Pressures.

Rule-2 Explanation 

Let us consider anyone gas in a gas mixture, say, O2 and its partial pressure is Po2. Now, if we keep this O2 gas in the same container at the same temperature, its pressure will be same as partial pressure.

Mathematical Derivation

The total pressure in a mixture of gases can be expressed as:

ptotal = p1 + p2 + .. + pn    = Σpi                                              (1)

where

ptotal = total pressure of mixture    (Pa, psi)

pi = partial pressure of individual gas   (Pa, psi)

Assuming that each gas behaves ideally – the partial pressure for each gas can be calculated from the Ideal gas Law as

pi = n1 R T / V                     (2)

where

n1 = the number of moles of the gas

R = universal gas constant (J/(mol K), lbf ft/(lb mol oR),  8.3145 (J/(mol K))

T = absolute temperature (K, oR)

V = volume (m3, ft3)

Example of Partial Pressure

We have taken a total of five gasses in five different containers of the same volume. The gasses are as follows:

Sl. No Name of Gasses Partial Pressure (kPa)
1 Oxygen (O2) P1 = 20.9
2 Nitrogen (N2) P2 = 78.1
3 Argon (Ar) P3 = 0.97
4 Water (H2O) P4 = 1.28
5 Carbon Di Oxide (CO2) P5 = 0.05

Now, as per Dalton’s law, total pressure of the mixture shall be, P

P = P1 + P2 + P3 + P4 + P5;

Here,

P = 20.9 + 78.1 + 0.97 + 1.28 + 0.05 kPa

P = 101.3 kPa, which is same as the right site container.

If we take the mixture and allow water vapour to be in the same container at the same temperature, we will see the partial pressure of water vapour.

Limitation of Dalton’s Law

There are certain limitation of Gibbs-Dalton’s law:

  • Dalton’s law is applicable for idea gases only.
  • Dalton’s law is applicable only for non-reacting gases.
  • This law deviates at high pressure.
  • It is also assumed that the interaction between the molecules of individual gas is the same as the molecules in the mixture.

Conclusion

Hence, we have got a very basic idea of Dalton’s law of partial pressure along with explanation, laws, examples.

Further Study

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