Dalton's law of partial pressure

John Dalton was an English chemist. In 1801, he studied the mixture of gases and proposed his law of partial pressures of gases. According to this law “ The total pressure exerted by all gases on the wall of the container is equal to the sum of partial pressure of each gas involved”. For example, if three different gas A, B and C are present the total pressure is the sum of the partial pressure of all gases

Pt=p_A + p_B +p_{C → (I) Dalton’s Law of Partial pressure}

Image contain container A B C and mixture container

Where,

Pt= total pressure
P_A is the pressure of gas A
p_Bis the pressure of gas B
p_C is the pressure of gas C

This law is obeyed if the gases involved behave ideally such that they do not react with each other.

What is the partial pressure of a gas?

The partial pressure of a gas is the pressure exerted by a component gas of the mixture if it is present all alone in the container of the same volume.

For example, We have four gas cylinders A, B, C, and D.’A’ with a volume of 20cm³ containing 20 cm3 of hydrogen (H₂) gas and it exerts a pressure of 100 torrs, while the second cylinder contains the same volume of helium (He) gas and exerts 50 torr pressure. Similarly, in the cylinder ‘C’, oxygen O₂ gas exerts a pressure of 400 torrs. If all these gases are transferred to a cylinder with the same volume, according to Dalton’s law, the total pressure exerts on the walls is the sum of partial pressure of each gas, equal to 550 torrs. provide the volume and temperature remain constant.

Pt = p_A + p_B +p_C = 100 + 50 + 400 = 550 torr

The rapidly moving gases are not interacting with each other and behaving independently. The pressure exerted on the walls of the container is due to the collision of gas molecules with the boundary. Therefore, the total pressure is the sum of the total number of collisions.

Molecules of each gas move independently, so ddthe genral gas equation can be applied to the individual gases.

p_(H2)V =nH2 Rt or p(H2) = n_H2RT/V → (ii)

p_(He)V =nH2 Rt or p_(He)= n_HeRT/V → (iii)

p_(O2)V =nO22 Rt or p(O2)= n_O2RT/V → (iv)

By putting these values in equation (i)

P_t= n_H2RT/V + n_HeRT/V + n_O2RT/V

P_t= (n_a +n_b+n_c)RTV

P_tV= n_t(RT) → (v)

This equation illustrates that the total pressure of the gas mixture depends upon the total no of moles of gases.

How to Calculate the partial pressure of a gas?

The partial pressure can be calculated by using the equation I and iv

P_t= n_t(RT)/V → (v)

P_O2=n_O2RT/V → (ii)

By dividing equation (ii) by (v)

P_O2/P_t=n_O2/n_t

P_O2=X_O2Pt

Where X_O2is the mole fraction of oxygen; n_O2/n_t=X_O2

Solved problems of Dalton’s law of partial pressure

Example:1

Calculate the pressure exerted by a mixture of 8.0 g of O2 gas and 2 grams of H2 gas in a 10-liter container at room temperature?

Solution:

To calculate the partial pressure of H2 and O2 firstly the moles of gases are calculated,

Moles of O₂ = 8/16=0.5

Moles of H₂=2/2.02=0.990

By applying the ideal gas equation

P=nRt/V → (vi)

P_H2 = (0.990 x 0.0821 x 273)/10liter

=2.20atm

P_O2 = (0.5 x 0.0821 x 273)/10

=1.12atm

By Dalton’s law P_t=P_H2 +P_O2

=2.20+1.12

=3.32 atm

Applications Dalton’s law

Collection of insoluble gas over water

The collection of gas over water is the best example of a mixture of gases. For example, During the preparation of oxygen gas (by the decomposition of KCLO3) which is insoluble in water the gas displaces water in the inverted container. Some of the water molecules remain in the gas phase. Hence the gas is the mixture of water vapors and oxygen. AT equilibrium condition the amount of water vapor remains constant. This method is used to evaluate the vapor pressure of unknown gas.

Application of Dalton law Image

Solved Example:

A freshly prepared oxygen is collected by the downward displacement of water from an inverted bottle. The water level becomes equal to the level of water in the trough. The pressure shown on the gauge is 747 mm Hg, and the temperature of the room is 27C. Calculate the partial pressure of oxygen? Vapour pressure of H20 at 27C is 26.739 mmHg.

Solution:

The total pressure inside the bottle is given by

P_total = P_O2 + P_H20

According to the condition, the water level inside the bottle is equalized, and the total pressure is equal to the barometer reading (atmospheric pressure) which is 747 atm,

P_total = P_atm = P_O2 + P_H2O

P_O2= 747-P_H20

=747-26.739

=720.261 mmHg

Oxygen level in airplanes

During flight at high altitude, the oxygen concentration is decreased hence the mixture of gases in the crew cabins is adjusted in such a way that the vapor pressure O2 is remain similar to the sea level.

Deep-sea divers

Scuba divers used a mixture of gases to breathe normally under water. It has been seen that when they go deep in the sea the partial pressure of all gases is increased so that N2 gas dissolves in the blood. By applying Dalton’s law the mixture is made which other gases to reduce the total pressure.

Distillation

The separation technique, in which different chemical substances are separated based upon the difference in their boiling point. In this method, the container is filled with a mixture and heated. the vapor produced is passed through their cold region i.e condenser. The vapor with lesser kinetic energy in the condenser drops in the collecting flask while the high kinetic energy vapor leaves the condenser.

Separation of immiscible liquids

In oil refineries, immiscible liquids like oil and water are separated by passing stripping steam, This process work on the principle of Dalton’s law of partial pressure. During steam distillation, when steam is passed through the mixture it reduces the partial pressure of the distillation column, hence low temperature is requieed.

Concepts Berg

What is John Dalton best known for?

John Dalton is famous for his laws of partial pressure and his atomic theory. In 1801 in his publication he proposed the laws of gas. After a few years, he developed an atomic model in which he states” All matter is composed of indivisible small building blocks called atoms.

What does Dalton’s law state?

Dalton’s law states that partial pressure is the pressure of any gas present in the mixture and total pressure exerted on the walls of the container is the sum of individual parts of participating ideal gases. SInce the volume and temperature remain constant.

Does Dalton s law of partial pressure apply when only the ratio of V T remains the same but the value of both V and T changes?

If the volume and temperature change, the kinetic energy of the gases changes because it depends upon the temperature. Therefore, Dalton’s law is only applicable when the temperature and pressure remain constant. Moreover, these laws become invalid if gases interact with each other.

How do I reduce the partial pressure by giving stripping steam in the distillation column?

In the distillation column, the steam strips from the side to reduce the vapor pressure of the column, hence the hydrocarbons are boiled at a low temperature.

Why is partial pressure proportional to concentration?

Partial pressure is given by the product of its mole fraction and the total pressure, Hence if its mole fraction is greater the partial pressure is also increased.

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