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Chemical Equilibrium - Explanation of Equilibrium Constants

Chemical Equilibrium

Chemical equilibrium

In an equilibrium system where a chemical reaction is occurring, if there is no net change in the concentrations of reactants and products, such a condition is called chemical equilibrium.

Equilibrium constant

The equilibrium constant gives an idea about the relationship between the products and reactants in the media at a given temperature. Let’s take the following chemical equilibrium system,

Chemical equilibrium eq 1

In the above reaction, A, B, C, and D are the reactants and products. a, b, c, and d are the stoichiometric ratios of each component. For the above reactions, the equilibrium constant (Kc) for concentration can be written as follows.

the equilibrium constant (Kc) for concentration

Where,

  • [A] =concentration of component A
  • [B] =concentration of component B
  • [C] =concentration of component C
  • [D] =concentration of component D

For the above system equilibrium constant can be expressed according to the mole fraction of each component.

the equilibrium constant (Kx) for mole fraction

Where,

  • XA = mole fraction of component A
  • XB = mole fraction of component B
  • XC = mole fraction of component C
  • XD = mole fraction of component D

If the system is a gaseous system, the equilibrium constant for pressure (Kp) can be written as follows,

the equilibrium constant for pressure (Kp)

Where,

  • PA = partial pressure of component A
  • PB = partial pressure of component B
  • PC = partial pressure of component C
  • PD = partial pressure of component D

Kc, Kx, and Kp are only dependent on the temperature.

Examples of Kc and Kp calculation

01. Haber process reaction

Haber process reaction - N2 + 3H2 = 2NH3

02. Partial dissociation of Sulfur trioxide

Partial dissociation of Sulfur trioxide - 2SO3 = 2SO2 + O2

03. Esterification reaction equilibrium

Esterification reaction equilibrium

The above system is a liquid equilibrium system. So, in this system, Kp is not considered.

Chemical equilibrium eq 8

If the above system is in an aqueous medium, and water is formed from the reaction, the concentration of the water remains constant. 

Chemical equilibrium eq 9

04. Ammonium hydrogen sulfide dissociation

Ammonium hydrogen sulfide dissociation - NH4SH = NH3 +H2S

In the above system, NH4SH is solid. Therefore, its concentration remains constant. So, the concentration of NH4SH is not included in the Kc expression. And a solid does not affect the pressure of the system. 

Chemical equilibrium eq 11

05. Calcium carbonate dissociation

Calcium carbonate dissociation - CaCO3 = CaO + CO2

06. The reaction between iron and water

The reaction between iron and water - 3Fe + 4H2O = 4H2 + Fe3O4

07. Dissociation of Phosphorous pentachloride

Dissociation of Phosphorous pentachloride - PCl5 = PCl3 + Cl2

In the above system, PCl5 liquid has separated from the gaseous phase. Therefore, the concentration of PCl5 is constant. 

Relationship between Kp and Kc in a gaseous equilibrium system

Let’s take the following reaction,

Chemical equilibrium eq 15

For the above system, Kc and Kp can be written as follows,

Chemical equilibrium eq 16

If all the above gases are ideal, the concentration of each component can be expressed as follows. To derive these expressions, the ideal gas law is used.

ideal gas equation

Where,

  • P = pressure
  • V = volume
  • n = number of mols of the substance
  • R = Ideal gas constant
  • T = Absolute temperature

According to the above equation, the partial pressure of each component can be written as follows,

Chemical equilibrium eq 18

Where [A], [B], [C], and [D] are concentrations of each component, and PA, PB, PC, and PD are partial pressure of each component. Let’s substitute the above expressions to the Kp equation,

Chemical equilibrium eq 19

Where Δn is the difference between the sum of the stoichiometric ratios of products and the sum of the stoichiometric ratios of reactants.

Chemical equilibrium eq 20

If one of the products or reactants is a liquid or a solid, the stoichiometric ratio of that component is not considered. 


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References and Attributes

Figures:

The cover image was created using an image by RF._.studio from Pexels


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