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Law of Mass Action

Mass Action Law in Learning Chemistry

Mass action law formula for balance chemical equation was first developed by two Norweigan chemists, Guldberg and Waage in 1867 for quantitative relation between the concentration of reactant and resultant equilibrium constant of the reaction. The law of mass action states, at a constant temperature, the rate of a chemical reaction is proportional to the active masses of reacting substances. Therefore, the definition and expression of active masses in mass action law is an important consideration of equilibrium chemistry. For ordinary systems of dilute solution and gas molecule, the active mass may be molar concentration and partial pressure but for pure crystalline solid or liquid, the active mass taken as unity since the rate of reaction does not effect equilibrium concentration formula.

Law of mass action and Equilibrium concentration of chemical reaction in chemistry


Definition of Active Mass in Equilibrium Reaction

Concentration formula effect by thermodynamics law. Therefore, the active mass of gas, solid and liquid defines as,

  • When the solution is dilute and the system behaves ideally the concentration represented as the molar concentration. The unit of molar concentration moles/lit. For example, esterification of acetic acid in the alcohol solution.
  • Partial gas pressure expressed in the atmosphere for the gas molecules when the pressure of the system is very low. For example, water gas reaction or reaction of hydrogen and carbon dioxide gas.
  • But for pure solid and pure liquid, active mass assumed to be unity since their mass does not effect the rate of reaction.

Definition of Concentration from Equilibrium Formula

Let us apply the equilibrium definition and mass action law to a general chemical reaction.

A + B ⇆ C + D

As the reaction proceeds in the forward direction, the concentration of reactants decreases, and the forward kinetics reaction rate also decreases. But when the products are getting accumulated in the system, the reverse reaction also starts.

Rate of forward reaction (Rf) ∝ CA × CB
∴ Rf = kf × CA × CB
Rate of backward reaction (Rb) ∝ CC × CD
∴ Rb = kb × CC × CD

Where CA, CB, and CC, CD are the concentration of forwarding and reverse reactions respectively in molar units. Kf and Kb are the rate constants at a given temperature.

Mass Action Law Formula in Chemistry

As the reactions proceed in the forward reaction rate decreasing but the reverse reaction rate increases and attained a state when they are equal. Therefore the point where forward and reverse reaction rates equal is called the equilibrium point of the chemical reaction. There will be no further change in the concentration of the system.

Therefore, at equilibrium, Rf = Rb
or, kf × CA × CB = kb × CC × CD

Whare CA, CB, CC and CD are the equilibrium point concentration of reactants and products. But kf/kb = kc = concentration equilibrium constant of a chemical reaction.

Mass Action Law Equilibrium Concentration

Let us consider a general balance chemical reaction to define mass action law in learning chemistry

Ɣ1A1 + Ɣ2A2 ⇆ Ɣ3A3 + Ɣ4A4
where Ɣ1, Ɣ2, Ɣ3, and Ɣ4 are stoichiometric coefficients.
∴ kc = (C3γ3 × C4γ4)/(C1γ1 × C2γ2)

where kC = concentration equilibrium constant of the reaction and C1, C2, C3, and C4 are the equilibrium concentration of the reactants and product. Therefore, the values of the kC of a chemical reaction from the mass action law effect the mode of writing or balance of the stoichiometric chemical equation. If a chemical equation multiplied by n then the general rule for writing equilibrium concentration n will be raised to the power.

kC = (k′C)n

kC, and k′c are not equal in magnitude. Therefore the concentration equilibrium constant depends on the modes of balancing chemical equations.

Pressure Equilibrium Constant Formula in Chemistry

When all the reactants and products are the gas-phase obey the ideal gas law or real gas laws, the concentration formula expressed in partial pressure by mass action law. Let the chemical equation for the above expression

Ɣ1A1 + Ɣ2A2 ⇆ Ɣ3A3 + Ɣ4A4
where Ɣ1, Ɣ2, Ɣ3, and Ɣ4 are stoichiometric coefficients.
∴ kP = (P3γ3 × P4γ4)/(P1γ1 × P2γ2)

Where kP = pressure equilibrium constant of the reaction. P1, P2, P3, and P4 are the equilibrium partial pressure of reacting components.

Mole Fraction Equilibrium Constant Formula

Ɣ1A1 + Ɣ2A2 ⇆ Ɣ3A3 + Ɣ4A4
where Ɣ1, Ɣ2, Ɣ3, and Ɣ4 are stoichiometric coefficients.
∴ kx = (x3γ3 × x4γ4)/(x1γ1 × x2γ2)

Where kx = mole fraction equilibrium constant and x1, x2, x3, and x4 are mole fraction of reacting components in chemistry.

kP and kC Relation from Mass Action Law

Let us consider the general equilibrium reaction which expresses the relation between kP and kC gas and liquid phase by mass action law.

Definition of concentration from mass action law formula in chemistry

Formation of hydrochloric acid solution from hydrogen and chlorine molecule. In this reaction, the total number of reactant molecules, and of resultant molecules are the same.

H2 + Cl2 ⇆ 2HCl
kP = kC (RT)2-(1+1) = KC

For the reactions in which the number of molecules of reactants differs from the resultant molecules of the chemical reaction.

PCl5 ⇆ PCl3 + Cl2
kP = kC (RT)(1+1) -1 = KC RT

This is the relation between kP and kC of the above chemical reaction.

Relation of kP and kx from Mass Action Law

kP = kx (P)Δγ

The mass of action law in equilibrium chemistry define before the thermodynamics approach developed and definition, formula, and the relation of the different equilibrium constant of balanced chemical reaction expressed in terms of active masses or molar concentration, the partial gas pressure, and mole fraction. Therefore, the law of mass action recognized that the chemical equilibrium is a dynamic, not static equilibrium. How the system behaves if any parameter like temp, pressure, catalyst, etc of the system at equilibrium changed describe by Le Chatelier and Van’t Hoff equation.