Kc and Kp, relation between Kc and Kp

1. Law of Mass Action

1. The Law of Mass Action states that the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants raised to their respective stoichiometric coefficients.
2. For a reversible reaction: aA + bB ⇌ cC + dD, the equilibrium expression is: 
   K_c = [C]^c[D]^d / [A]^a[B]^b
3. The equilibrium constant (K_c) is dimensionless and depends on temperature.
4. The concentrations of reactants and products are expressed in moles per liter (M).

2. Equilibrium Constant K_c

1. K_c is the equilibrium constant in terms of concentration.
2. It is applicable to homogeneous reactions (all reactants and products in the same phase).
3. For heterogeneous reactions, only the concentrations of gaseous and aqueous species are considered.
4. The value of K_c indicates the extent of the reaction:
   • If K_c > 1, the reaction favors products.
   • If K_c < 1, the reaction favors reactants.

3. Equilibrium Constant K_p

1. K_p is the equilibrium constant in terms of partial pressure of gases.
2. It is used for reactions involving gaseous species.
3. Partial pressures are usually expressed in units of atm or Pa.
4. The equilibrium expression in terms of partial pressures is: 
   K_p = (P_C)^c(P_D)^d / (P_A)^a(P_B)^b

4. Relation Between K_c and K_p

1. The relationship between K_c and K_p is given by the equation: 
   K_p = K_c(RT)^Δn
2. Here:
   • R is the gas constant (0.0821 L·atm·mol⁻¹·K⁻¹).
   • T is the temperature in Kelvin.
   • Δn is the change in the number of moles of gases (moles of gaseous products - moles of gaseous reactants).
3. For reactions where Δn = 0, K_p = K_c.

5. Key Points for Competitive Exams

1. Law of Mass Action describes the dependence of reaction rate on reactant concentrations.
2. K_c is used for reactions in terms of concentration, while K_p is used for gaseous reactions in terms of partial pressures.
3. The value of K_c or K_p indicates the direction of the reaction:
   • K > 1: Favors products.
   • K < 1: Favors reactants.
4. The relationship between K_c and K_p depends on Δn and temperature.
5. Equilibrium constants are temperature-dependent and do not change with pressure or concentration changes.
6. Only gaseous and aqueous species are included in equilibrium expressions; solids and liquids are excluded.
7. The equilibrium constant does not provide information about the rate of the reaction.
8. Examples of equilibrium constants are crucial for understanding industrial processes like the Haber process for ammonia production.
9. Understanding K_c and K_p is essential for solving numerical problems in physical chemistry.