Understanding the Equilibrium Constant Kp
Kp is a specific form of the equilibrium constant used for reversible reactions involving gaseous reactants and products. It expresses the ratio of the partial pressures of products to reactants at chemical equilibrium, each raised to the power of its stoichiometric coefficient in the balanced chemical equation. Kp provides a quantitative measure of the extent to which a gaseous reaction proceeds towards products at a given temperature.
Formulating the Kp Expression
For a general reversible gaseous reaction like aA(g) + bB(g) ⇌ cC(g) + dD(g), where a, b, c, and d are the stoichiometric coefficients, the expression for Kp is written as (P_C^c * P_D^d) / (P_A^a * P_B^b). Here, 'P' denotes the partial pressure of each gaseous species at equilibrium. It is crucial to remember that only gaseous species are included in the Kp expression; solids and liquids are excluded because their partial pressures remain constant.
A Practical Chemical Example
Consider the industrial synthesis of ammonia: N₂(g) + 3H₂(g) ⇌ 2NH₃(g). The equilibrium constant Kp for this reaction would be expressed as P(NH₃)² / (P(N₂) * P(H₂)²). If, at a specific temperature, the partial pressures at equilibrium are P(N₂) = 10 atm, P(H₂) = 30 atm, and P(NH₃) = 5 atm, then Kp = (5)² / (10 * 30³) = 25 / (10 * 27000) = 25 / 270000 ≈ 0.0000926. This small value suggests that the reactants are favored at equilibrium.
Importance and Relationship with Kc
Kp is vital in fields such as chemical engineering, atmospheric science, and industrial chemistry for predicting the feasibility and yield of gaseous reactions. It is related to Kc, the equilibrium constant expressed in terms of molar concentrations, by the equation Kp = Kc(RT)^Δn. In this formula, R is the ideal gas constant, T is the absolute temperature in Kelvin, and Δn is the difference between the sum of the stoichiometric coefficients of gaseous products and gaseous reactants (Δn = (c+d) - (a+b)).