14.3
Homogeneous Equilibria for Gaseous Reactions
Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentra…
For chemical reactions, where the reactants and products are all gases, the equilibrium constant can also be calculated using the individual partial pressures rather than their molar concentrations.
Thus, when gases A and B convert to gases C and D in a reversible reaction, the equilibrium expression can be written instead as the partial pressure of each gas, raised to their stoichiometric coefficients. The equilibrium constant is designated as Kp, where the subscript p indicates pressure.
For a given gaseous reaction, Kp is not necessarily equal to Kc, because the partial pressure of a gas and its molar concentration are separate values. However, a relationship can be derived between the two constants using the ideal gas equation and the definition of molarity.
To derive this relationship, consider the equilibrium expressions for Kc and Kp for the given chemical reaction.
The ideal gas equation relates the pressure of a gas to its number of moles and its volume at a given temperature. Substituting the ratio of moles to volume for molarity in the ideal gas equation allows the pressure of an ideal gas to be expressed in terms of its molar concentration.
In this way, the individual partial pressures in the expression for Kp can be substituted for the concentration equivalent of each gas. The stoichiometric coefficients remain unchanged.
In the modified expression of Kp, the ratio of the concentration of the products to the concentration of reactants can be substituted for Kc. This equation gives the relationship between the two constants — Kp equals Kc times RT raised to the sum of the coefficients of the products minus the sum of the coefficients of the reactants.
The difference between the coefficients of gaseous reactants and products can be represented as Δn.
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Q1: What is the difference between Kp and Kc for gaseous reactions?
Kp and Kc are equilibrium constants expressed in different units. Kc uses molar concentrations of gases, while Kp uses partial pressures. They are not necessarily equal because partial pressure and molar concentration are separate values. However, they are related through the ideal gas equation and temperature, allowing conversion between the two constants.
Q2: How do you write the equilibrium expression using partial pressures?
For a gaseous reaction, the equilibrium expression using partial pressures is written as Kp, where each reactant and product partial pressure is raised to its stoichiometric coefficient. For example, in the reaction A + B ⇌ C + D, Kp equals the partial pressure of C times the partial pressure of D, divided by the partial pressure of A times the partial pressure of B.
Q3: What is the mathematical relationship between Kp and Kc?
The relationship between Kp and Kc is expressed as: Kp = Kc(RT)^Δn, where R is the gas constant, T is temperature in Kelvin, and Δn is the difference between the sum of product coefficients and the sum of reactant coefficients. This equation is derived by substituting the ideal gas law into the equilibrium expression.
Q4: What does Δn represent in the Kp and Kc relationship?
Δn represents the change in the number of moles of gas during the reaction. It is calculated as the sum of stoichiometric coefficients of gaseous products minus the sum of stoichiometric coefficients of gaseous reactants. This value determines how temperature and pressure changes affect the relationship between Kp and Kc.
Q5: How does the ideal gas equation help derive the Kp and Kc relationship?
The ideal gas equation (PV = nRT) relates pressure to molar concentration. By rearranging it to express pressure in terms of molarity, partial pressures in the Kp expression can be substituted with concentration equivalents. This substitution, combined with the definition of Kc, yields the mathematical relationship between the two equilibrium constants.
Q6: Why must you use Kp instead of Kc for gas-phase equilibrium calculations?
Kp is used for gas-phase reactions because it directly relates to the partial pressures of gases, which are experimentally measurable quantities. While Kc uses concentrations, Kp is often more convenient for gaseous systems where pressure data is readily available. Both are valid; the choice depends on the available experimental data and the specific application.
Q7: When does Δn equal zero, and what does this mean for Kp and Kc?
Δn equals zero when the total number of moles of gaseous products equals the total number of moles of gaseous reactants. In this case, (RT)^Δn equals one, so Kp equals Kc regardless of temperature. This simplifies calculations for reactions where the number of gas molecules remains constant.