The vapor pressure of water at 25 °C is 0.0313 atm. Cal- culate the values of Kp and Kc at 25 °C for the equilibrium H2O1l2 ∆ H2O1g2.

Verified step by step guidance

1. Step 1: Understand the problem. We are given the vapor pressure of water at 25 °C and we are asked to calculate the values of Kp and Kc for the equilibrium H2O(l) ⇌ H2O(g). Kp is the equilibrium constant for pressure and Kc is the equilibrium constant for concentration.
2. Step 2: Write the equilibrium expression for Kp. For the reaction H2O(l) ⇌ H2O(g), the equilibrium expression for Kp is Kp = P(H2O(g)). The pressure of the liquid phase is not included in the equilibrium expression because it is a pure liquid.
3. Step 3: Substitute the given vapor pressure into the equilibrium expression for Kp. The vapor pressure of water at 25 °C is given as 0.0313 atm, so Kp = 0.0313.
4. Step 4: Write the equilibrium expression for Kc. For the reaction H2O(l) ⇌ H2O(g), the equilibrium expression for Kc is Kc = [H2O(g)]. The concentration of the liquid phase is not included in the equilibrium expression because it is a pure liquid.
5. Step 5: Convert the vapor pressure to concentration to find Kc. Use the ideal gas law, PV = nRT, to convert pressure to concentration. The concentration of a gas is n/V, so P = nRT/V can be rewritten as P = CRT, where C is the concentration. Therefore, C = P/RT. Substitute the given vapor pressure and the values of R (0.0821 L·atm/K·mol) and T (25 °C = 298 K) into the equation to find Kc.

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. For water at 25 °C, the vapor pressure of 0.0313 atm indicates the tendency of water molecules to escape from the liquid phase into the gas phase. This concept is crucial for understanding the behavior of substances in equilibrium and is foundational for calculating equilibrium constants.

Equilibrium Constant (Kp and Kc)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium. Kp is used for gas-phase reactions and is expressed in terms of partial pressures, while Kc is used for reactions in solution and is expressed in terms of molar concentrations. The relationship between Kp and Kc is given by the equation Kp = Kc(RT)^(Δn), where Δn is the change in moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

Phase Equilibrium

Phase equilibrium occurs when the rates of the forward and reverse processes of a phase change are equal, resulting in no net change in the amounts of each phase. In the context of the reaction H2O(l) ⇌ H2O(g), this equilibrium is influenced by temperature and pressure. Understanding phase equilibrium is essential for calculating Kp and Kc, as it helps to determine the concentrations or pressures of the reactants and products at equilibrium.