Final answer:
The equilibrium-constant expression for the evaporation of water is Kp = PH₂O(g), with the liquid water's contribution being built into Kp because it is a constant. To determine spontaneity at 298 K, we assess ΔG, which must be negative for the process to be spontaneous. For laundry to dry, the air's PH₂O must be lower than water's equilibrium vapor pressure.
Step-by-step explanation:
The equilibrium-constant expression for the evaporation of water is written in terms of the partial pressures of the liquid and gaseous forms. For the evaporation of water (H₂O(l) → H₂O(g)), we can simplify the expression because the partial pressure of a pure liquid is constant and can thus be incorporated into the equilibrium constant. Therefore, the equilibrium constant, Kp, for the evaporation of water is expressed only in terms of the partial pressure of water in the gaseous phase (PH₂O(g)).
The equation for the equilibrium constant is Kp = PH₂O(g). Because H₂O(l) is a pure liquid, its partial pressure does not appear in the expression. To determine if the evaporation of water is spontaneous at a given temperature and partial pressure of water, the Gibbs free energy change (ΔG) is used. Spontaneity is indicated by a negative ΔG value.
At 298 K, if the partial pressure of water, PH₂O, is 0.011 atm, use the equation ΔG = -RTlnK to calculate ΔG and determine if the process is spontaneous. In the context of drying laundry, the PH₂O must be lower than the equilibrium vapor pressure of water at that temperature for evaporation to occur and allow laundry to dry.