Considering Phase EquilibriumFor a gas-liquid system in

Chapter 14, Problem 86P

(choose chapter or problem)

For a gas–liquid system in equilibrium at temperature T and pressure p, Raoult’s law models the relation between the partial pressure of substance i in the gas phase, \(p_{i}\), and the mole fraction of substance i in the liquid phase, \(y_{i}\), as follows:

\(p_{i}=y_{i} p_{\text {sat }, i}(T)\)

where \(p_{\mathrm{sat}, i}(T)\) is the saturation pressure of pure i at temperature T. The gas phase is assumed to form an ideal gas mixture; thus, \(p_{i}=x_{i} p\) where \(x_{i}\) is the mole fraction of i in the gas phase. Apply Raoult’s law to the following cases, which are representative of conditions that might be encountered in ammonia–water absorption systems (Sec. 10.5):

(a) Consider a two-phase, liquid–vapor ammonia–water system in equilibrium at 20°C. The mole fraction of ammonia in the liquid phase is 80%. Determine the pressure, in bar, and the mole fraction of ammonia in the vapor phase.

(b) Determine the mole fractions of ammonia in the liquid and vapor phases of a two-phase ammonia–water system in equilibrium at 40°C, 12 bar.