An engineer attempts to purify ethanol from a water-ethanol mixture through repeated distillation. After many stages, the distillate stabilizes at 95.6 mol% ethanol and cannot be made purer regardless of how many additional stages are added. Why?
AA minimum-boiling azeotrope exists at this composition: the vapor and liquid phases have identical compositions, so distillation produces no further enrichment — the driving force for separation disappears
BEthanol and water form an ideal solution at high ethanol concentrations, so Raoult's law applies exactly and there is no vapor pressure difference to exploit
CThe boiling point of the mixture rises to match pure water's boiling point at this composition, halting further distillation
DThe activity coefficients approach zero at high ethanol concentrations, eliminating the fugacity difference between phases
The ethanol-water system shows positive deviation from Raoult's law — A-B (ethanol-water) interactions are weaker than A-A and B-B interactions, so the mixture has higher vapor pressure than Raoult's law predicts. This positive deviation creates a maximum in the total vapor pressure curve, which corresponds to a minimum-boiling azeotrope at 95.6 mol% ethanol, 78.1°C at 1 atm. At the azeotrope, vapor and liquid compositions are identical; evaporating the liquid produces vapor of the same composition. No amount of additional distillation stages can move past this composition. Absolute (100%) ethanol requires a different process such as molecular sieves or azeotropic distillation with a third component.
Question 2 Multiple Choice
Two liquid species A and B have weaker A-B intermolecular interactions than either A-A or B-B interactions. What does this imply for their solution behavior?
APositive deviation from Raoult's law (γᵢ > 1): molecules 'prefer' like neighbors and escape into the vapor more readily than Raoult's law predicts, raising vapor pressure above the ideal prediction
BNegative deviation from Raoult's law (γᵢ < 1): weaker cross-interactions mean the mixture is less stable, so vapor pressure is lower than ideal
CIdeal solution behavior (γᵢ = 1): differences in intermolecular forces only matter for the enthalpy of mixing, not for vapor pressure
DA maximum-boiling azeotrope: weaker cross-interactions cause the mixture to boil at a higher temperature than either pure component
When A-B interactions are weaker than A-A or B-B, each molecule is less 'held' by its neighbors in solution than it would be in the pure liquid. Molecules escape into the vapor more easily, raising the partial pressure of each component above the xᵢPᵢˢᵃᵗ prediction of Raoult's law. Activity coefficients γᵢ > 1 quantify this excess tendency to vaporize. The ethanol-acetone system is a classic example. Negative deviation (option B) results from the opposite: unusually strong cross-interactions (e.g., hydrogen bonding between unlike molecules) that make the liquid more stable and reduce vapor pressure below Raoult's law.
Question 3 True / False
For an ideal solution, the activity coefficient γᵢ equals 1 for all components, and the enthalpy of mixing is zero.
TTrue
FFalse
Answer: True
An ideal solution is defined by the condition that all intermolecular interactions are equal (A-A = B-B = A-B). This means mixing is a purely entropic process: ΔH_mix = 0 and ΔV_mix = 0. With no energetic preference for any neighbor, the tendency of each component to vaporize is proportional only to its mole fraction, giving pᵢ = xᵢPᵢˢᵃᵗ (Raoult's law) and γᵢ = 1. Activity coefficients are 1 for all compositions and all components simultaneously. Ideal behavior is a reasonable approximation for chemically very similar species, such as benzene-toluene or isotopic mixtures.
Question 4 True / False
A maximum-boiling azeotrope, such as the HCl-water system, arises from positive deviation from Raoult's law.
TTrue
FFalse
Answer: False
Maximum-boiling azeotropes arise from negative deviation (γᵢ < 1), caused by unusually strong cross-species interactions. Stronger A-B attraction relative to A-A and B-B holds molecules in the liquid phase more tightly, reducing vapor pressure below the Raoult's law prediction. The vapor pressure curve shows a minimum at the azeotrope composition, corresponding to a maximum in boiling point — the mixture is hardest to vaporize at that composition. Positive deviation creates a vapor pressure maximum (minimum-boiling azeotrope). The HCl-water system has strong HCl-H₂O hydrogen bonding interactions, producing negative deviation and a maximum-boiling azeotrope at ~20% HCl.
Question 5 Short Answer
Why is an azeotrope a fundamental limitation for distillation engineers, and what does its existence reveal about the thermodynamics of the liquid mixture?
Think about your answer, then reveal below.
Model answer: Distillation relies on the vapor phase being richer in the more volatile component than the liquid phase — this composition difference is what each stage exploits. At an azeotrope, the vapor and liquid have identical compositions: K_i = yᵢ/xᵢ = 1 for all components. Evaporating the liquid produces vapor of the same composition, so no separation occurs regardless of the number of stages or reflux ratio. This is a thermodynamic limit, not an engineering one. The azeotrope's existence reveals that activity coefficients are non-unity: the liquid mixture has strong molecular interactions (positive or negative deviation) that cause the total vapor pressure curve to have a local extremum. At that extremum, the Gibbs-Duhem equation constrains the partial pressures to converge to equal compositions in both phases.
Engineers bypass azeotropes by pressure-swing distillation (azeotrope composition shifts with pressure if the components' vapor pressures have different pressure dependencies), extractive distillation (adding a third solvent that breaks the azeotrope), or entirely different separation technologies. The ethanol-water azeotrope is why fuel-grade ethanol (denatured, ~96%) is cheap but absolute ethanol is expensive.