##  [Vapor–Liquid Equilibrium Ratio](/vapor-liquid-equilibrium-ratio-0) 

 Definition

The equilibrium ratio Ki (K‑value) for component i defined as Ki = yi/xi, the ratio of the component mole fraction in the vapor phase (yi) to its mole fraction in the liquid phase (xi) at vapor–liquid thermodynamic equilibrium under specified temperature and pressure conditions; Ki is unitless and is a function of composition, temperature and pressure (and nonideality).

 

 

 

 

 

 





## Principle

Principle

At equilibrium, yi = Ki xi; for Ki > 1 component i is relatively more volatile (favors vapor) and for Ki < 1 it is relatively less volatile (favors liquid). Ki permits stagewise and column calculations when local equilibrium assumptions apply.

 

 

 

 

 





## Demonstration

Demonstration

Illustrative Scenario → Situation: Single‑stage vapor–liquid contact at known T and P. → Recognition: Measured xi and yi satisfy yi ≈ Ki(xi,T,P). → Action: Use Ki to predict vapor composition after equilibrium contact or to compute the number of theoretical stages in a distillation calculation using equilibrium‑based methods. → Consequence: Predictions match equilibrium‑limited separation behavior; deviations indicate non‑equilibrium, strong nonideality, or incorrect Ki data.

 

 

 

 

## Misapplication

Misapplication

Treating Ki as a constant independent of temperature, pressure or composition. The error appears plausible because Ki is often tabulated; the semantic error is using a single Ki value outside its valid T–P–composition range or for systems with strong activity or fugacity effects without applying activity/fugacity corrections or more detailed VLE models.

 

 

 

 

 





## Consequence

Consequence

Applying incorrect Ki values yields erroneous design and control outcomes: underpredicting separation difficulty may produce columns with insufficient stages; overreliance on tabulated Ki at different conditions can lead to off‑spec product or inefficient operation. The causal mechanism is incorrect phase composition prediction feeding column balances and stage calculations.

 

 

 

 

## Reversal

Reversal

Ki loses utility where local vapor–liquid equilibrium does not apply: reactive systems not at chemical equilibrium, rapid flows where mass transfer prevents equilibrium on a stage, or where two liquid phases exist; also in presence of azeotropes Ki can vary nonmonotonically with composition and standard assumptions fail.

 

 

 

 

 





## Boundary

Boundary

Clearly within: Binary or multicomponent systems at well‑defined T and P where vapor and liquid are in thermodynamic equilibrium. Boundary case: Strongly nonideal mixtures that require activity coefficient models to compute Ki. Clearly outside: Systems with solids, supercritical single‑phase conditions, or kinetically hindered (non‑equilibrium) phase contact.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Practical tension between using empirical Ki correlations (simple, convenient) and rigorous thermodynamic models (activity/fugacity‑based) that are more accurate for nonideal or extreme conditions but require more data and computation.

 

 

 

 

 





## Synthesis

Synthesis

Ki is a convenient, local equilibrium descriptor of relative volatility that simplifies design calculations, but it must be applied with explicit attention to its dependence on temperature, pressure and nonideality or replaced by activity‑/fugacity‑based equilibrium relations when those effects are significant.