Relative volatility is a number that tells you how easy or hard it is to separate two chemicals from each other by distillation. It compares how readily one component evaporates versus another in a liquid mixture. When the value is far above 1, the two components behave very differently when heated, making separation straightforward. When it’s close to 1, their boiling behaviors are nearly identical, and pulling them apart becomes expensive, slow, or even impossible with simple distillation.
What Relative Volatility Actually Measures
Every liquid has a tendency to turn into vapor. Some liquids, like acetone, evaporate aggressively at room temperature. Others, like heavy oils, barely evaporate at all. Relative volatility captures the difference between two components in a mixture by expressing it as a single ratio, typically written with the Greek letter alpha (α).
In the simplest case, for an ideal mixture of two components A and B, relative volatility is the ratio of their pure vapor pressures:
α = P°A / P°B
Here, P°A is the vapor pressure of pure component A (the lighter, more volatile one), and P°B is the vapor pressure of pure component B (the heavier one). Because the lighter component always goes in the numerator, α is always greater than or equal to 1. A value of exactly 1 means both components evaporate at the same rate, and no separation by distillation is possible.
The Formula Using Liquid and Vapor Compositions
The vapor-pressure ratio works well for ideal mixtures, but real-world separation depends on what’s actually happening inside a distillation column. Engineers need to know how the composition of the vapor differs from the composition of the liquid at equilibrium. This leads to a more general form of relative volatility:
α = (yA · xB) / (yB · xA)
In this equation, y represents the mole fraction of each component in the vapor phase, and x represents the mole fraction in the liquid phase. What this formula really says is: if component A is enriched in the vapor compared to the liquid much more than component B is, then α will be large and separation will be easy. If both components show up in the vapor in roughly the same proportions as in the liquid, α will be close to 1 and separation will be painful.
There’s another way to express the same idea. Each component has a K-value, defined as K = y/x for that component. Relative volatility is simply the ratio of K-values: α = KA / KB. For ideal systems, this collapses back to the pure vapor pressure ratio.
Why the Value of Alpha Matters So Much
Relative volatility directly controls how many stages (or trays) a distillation column needs and how much energy it consumes. The Fenske equation, a foundational tool in distillation design, calculates the minimum number of theoretical stages as:
Smin = log(SF) / log(αavg)
SF is the “separation factor,” which captures how pure you need the final products to be. The key takeaway is that α sits in the denominator inside a logarithm. As α gets closer to 1, log(α) shrinks toward zero, and the required number of stages climbs rapidly. A mixture with α = 2.0 might need a modest column. A mixture with α = 1.05 could need a tower with dozens or even hundreds of trays.
As a rough guide, separations with α above about 2 are considered relatively easy. Values between 1.2 and 2.0 are moderate and require careful column design. Below about 1.1, separation becomes very difficult and expensive. And at exactly 1.0, conventional distillation simply cannot do the job.
When Alpha Equals 1: Azeotropes
An azeotrope is a specific mixture composition where the liquid and vapor have exactly the same makeup. At that point, relative volatility equals 1, and boiling the mixture produces vapor that is identical to the liquid. No amount of additional distillation stages will improve the separation.
The classic example is ethanol and water. You can distill a dilute ethanol solution and steadily increase its concentration, but once you reach about 95.6% ethanol, the mixture forms an azeotrope. The vapor coming off has the same 95.6% composition as the liquid, so simple distillation hits a wall. To push past this limit, engineers turn to techniques like pressure-swing distillation (running a second column at a different pressure where the azeotrope composition shifts), adding a third chemical to break the azeotrope, or using molecular sieves.
How Temperature and Pressure Affect Alpha
Relative volatility is not a fixed property of a pair of chemicals. It changes with temperature and pressure. Both components’ vapor pressures increase as temperature rises, but they don’t increase at the same rate. In general, the ratio of vapor pressures tends to converge as temperature goes up, meaning α typically decreases at higher temperatures and higher pressures.
This is why vacuum distillation can be useful for close-boiling mixtures. Lowering the system pressure lowers the boiling temperature, which often increases the difference in volatility between the two components, making them easier to separate. It also protects heat-sensitive materials from thermal degradation. On the other hand, operating at higher pressure can sometimes shift azeotropic compositions or eliminate them entirely, which is the basis of pressure-swing distillation.
A Practical Example: Benzene and Toluene
Benzene and toluene are one of the most commonly cited textbook pairs because they behave nearly ideally when mixed. Benzene boils at 80 °C and toluene at 111 °C, a 31-degree gap that gives a comfortable relative volatility of roughly 2.3 to 2.5 at atmospheric pressure. This means benzene preferentially enters the vapor phase about 2.4 times more than toluene does, and the separation can be accomplished with a relatively short distillation column of around 15 to 20 trays.
Contrast that with separating isomers of xylene, where boiling points differ by just a few degrees and α hovers near 1.02. That separation is so difficult by distillation that industrial plants use superfractionation columns with hundreds of trays, or skip distillation entirely in favor of crystallization or adsorption.
Non-Ideal Mixtures and Activity Coefficients
The simple vapor-pressure ratio only works perfectly for ideal mixtures, where molecules of each component interact with each other the same way they interact with themselves. Most real mixtures aren’t ideal. Polar molecules mixed with nonpolar ones, for instance, can show dramatic deviations.
For non-ideal systems, the relative volatility calculation includes activity coefficients (γ), which correct for how molecules in the liquid phase attract or repel each other. The modified expression becomes: α = (γA · P°A) / (γB · P°B). When the activity coefficient of the lighter component is greater than 1, it means that component “wants” to escape the liquid more than its pure vapor pressure would suggest, effectively boosting the relative volatility. This is actually the principle behind extractive distillation: adding a solvent that selectively increases the activity coefficient of one component, artificially widening the gap between the two and making separation feasible where it otherwise wouldn’t be.