RUŌOD Lab

Mastery course · Advanced Perfumery Chemistry

Evaporation Thermodynamics: Clausius–Clapeyron at the Blotter

How temperature and enthalpy of vaporization set evaporation speed, why skin warmth reorders a perfume, and a simple model of how long each material lasts.

Mastery 55 min study By the RUŌOD Lab team Updated

In short

A material evaporates as fast as its partial pressure at the surface lets it, and that pressure rises exponentially with temperature at a rate set by its enthalpy of vaporization. So warmth does not just speed a perfume up: materials with a large enthalpy of vaporization speed up more than the rest, which can reorder the drydown. A simple film model then gives each material a lifetime inversely proportional to its effective vapor pressure.

What you will learn

  • Use the Clausius–Clapeyron equation to estimate how vapor pressure changes between room and skin temperature
  • Derive a first-order model of how a dilute odorant depletes from an evaporating film
  • Explain why materials with a high enthalpy of vaporization accelerate most on warm skin
  • Judge where the simple model fails

Before this lesson: Raoult's Law and the Headspace of a Perfume, Balance Volatility Across a Formula

Before you start

You need the partial-pressure expression from Raoult's law and the headspace, the bench sense of volatility from balancing volatility, natural logarithms and one first-order differential equation.

Temperature: the Clausius–Clapeyron equation

Integrating the Clapeyron relation for a liquid–vapor boundary, with the vapor treated as ideal and the enthalpy of vaporization ΔHvap taken as constant, gives

ln(P2/P1) = −(ΔHvap/R)·(1/T2 − 1/T1)

with R = 8.314 J/(mol·K) and temperatures in kelvin. Worked for 25 °C (298.15 K) to 32 °C (305.15 K), a plausible skin-surface figure:

Factor by which vapor pressure rises from 25 °C (enthalpies illustrative)
ΔHvapTo 20 °CTo 32 °C
50 kJ/mol× 0.71× 1.59
70 kJ/mol—× 1.91

Heavier, more strongly associating molecules tend to have larger enthalpies of vaporization. On warm skin they gain on the volatile materials, which is one reason a base can seem to arrive sooner on skin than on a blotter at room temperature. That is a mechanism worth testing, not a guaranteed effect: skin also absorbs.

Time: a film model

Treat a thin, well-mixed liquid film on an inert surface. The flux of component i into moving air is

Ji = k · γi · xi · Pi* / (R T)

in mol per unit area per second, where k is a mass-transfer coefficient (a velocity) set by the air movement and the geometry. For a dilute odorant in a film whose total moles N change slowly — a fixative-rich base, or an early stage when the solvent dominates — xi = ni/N, and the moles left on area A obey

dni/dt = −(k A γi Pi* / (N R T)) · ni

which is first-order decay: ni(t) = ni(0)·e−t/τi, with τi = N R T / (k A γi Pi*) and a half-life of τi·ln 2.

The model's most useful prediction is a ratio. Two dilute materials in the same film, under the same air, last in inverse proportion to γP*: a material with one tenth the effective vapor pressure lasts ten times as long. Absolute times depend on k, N and A, which no formula records, so the model ranks and scales lifetimes rather than predicting minutes.

Where it breaks down

  • N is not constant. Once ethanol has gone, the film is the concentrate itself, and every mole fraction rises as the volatile materials leave. The decay is no longer first order, and late materials can appear to "bloom".
  • γ changes as the film changes. An odorant's activity in an ethanol-rich film is not its activity in the waxy residue an hour later.
  • Surfaces are not inert. Paper adsorbs; skin absorbs and contributes lipids and water. That is why skin interactions and fabric tests are separate subjects.
  • Constant ΔHvap is an approximation that holds over narrow temperature ranges, which room-to-skin is.

In professional practice

Evaporation and diffusion models of this kind are used in fragrance engineering to predict performance before a panel is convened. For a perfumer the payoff is diagnostic: a top note that vanishes in minutes on warm skin, a woody material that seems louder in summer, or a blotter test that disagrees with a wear test are all predicted, at least in direction, by these two equations.

Open questions

How much of the difference between blotter and skin drydowns is temperature, and how much is absorption into skin? Separating the two needs controlled surfaces at matched temperatures. That is a feasible independent study: heated glass or a temperature-controlled plate against paper, at the same temperature, with a blinded panel.

Practical exercise: Model a drydown, then test it on blotters

About 180 minutes · You will have: a predicted order and relative lifetime for four materials, compared with your own timed blotter observations at two temperatures

Choose four materials spanning the volatility range, each diluted to 10% in ethanol. Look up or estimate each vapor pressure at 25 °C and record the source.

  1. Predict the order in which they disappear from a blotter and their relative lifetimes from 1/P*, assuming γ ≈ 1. State the assumption.
  2. Dip two blotters per material. Keep one set at room temperature and one in a warm, still place at a temperature you measure (a thermometer beside the blotters).
  3. Smell blind (a helper codes the strips) at fixed intervals, recording "clearly present", "faint" or "gone".
  4. Compare the observed order and the warm/room ratio with your predictions, including the Clausius–Clapeyron factor if you can find an enthalpy of vaporization.

You have done this well if the prediction was written down before smelling, the strips were coded, temperatures were measured rather than assumed, and your conclusion separates what the model got right in direction from where it failed, with a reason drawn from the list above.

Common mistakes

  • Temperatures in Celsius. The equation needs kelvin; a Celsius slip gives nonsense.
  • Reading absolute times from the model. It gives ratios unless you measure k, A and N.
  • Testing warm and cool strips in different rooms. Air movement changes k; keep everything but temperature equal.

Safety

Work with diluted materials on paper strips, not skin, in a ventilated room away from flames: ethanol is flammable and warm places concentrate its vapor. Read each material's SDS first and follow the safe handling lesson.

Key terms

Enthalpy of vaporization
The heat needed to turn one mole of a liquid into vapor at constant pressure. The larger it is, the more steeply the vapor pressure rises with temperature.
Clausius–Clapeyron equation
ln(P2/P1) = −(ΔHvap/R)(1/T2 − 1/T1): how vapor pressure changes with temperature, assuming the enthalpy of vaporization is constant over the range.
Evaporative flux
The amount of a component leaving a surface per unit area per unit time. It is proportional to the component's partial pressure at the surface, through a mass-transfer coefficient that depends on air movement.

Knowledge check

1. Between 25 °C and 32 °C, a material with ΔHvap = 70 kJ/mol increases its vapor pressure by about what factor?
Show the answer

1.9. ln(P2/P1) = (70000/8.314)(1/298.15 − 1/305.15) ≈ 0.648, so the factor is about 1.91. A 50 kJ/mol material rises by only about 1.59.

2. In the dilute first-order model, what sets a material's half-life on the blotter?
Show the answer

It is inversely proportional to its activity coefficient times pure vapor pressure. The depletion rate constant is proportional to γP*, so the half-life is proportional to 1/(γP*), other things equal.

3. Why can skin temperature change the order of a perfume's drydown, not just its speed?
Show the answer

Materials with different enthalpies of vaporization accelerate by different factors. Each material's vapor pressure scales by its own exp factor, so a high-ΔHvap material gains relative to a low-ΔHvap one.

4. Which assumption of the simple model fails first on real skin?
Show the answer

That the film is a well-mixed liquid on an inert surface. Skin absorbs, holds lipids and water, and has its own temperature gradients; the film is neither inert nor well mixed.

Sources

  • Atkins P, de Paula J, Keeler J. Atkins' Physical Chemistry (Oxford University Press) — The Clausius–Clapeyron equation and its assumptions
  • Perfume and Flavor Engineering: A Chemical Engineering Perspective. Molecules, 2021 (review) — Evaporation and diffusion models of perfumes
  • NIST Chemistry WebBook — Vapor-pressure and phase-change data, including enthalpies of vaporization where measured

Further reading and materials

Written and reviewed by the RUŌOD Lab team. This is general education, not legal, regulatory, medical or safety advice. Example dilutions and exercises are for learning, are not validated products, and have not been safety-assessed. Completing a lesson confers no qualification. How we check these lessons.