What the Clausius-Clapeyron Equation Describes

Every liquid exerts a vapour pressure: molecules escape the surface into the gas phase until escape and return balance. That pressure rises with temperature, and it rises exponentially rather than linearly. The Clausius-Clapeyron equation is the quantitative statement of that relationship, derived from the requirement that two phases in equilibrium have equal chemical potential.

The integrated two-point form used here — the natural log of the pressure ratio equals minus ΔH over R, times the difference of reciprocal temperatures — is the workhorse version. Given any three of the four quantities it returns the fourth, which is why it appears in every physical chemistry course and in a great deal of practical engineering. Boiling is simply the special case where vapour pressure reaches ambient pressure, so every question about boiling points at altitude, in vacuum, or under pressure is this equation in disguise.

Why Temperature Must Be Absolute

The single most common error in applying this equation is using Celsius. The expression contains 1/T, and a reciprocal only carries physical meaning on an absolute scale where zero means zero thermal energy. At 0 °C the Celsius reciprocal is undefined; below it, the sign inverts and the result becomes nonsense rather than merely inaccurate.

This calculator accepts Celsius and Fahrenheit because that is how temperatures are usually recorded, but it converts to Kelvin before any arithmetic and displays both values in the breakdown table so the conversion is auditable. If you are checking work done by hand, the Kelvin figures in that table are the ones to compare against.

The Three Assumptions and Where They Fail

The integrated form is not exact. Reaching it requires three simplifications: that the vapour behaves ideally, that the liquid's molar volume is negligible beside the vapour's, and that ΔH is constant over the temperature range. The first two hold very well at pressures and temperatures far below the critical point, where vapour is dilute and liquid volume is genuinely tiny by comparison.

The constant-ΔH assumption is the one that fails first. Enthalpy of vaporisation decreases as temperature rises, falling to exactly zero at the critical point, where the distinction between liquid and gas disappears entirely. Over a 20 K span the error is negligible; over 100 K it becomes several percent; approaching the critical point the equation fails outright. This calculator flags both conditions — wide spans and proximity to the critical temperature of the selected substance — rather than silently returning a confident wrong answer. When you need accuracy across a wide range, the Antoine equation with fitted empirical constants is the correct tool.

Practical Uses: Altitude, Vacuum, and Measuring ΔH

The everyday application is boiling point at altitude. Denver's 84 kPa puts water's boiling point near 95 °C; the summit of Everest at roughly 34 kPa brings it to about 71 °C. Food cooks more slowly not because the water boils reluctantly but because boiling water is simply not as hot, which is why pressure cookers exist — raising the pressure raises the boiling point and speeds the chemistry.

In the laboratory the equation is more often run in reverse, to measure ΔH. Record vapour pressure at several temperatures, plot the natural log of pressure against reciprocal absolute temperature, and fit a line: the slope is minus ΔH over R. The linearity of that plot is itself the evidence that the assumptions hold across your range, which makes the experiment self-validating. Professional Mode reports that slope along with the entropy of vaporisation and its deviation from Trouton's rule — a quick check that a computed ΔH is physically plausible, since most normal liquids cluster near 88 J/(mol·K) and large positive deviations reliably signal hydrogen bonding.