Clausius–Clapeyron calculator

A Clausius–Clapeyron equation calculator turns two vapor pressures, one known absolute temperature, and the enthalpy of vaporization into the second boiling or condensation temperature on the vapor-pressure curve. Enter P1 at T1, the target vapor pressure P2, and ΔHvap (with an optional gas constant R that defaults to the SI value); the tool rearranges the two-point form ln of P2 over P1 equals ΔHvap over R times one over T1 minus one over T2, then returns T2 in kelvin with inverse temperatures, the log pressure ratio, a short message, and ordered substitution steps. Homework checks, lab estimates of boiling point under reduced pressure, and coding kata expected values all need that same deterministic T2 without a spreadsheet.

What the two-point Clausius–Clapeyron equation solves

The Clausius–Clapeyron relation links how equilibrium vapor pressure changes with temperature for a pure liquid or solid when the enthalpy of vaporization or sublimation can be treated as roughly constant over a modest temperature interval. In the integrated two-point form, the natural logarithm of the pressure ratio P2 over P1 equals the enthalpy of vaporization divided by the gas constant, times the difference of reciprocal absolute temperatures one over T1 minus one over T2.

Solving for the unknown temperature gives T2 equals one divided by the quantity one over T1 minus R over ΔHvap times ln of P2 over P1. Absolute temperatures must be in kelvin; pressures may be in any unit as long as both P1 and P2 use the same unit because only their ratio appears.

Enthalpy and R must share energy units: with the default R of about eight point three one four joules per mole per kelvin, enter ΔHvap in joules per mole; if your table lists kilojoules per mole, either multiply ΔH by one thousand or pass a matching R near zero point zero zero eight three. Zero vapor pressure is not allowed: ln of a zero or infinite ratio is undefined, and that failure mode is the documented error path for this capability.

The check path recomputes the same intermediate log and reciprocal temperatures with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests or worksheets.

Practical tips, units, limits, and related searches

Convert Celsius to kelvin before calling: add two hundred seventy-three point one five to °C; never pass bare Celsius into t1. Keep P1 and P2 in the same pressure unit so the ratio is dimensionless and unit-free. Prefer ΔHvap and R in matching energy units rather than mixing kJ and J without adjusting R.

Prefer this capability when you already have two pressures, one temperature, and ΔHvap and only need T2; if your source is a word problem in °C, convert first. Round-trip checks are easy: recompute ln of P2 over P1 by hand, form one over T2 from the published formula, invert it, and confirm it equals the published t2 within the same twelve-decimal rounding.