Given a reference point (T₁, P₁) and the enthalpy of vaporisation ΔH_vap, the Clausius-Clapeyron equation predicts the vapor pressure P₂ at any other temperature T₂ in real time. Vapor pressure rises exponentially with temperature, and the same relation underpins boiling-point, distillation and weather calculations. Explore it through the in-flask molecular animation, the P–T curve and the ln P − 1/T line.
Parameters
Reference temperature T₁
K
Absolute temperature of the reference point with known vapor pressure (water normal boiling point = 373.15 K)
Reference pressure P₁
kPa
Known vapor pressure at T₁ (standard atmospheric pressure = 101.325 kPa)
Enthalpy of vaporisation ΔH_vap
kJ/mol
Energy needed to vaporise one mole of liquid (water = 40.7, ethanol = 38.6, acetone = 29, benzene = 30.7)
Evaluation temperature T₂
K
Target temperature whose vapor pressure you want to predict (127 °C = 400 K example)
Results
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Temperature change ΔT (K)
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Vapor pressure P₂ (kPa)
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Pressure ratio P₂/P₁
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ln(P₂/P₁)
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ΔH/R (K)
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Boiling-point trend
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Closed flask in vapor-liquid equilibrium — evaporation / condensation animation
Molecules constantly escape from the liquid into the vapor space, while an equal number condense back. Raising the temperature increases the upward flux and the vapor density (= vapor pressure) grows exponentially.
Vapor-pressure curve P(T) — exponential rise with temperature
Vapor pressure grows exponentially with temperature; the larger the enthalpy of vaporisation, the steeper that rise. R is the gas constant 8.314 J/(mol·K), T is absolute temperature [K], and ΔH_vap must be supplied in J/mol.
Closed-form prediction of P at any temperature T from a reference point (T₁, P₁). This is the form used to draw the P–T curve. The boiling point at a given ambient pressure P_amb is the T that satisfies P(T) = P_amb.
What is the Clausius-Clapeyron Equation?
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I hear "vapor pressure" thrown around all the time, but it's a fuzzy idea for me. Does room-temperature water actually have a vapor pressure?
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Good question — yes, it does. At every temperature a liquid can push back against its own vapor up to a certain pressure, and that's its vapor pressure. For water it's about 2.3 kPa at 20 °C, 1 atmosphere at 100 °C, and more than 15 atmospheres at 200 °C. That's why a sealed bottle of water left in a hot car balloons out — the vapor pressure inside is just climbing with the temperature.
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Wait — 2.3 to 101 kPa, that's about 45 times! The temperature only went up by a factor of four. Why such a dramatic jump?
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That's exactly the most striking thing about this equation. Vapor pressure rises not linearly but exponentially with temperature. Clausius and Clapeyron worked it out in the mid-1800s: ln(P₂/P₁) = −ΔH_vap/R × (1/T₂ − 1/T₁), so ln P is linear in 1/T. Bumping T up a little nudges 1/T down a little, which moves ln P up proportionally, which means P itself moves up exponentially. Compare the ln P − 1/T straight line on the right with the steep exponential climb of the P − T curve next to it.
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ΔH_vap is the enthalpy of vaporisation, right? What role does it actually play here?
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ΔH_vap is the energy needed to tear one mole of molecules out of the intermolecular bonds in the liquid and turn them into vapor. The larger that energy, the more dramatically the liquid responds to heating — heat it a little and suddenly a lot more of it can escape. Water has a fairly large ΔH_vap (40.7 kJ/mol), so it boils high at 100 °C; ethanol (38.6) and acetone (29) boil lower. Try sliding ΔH_vap between 30 and 50 in the panel — you'll see the slope of the ln P line change drastically.
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Got it. So the "boiling point" must come out of this equation as well? I've heard that water boils at 87 °C on top of Mount Fuji.
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Exactly the right intuition. The boiling point is just the temperature where the vapor pressure equals the surrounding total pressure. On Mt. Fuji the air pressure drops to about 0.65 atm, so water boils as soon as its vapor pressure reaches 0.65 atm, which is roughly 87 °C. A pressure cooker does the opposite: it lifts the inside pressure to about 2 atm, so the boiling point climbs to 120 °C and tough beans become tender quickly. In this tool, the T₂ that gives P₂ = 101.325 kPa is exactly the standard boiling point.
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That's neat! Can the same equation also explain distillation columns and weather-forecast "humidity"?
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Both rest on it. A distillation column separates components by exploiting the difference in vapor pressure each one has at every tray temperature. Relative humidity is just (current water-vapor partial pressure) ÷ (saturation vapor pressure at that temperature), which is why a window fogs up on a cold morning even though the absolute water content is unchanged — the saturation pressure has fallen. The cloud-base height (the dew point) is the altitude at which a rising parcel of air cools enough for its water-vapor pressure to catch up with the saturation curve. Drying, paint-booth solvent control, pharmaceutical freeze-drying, semiconductor outgassing — they all extend from this single equation.
Frequently Asked Questions
It describes how the vapor pressure of a pure liquid (or solid) in equilibrium with its own vapor changes with temperature. Derived in the mid-nineteenth century, it says that ln P plotted against 1/T is nearly a straight line of slope −ΔH_vap/R. The practical consequence is that a small rise in temperature produces a surprisingly large (exponential) rise in vapor pressure: water has only 2.3 kPa at 20 °C but reaches 101 kPa at 100 °C, which is why it boils there at atmospheric pressure. It underpins distillation, drying, meteorology, pressure cookers and every other process that involves evaporation.
ΔH_vap is the energy required to break the intermolecular bonds and free one mole of liquid into the vapor phase, and it sets the magnitude of the slope of the ln P − 1/T line (−ΔH_vap/R). The larger ΔH_vap, the steeper the line and the stronger the vapor-pressure response to heating. Water has a relatively large ΔH_vap ≈ 40.7 kJ/mol and therefore a high boiling point; ethanol (38.6) and acetone (29) are smaller and boil lower. Conversely, liquids with small ΔH_vap have high vapor pressures even at low temperatures and are highly volatile.
Two simplifying assumptions are built in. First, the vapor is treated as an ideal gas and the molar volume of the liquid is neglected compared with that of the vapor. Second, ΔH_vap is taken as constant over the temperature range. Both are accurate to within 1–few % near the boiling point and at moderate temperatures, but they break down close to the critical point (374 °C / 22 MPa for water), where vapor and liquid densities approach each other. For high accuracy across a wide temperature range, the Antoine or Wagner equations are used instead.
Boiling point is the temperature at which the vapor pressure equals the surrounding total pressure. At one standard atmosphere (101.325 kPa), water reaches a vapor pressure of 1 atm exactly at 100 °C, and vaporisation begins inside the liquid. On Mount Fuji where the pressure drops to about 0.65 atm, the boiling point falls to about 87 °C. In a pressure cooker held at 2 atm, water boils only at about 120 °C and cooking is much faster. In this tool, the temperature T₂ that gives P₂ = 101.325 kPa is precisely the standard boiling point of the substance.
Real-World Applications
Distillation and separation: Distillation columns in oil refineries and chemical plants separate mixtures by exploiting the difference in vapor-pressure curves (and therefore boiling points) between components. The temperature and pressure profile of each tray is designed on top of the Clausius-Clapeyron relation, combined with Raoult's law and activity-coefficient models. Vacuum distillation — lowering the pressure to drop the boiling point and vaporise heat-sensitive species at lower temperatures — is a direct application of the same equation.
Meteorology, humidity and cloud formation: The dew point is the temperature at which the moisture in the air just saturates the vapor-pressure curve, which is where dew, fog and the base of clouds appear. The cloud-base altitude follows from how high a parcel of air must rise (and thus cool adiabatically) before its water-vapor pressure reaches the saturation curve. The intensification of tropical storms with sea-surface temperature, and the famous "~7 % more atmospheric moisture per 1 °C of warming", both follow the so-called Clausius–Clapeyron scaling.
Pressure cookers, cooking and altitude correction: A pressure cooker held at about 2 atm shifts the boiling point of water up to roughly 120 °C, accelerating hydrolysis reactions and making meat and beans tender in a fraction of the time. Conversely, at 3000 m elevation atmospheric pressure drops to about 70 kPa, so water boils at only 90 °C and pasta or rice never fully cook from the inside — every high-altitude recipe adjustment is rooted in this equation.
Vacuum drying, freeze-drying and semiconductor manufacturing: Freeze-drying of pharmaceuticals and instant coffee works by dropping the pressure until the sublimation pressure of ice exceeds the surroundings, so the ice goes straight to vapor. Outgassing control in semiconductor cleanrooms, the boiling-point management of lithium-ion battery electrolytes and solvent evaporation in paint booths all begin from this equation. In multi-phase CFD, it is also embedded as the saturation-pressure table inside cavitation/Lee-model phase-change source terms.
Common Misconceptions and Pitfalls
The most frequent mistake is to treat ΔH_vap as a single, temperature-independent number. The textbook derivation does indeed assume ΔH_vap constant over the integration range, but in reality it decreases gently with temperature and vanishes at the critical point. For water it is about 44.0 kJ/mol at 25 °C, 40.7 at 100 °C and roughly 35 kJ/mol at 200 °C. A 30 °C-wide extrapolation usually stays within 1 % of reality, but for ranges of 100 °C or more you should either move the reference point closer to the target or switch to an extended form (the Watson correlation, the Antoine equation, etc.) that carries an explicit temperature dependence.
A second classic pitfall is plugging temperatures in degrees Celsius into the formula. The Clausius-Clapeyron equation contains 1/T, so every temperature must be in absolute units (kelvin). If you "calculate" the vapor-pressure ratio between 20 °C and 100 °C as 1/20 − 1/100, you will be off by orders of magnitude from the correct (1/293.15 − 1/373.15). Likewise, mind the units of ΔH_vap: with R = 8.314 J/(mol·K), the enthalpy must be entered in J/mol. If you express ΔH_vap in kJ/mol you must multiply by 1000 (this tool does the conversion internally for you).
Finally, the Clausius-Clapeyron equation is a pure-substance relation and cannot be applied directly to mixtures, aqueous solutions or surfactant-loaded liquids. Salt water has a lower vapor pressure than pure water (a colligative property described by Raoult's law); ethanol–water mixtures exhibit composition-dependent vapor-pressure surfaces with azeotropes. These require Raoult's law combined with activity-coefficient models (NRTL, UNIQUAC) to handle correctly. Treat the output of this tool as a reference value "as if the liquid were a pure substance characterised by the given ΔH_vap".
How to Use
Enter reference temperature (T₁) in Kelvin and corresponding vapor pressure (P₁) in kPa—obtain these from steam tables or refrigerant datasheets (e.g., water at 373.15 K = 101.325 kPa).
Input enthalpy of vaporization (ΔH_vap) in kJ/mol from thermodynamic property tables (water: 40.66 kJ/mol at normal boiling point; ammonia: 23.25 kJ/mol at 239.73 K).
Specify new temperature (T₂) in Kelvin; the simulator calculates P₂ using ln(P₂/P₁) = −(ΔH_vap/R) × (1/T₂ − 1/T₁), where R = 8.314 J/(mol·K).
Clausius-Clapeyron remains accurate within ~10°C of the reference state; beyond 20 K deviation, subcooled/superheated region effects reduce reliability for engineering calculations.
For multi-component mixtures (e.g., natural gas blends), apply the equation separately to each component using pure-fluid ΔH_vap values, then combine partial pressures.
Industrial pressure vessels and HVAC systems use this relationship to verify safety margins; a 5 K temperature excursion in ammonia chillers (~23 kJ/mol) shifts vapor pressure ~12–15%, requiring relief valve recalibration.
Extract ΔH_vap from NIST Webbook or manufacturer datasheets at your operating point; interpolate if necessary to avoid 3–5% prediction errors.