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Vapor Pressure Calculator

Ready to calculate
Clausius-Clapeyron + Raoult.
Multi-unit T & P.
ΔH_vap + solution P.
100% Free.
No Data Stored.

How it Works

01Pick a Method

Clausius-Clapeyron (T,P pairs → ΔH_vap) or Raoult's Law (mole fraction × pure solvent → solution).

02Enter Values with Units

Multi-unit support: temperature (°C/°F/K), pressure (Pa/kPa/bar/atm/mmHg/torr/psi). Auto-conversion.

03Apply the Equation

Clausius: ΔH = −R·ln(P₂/P₁)/(1/T₂−1/T₁). Raoult: P_solution = x_solvent · P°_solvent.

04Read Result + Interpretation

Output in multiple unit systems with full breakdown and reference values for comparison.

What is a Vapor Pressure Calculator?

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid (or solid) phase at a given temperature — and it's the foundational quantity behind boiling, evaporation, distillation, atmospheric humidity, and every phase-equilibrium calculation in chemistry. Two relationships dominate vapor-pressure work: Clausius-Clapeyron (1834) for the temperature dependence of pure-substance vapor pressure, and Raoult's Law (1887) for vapor pressure lowering in ideal solutions. Our Vapor Pressure Calculator implements both in a single tool with a mode-toggle.

Clausius-Clapeyron mode takes initial and final temperatures + pressures and computes the enthalpy of vaporization ΔH_vap via ΔH = −R · ln(P₂/P₁) / (1/T₂ − 1/T₁). This is the standard physical-chemistry experiment for measuring ΔH_vap from two paired (T, P) measurements — typical reference values: water 40.65 kJ/mol; ethanol 38.6; methanol 35.3; ammonia 23.4; mercury 59.1; benzene 30.7. Raoult's Law mode takes the solvent mole fraction and the pure-solvent vapor pressure and computes the solution vapor pressure via P_solution = x_solvent × P°_solvent — the foundation of all colligative-property calculations (boiling-point elevation, freezing-point depression, osmotic pressure).

Multi-unit input throughout: temperature in °C / °F / K; pressure in 7 systems (Pa, kPa, bar, atm, mmHg, torr, psi). Output includes the result in multiple equivalent units plus a transparent calculation breakdown showing every intermediate step. Smart warnings catch the common errors: negative ΔH_vap (signals reversed T/P pairing — P₁ must correspond to T₁), unrealistic ΔH_vap (outside the 5-200 kJ/mol typical range), Raoult's-law non-ideality concerns at low solvent mole fractions (< 0.5), and ionic-solute van't Hoff factor reminders. Designed for physical-chemistry coursework, calorimetry / thermal-analysis labs computing ΔH_vap, distillation column design, atmospheric-science work, and any researcher needing a fast vapor-pressure relationship — runs entirely in your browser, no account, no data stored.

Pro Tip: Pair this with our Vapour Pressure of Water Calculator for the Antoine equation specifically for water, our Molality Calculator for colligative-property work, our Molarity Calculator for solution chemistry, or our Gibbs Phase Rule Calculator for multi-phase equilibria.

How to Use the Vapor Pressure Calculator?

Pick a Method: Clausius-Clapeyron for the temperature-dependence of pure-substance vapor pressure (the standard ΔH_vap measurement). Raoult's Law for the vapor-pressure lowering of an ideal solution by a non-volatile solute.
For Clausius-Clapeyron — Enter T₁, T₂, P₁, P₂: the calculator computes ΔH_vap. Critical: P₁ must correspond to T₁ and P₂ to T₂. If you swap them, you'll get a negative ΔH_vap (the calculator warns). Multi-unit input: T in °C / °F / K, P in 7 unit systems.
For Raoult's Law — Enter x_solvent and P°_solvent: mole fraction of solvent (range 0-1, where 1 = pure solvent and 0 = no solvent), and the vapor pressure of the PURE solvent at that temperature. The calculator returns the solution vapor pressure P = x · P°.
Apply the Equations: Clausius-Clapeyron: ΔH_vap = −R · ln(P₂/P₁) / (1/T₂ − 1/T₁), where R = 8.314 J/(mol·K). Raoult: P_solution = x_solvent × P°_solvent. Both are derived from fundamental thermodynamic principles.
Read Output in Multiple Unit Systems: Clausius gives ΔH_vap in kJ/mol and J/mol; Raoult gives P in Pa, kPa, mmHg, atm. Cross-check against your reference document or supplier datasheet.
Verify Reasonableness: ΔH_vap typically 5-200 kJ/mol (helium 0.083 outlier; molecular liquids 20-80 kJ/mol; metals 50-300 kJ/mol). Raoult solution P should be LESS than P° for any non-volatile solute (vapor pressure lowering). Out-of-range values warrant rechecking inputs.
For Non-Ideal Cases: Raoult's law is exact for ideal solutions only. For ionic solutes apply the van't Hoff factor i (NaCl ≈ 2, CaCl₂ ≈ 3). For concentrated solutions or polar/non-polar mismatches, use activity coefficients γ (P = γ · x · P°) from Margules, Wilson, or NRTL models.
For Wide T Ranges in Clausius-Clapeyron: the constant-ΔH approximation breaks down across > 50 K because ΔH_vap actually decreases with T (vanishes at critical point). For high-precision wide-range work, use the integrated Antoine equation or full Wagner equation of state.

How are vapor pressure relationships calculated?

Vapor pressure relationships are the foundation of phase-equilibrium chemistry — every distillation column, every humidity calculation, every freezing-point measurement traces back to Clausius-Clapeyron and Raoult's law. Both equations were derived from first principles in the 19th century and remain accurate to ~1-5% for typical applications.

References: Rudolf Clausius (1834) and Émile Clapeyron — Clausius-Clapeyron equation; François-Marie Raoult (1887) — Raoult's Law; Atkins' Physical Chemistry (12th ed.); Levine's Physical Chemistry (7th ed.); CRC Handbook of Chemistry and Physics.

Clausius-Clapeyron Equation

Differential form: dP/dT = ΔH_vap · P / (R · T²).

Integrated form (constant ΔH): ln(P₂/P₁) = −(ΔH_vap/R) × (1/T₂ − 1/T₁).

Rearranged for ΔH: ΔH_vap = −R · ln(P₂/P₁) / (1/T₂ − 1/T₁) = R · ln(P₂/P₁) / (1/T₁ − 1/T₂).

Raoult's Law

P_solution = x_solvent × P°_solvent.

Vapor-pressure lowering: ΔP = P° − P = (1 − x_solvent) × P° = x_solute × P°.

For ionic solutes, apply van't Hoff factor i: x_solvent_effective = (1 − i × n_solute / n_total). For NaCl (i=2): a 0.1 mole-fraction NaCl solution behaves like a 0.2 mole-fraction non-electrolyte solute solution.

Worked Example — Compute ΔH_vap of Water

Water boils at 100 °C (373.15 K) at 1 atm (101325 Pa). At 80 °C (353.15 K), water vapor pressure is 47373 Pa.

  • T₁ = 353.15 K, P₁ = 47373 Pa.
  • T₂ = 373.15 K, P₂ = 101325 Pa.
  • ln(P₂/P₁) = ln(101325/47373) = ln(2.139) = 0.7603.
  • 1/T₂ − 1/T₁ = 1/373.15 − 1/353.15 = 0.002680 − 0.002831 = −0.000152 K⁻¹.
  • ΔH_vap = −R × 0.7603 / (−0.000152) = 8.314 × 0.7603 / 0.000152 = 41,584 J/mol = 41.58 kJ/mol.
  • Reference: ΔH_vap(water at 100 °C) = 40.65 kJ/mol. Agreement < 3% — close to experiment, slightly high because ΔH actually decreases with T (the constant-ΔH assumption is approximate).

Worked Example — Raoult Lowering by Sucrose

Dissolve 0.1 mol of sucrose in 0.9 mol water → x_water = 0.9. Pure water at 25 °C: P° = 3169 Pa.

  • P_solution = 0.9 × 3169 = 2852 Pa.
  • Vapor-pressure lowering ΔP = 3169 − 2852 = 317 Pa = 10.0% of P°.
  • Equivalent: 0.10 × 3169 = 317 Pa = ΔP — directly proportional to mole fraction of solute (= 1 − x_solvent).

Worked Example — NaCl Solution (Ionic, Use van't Hoff i)

0.1 m NaCl in water at 25 °C. NaCl dissociates → Na⁺ + Cl⁻; van't Hoff i ≈ 1.87 (slightly less than 2 from ion pairing).

  • Effective solute mole fraction: x_solute_eff = 0.1 × i × MW_water / 1000 = 0.1 × 1.87 × 18.015 / 1000 = 0.00337.
  • x_water_eff = 1 − 0.00337 = 0.99663.
  • P_solution = 0.99663 × 3169 = 3158.3 Pa.
  • ΔP = 3169 − 3158.3 = 10.7 Pa.
  • For comparison: 0.1 m sucrose (i = 1) → ΔP = 5.7 Pa (about half).

Reference ΔH_vap Values (kJ/mol at boiling point)

  • Helium (4.22 K): 0.083.
  • Hydrogen (20.4 K): 0.904.
  • Methane (111.7 K): 8.19.
  • Ethane (184.6 K): 14.69.
  • Ammonia (239.8 K): 23.4.
  • Methanol (337.8 K): 35.3.
  • Ethanol (351.4 K): 38.6.
  • Water (373.15 K): 40.65.
  • Acetic acid (391.0 K): 23.7 (low because of dimerization in vapor).
  • Benzene (353.2 K): 30.72.
  • Mercury (629.7 K): 59.1.
  • Sulfuric acid (610 K): 99.0.
  • Sodium (1156 K): 96.96.
  • Iron (3134 K): 340.
  • Tungsten (5828 K): 800 (highest of common metals).
Real-World Example

Worked Example — Predict Boiling Point at Mt. Everest

Question: A hiker at Mt. Everest base camp (5300 m altitude, atmospheric pressure ~395 mmHg) wants to know at what temperature water boils. Use Clausius-Clapeyron with reference: water at 100 °C (373.15 K) has vapor pressure exactly 760 mmHg.

Step 1 — Set Up the Reverse Problem.

  • P₁ = 760 mmHg, T₁ = 373.15 K (sea level reference).
  • P₂ = 395 mmHg (target: ambient at altitude), T₂ = ? (boiling point at altitude).
  • ΔH_vap(water) ≈ 40.65 kJ/mol = 40650 J/mol.

Step 2 — Rearrange Clausius-Clapeyron for T₂.

  • ln(P₂/P₁) = −(ΔH/R) × (1/T₂ − 1/T₁).
  • 1/T₂ = 1/T₁ − R × ln(P₂/P₁) / ΔH.
  • 1/T₂ = 1/373.15 − (8.314 × ln(395/760)) / 40650.
  • 1/T₂ = 0.002680 − (8.314 × (−0.6553)) / 40650.
  • 1/T₂ = 0.002680 + 0.0001341 = 0.002814.
  • T₂ = 1 / 0.002814 = 355.4 K = 82.2 °C.

Step 3 — Verify with Calculator (forward direction).

  • Enter T₁ = 373.15 K, P₁ = 760 mmHg, T₂ = 355.4 K, P₂ = 395 mmHg.
  • ΔH = −8.314 × ln(395/760) / (1/355.4 − 1/373.15) = −8.314 × (−0.655) / (−0.0001340) = 40,648 J/mol ≈ 40.65 kJ/mol.
  • Matches reference ΔH_vap(water) ✓.

Step 4 — Practical Implications at 82 °C Boiling Point.

  • Cooking: at 82 °C, eggs don't fully cook (white sets at ~63 °C, yolk at 70 °C — works); pasta and rice take ~50% longer; brown rice may not soften adequately.
  • Sterilization: 82 °C for 10 min kills most bacteria but NOT spore-formers (Geobacillus stearothermophilus, Clostridium botulinum spores) — use pressure cooker for sterilization at altitude.
  • Tea / coffee: brewing temperatures at 82 °C are below the optimal 90-96 °C — taste affected; use insulated kettles and immediate brewing.
  • Distillation: ethanol BP at altitude = 78 °C - 6 °C ≈ 72 °C; gasoline BP shifts down by ~7 °C — adjust still operating temperatures.

Step 5 — Boiling-Point vs Altitude Reference Table.

  • Sea level (760 mmHg): 100.0 °C.
  • Denver (1600 m, ~630 mmHg): 95.4 °C.
  • Mexico City (2240 m, ~580 mmHg): 92.9 °C.
  • La Paz, Bolivia (3650 m, ~490 mmHg): 88.4 °C.
  • Everest base camp (5300 m, ~395 mmHg): 82.2 °C.
  • Everest summit (8849 m, ~240 mmHg): ~70 °C.
  • Rule of thumb: ~1 °C BP drop per 280 m altitude gain.

Who Should Use the Vapor Pressure Calculator?

1
Standard graduate-level p-chem experiment: measure vapor pressure at two temperatures with a water-displacement or pressure-transducer apparatus, apply Clausius-Clapeyron, get ΔH_vap. Accuracy ±5% with care.
2
Predict vapor-liquid equilibria from Clausius-Clapeyron + Raoult's law for binary mixtures; compute relative volatilities and minimum reflux ratios. Standard in McCabe-Thiele method.
3
Compute saturation vapor pressure of water at any T for relative humidity, dew point, frost point, and cloud-microphysics calculations. Standard input for weather-modeling and climatology.
4
Sizing humidification / dehumidification systems requires vapor-pressure data across the operating-T range. Standard ASHRAE psychrometric chart underpinned by Clausius-Clapeyron.
5
Boiling-point shifts at altitude affect both brewing (mash conversion temperatures) and distilling (ethanol BP shifts). Calculator gives the corrected BP and still-temperature targets.
6
Autoclave sterilization, freeze-drying (lyophilization), and vacuum distillation all depend on vapor pressure across operating ranges. Calculator handles design calculations.
7
Both Clausius-Clapeyron and Raoult's law are explicit AP/IB curriculum topics. Calculator handles arithmetic so students focus on conceptual understanding and unit conversions.

Technical Reference

Clausius-Clapeyron — Origin and Derivation. Émile Clapeyron (1799-1864) derived the differential equation dP/dT = ΔH/(T·ΔV) in 1834 from Carnot-cycle considerations applied to a phase transition. Rudolf Clausius (1822-1888) recognized in 1850 that for vapor-liquid equilibria where the vapor is approximately ideal and ΔV ≈ V_vapor = RT/P, the equation simplifies to dP/dT = ΔH · P / (R · T²). Integrating with ΔH constant gives ln(P₂/P₁) = −(ΔH/R) × (1/T₂ − 1/T₁). Validity assumptions: (a) vapor behaves as ideal gas (good for P < 10 bar); (b) liquid molar volume is negligible compared to vapor; (c) ΔH_vap is constant across the T range (good for ~50 K; ΔH actually decreases with T and vanishes at T_c).

Raoult's Law — Origin. François-Marie Raoult (1830-1901) measured vapor pressures of solutions of various non-volatile solutes in different solvents and discovered the proportionality P_solution / P°_solvent = x_solvent in 1887. The law is exact for IDEAL solutions — those where solvent-solute interactions are equivalent to solvent-solvent and solute-solute interactions. Applies most accurately for: dilute solutions of non-volatile non-electrolyte solutes (sucrose, urea, glucose); structurally similar molecules (benzene/toluene, ethanol/methanol); enantiomer mixtures; gases of similar molecular size and polarity.

ΔH_vap Reference Values (CRC Handbook). All in kJ/mol at the normal boiling point unless noted:

  • Hydrogen 0.904 (BP 20.4 K).
  • Helium 0.083 (BP 4.22 K) — lowest of all elements.
  • Nitrogen 5.57 (BP 77.4 K); Oxygen 6.82 (BP 90.2 K); Argon 6.43 (BP 87.3 K).
  • Methane 8.19 (BP 111.7 K); Ethane 14.69 (BP 184.6 K); Propane 19.04 (BP 231.0 K).
  • Ammonia 23.35 (BP 239.8 K); HCl 16.15 (BP 188.0 K); H₂S 18.67 (BP 213.5 K).
  • Methanol 35.3 (BP 337.8 K); Ethanol 38.6 (BP 351.4 K); 1-Propanol 41.4 (BP 370.4 K).
  • Acetone 31.3 (BP 329.2 K); Benzene 30.72 (BP 353.2 K); Toluene 33.18 (BP 383.8 K).
  • Water 40.65 (BP 373.15 K) — high because of extensive H-bonding.
  • Acetic acid 23.7 (BP 391.0 K) — anomalously low because acetic acid dimerizes in vapor (effectively two molecules form one dimer, halving the entropy of vaporization).
  • Mercury 59.1 (BP 629.9 K); Sulfuric acid 99.0 (BP 610 K).
  • NaCl 234 (BP 1738 K); Sodium 96.96 (BP 1156 K); Iron 340 (BP 3134 K).
  • Tungsten 800 (BP 5828 K) — highest of common metals; basis of incandescent-bulb filaments.

Trouton's Rule. An empirical regularity: ΔH_vap / T_BP ≈ 88 J/(mol·K) for most non-associated liquids. Examples: water 109, ethanol 110, benzene 87, methanol 105, acetone 95. Deviations: hydrogen-bonded liquids (water, alcohols, amines, carboxylic acids) are HIGH (~100-120 J/mol/K) due to extra entropy gain on breaking H-bonds. Strongly-associated vapors (acetic acid dimers, NO₂/N₂O₄ equilibrium) are LOW. Useful for estimating ΔH_vap when only T_BP is known: ΔH_vap(estimate) = 88 × T_BP / 1000 in kJ/mol.

Van't Hoff Factor (i) for Ionic Solutes in Raoult's Law.

  • Non-electrolyte (sucrose, glucose, urea): i = 1.
  • 1:1 strong electrolyte (NaCl, KCl, NH₄Cl): theoretical 2, experimental 1.85-1.95 (slight ion-pairing).
  • 1:2 electrolyte (CaCl₂, MgCl₂, BaCl₂): theoretical 3, experimental 2.6-2.8.
  • 2:1 electrolyte (Na₂SO₄, K₂CO₃): theoretical 3, experimental 2.3-2.7.
  • 3:1 electrolyte (AlCl₃, FeCl₃): theoretical 4, experimental 3.2-3.5.
  • Weak electrolyte (HF, acetic acid, NH₃): i = 1 + α(ν − 1), where α is degree of dissociation; for 0.1 m acetic acid, α ≈ 1.3%, i ≈ 1.013.

Beyond Raoult — Activity Coefficients. For non-ideal solutions, replace x_solvent with γ_solvent × x_solvent in Raoult's law: P = γ · x · P°. Positive deviations (γ > 1, higher P than Raoult predicts) occur for mismatched polarity (ethanol/hexane, water/dioxane). Negative deviations (γ < 1, lower P) occur for enhanced attractions (acetone/chloroform via H-bonding, HCl/water via dissociation). Activity-coefficient models: Margules (1-parameter), van Laar (2-parameter), Wilson (3-parameter), NRTL (4-parameter), UNIFAC (group-contribution, predictive). Standard in process simulators (Aspen Plus, ChemCAD, Pro/II).

Connection to Boiling Point and Phase Diagrams. A liquid boils when its vapor pressure equals the ambient atmospheric pressure. The Clausius-Clapeyron equation maps the vapor-pressure curve (P vs T) onto the phase diagram's liquid-vapor coexistence line, ending at the critical point (where ΔH_vap = 0 and liquid + vapor become indistinguishable). For water: critical T = 374 °C, critical P = 220.6 bar. Practical: the Clausius-Clapeyron equation predicts boiling-point shifts at altitude — water boils at 70 °C at the summit of Mt. Everest (atmospheric P ≈ 240 mmHg ≈ 32 kPa). Pressure cookers raise boiling point to 120 °C at 2 atm — basis of sterilization. References: Clausius (1834); Clapeyron; Raoult (1887); Atkins' Physical Chemistry (12th ed., Chapter 4); Levine's Physical Chemistry (7th ed.); CRC Handbook of Chemistry and Physics; NIST WebBook.

Conclusion

Vapor pressure relationships are the foundation of phase-equilibrium chemistry — Clausius-Clapeyron for the temperature-dependence of pure-substance vapor pressure, and Raoult's Law for vapor-pressure lowering in ideal solutions. Together they cover ~95% of vapor-pressure problems in undergraduate and early graduate physical chemistry. The math is two formulas — ΔH_vap = −R · ln(P₂/P₁) / (1/T₂ − 1/T₁) for Clausius and P_solution = x_solvent · P°_solvent for Raoult — but the conceptual implications span boiling, distillation, atmospheric humidity, and every colligative property.

Three operational reminders: (1) Clausius-Clapeyron assumes constant ΔH_vap — accurate over ~50 K but breaks down for wide ranges where ΔH actually decreases with T (and vanishes at the critical point). For wide-range high-precision work use the integrated Antoine equation or Wagner equation of state. (2) Raoult's law is exact for ideal solutions — for ionic solutes apply the van't Hoff factor i (NaCl ≈ 2, CaCl₂ ≈ 3); for concentrated or non-ideal solutions use activity coefficients γ from Margules, Wilson, or NRTL models. (3) P₁ MUST correspond to T₁ in Clausius-Clapeyron — pairing them wrong gives an unphysical negative ΔH_vap; the calculator warns when this happens.

Frequently Asked Questions

What is the Vapor Pressure Calculator?
It implements two foundational vapor-pressure relationships in physical chemistry. Clausius-Clapeyron mode: enter T₁, T₂, P₁, P₂ → returns ΔH_vap (enthalpy of vaporization) via ΔH = −R · ln(P₂/P₁) / (1/T₂ − 1/T₁). Raoult's Law mode: enter mole fraction of solvent and pure-solvent vapor pressure → returns solution vapor pressure via P = x · P°. Multi-unit support: T in °C/°F/K; P in 7 systems (Pa, kPa, bar, atm, mmHg, torr, psi).

Pro Tip: Pair this with our Vapour Pressure of Water Calculator for the Antoine equation specifically for water.

What is the Clausius-Clapeyron equation?
ln(P₂/P₁) = −(ΔH_vap/R) × (1/T₂ − 1/T₁). Derived by Émile Clapeyron (1834) and Rudolf Clausius (1850), it describes how vapor pressure changes with temperature for a pure substance. Assumes vapor is ideal, liquid volume is negligible, and ΔH_vap is constant. Three uses: (1) compute ΔH_vap from two (T, P) measurements; (2) predict P at a new T given (T₁, P₁) and ΔH; (3) predict T at a new P (e.g. boiling point at altitude). The calculator implements use (1).
What is Raoult's law?
P_solution = x_solvent × P°_solvent, where x_solvent is the mole fraction of solvent and P°_solvent is the vapor pressure of the pure solvent at that temperature. Discovered by François-Marie Raoult (1887). States that the partial vapor pressure of a solvent above an ideal solution equals (mole fraction of solvent) × (pure-solvent vapor pressure). Vapor-pressure lowering: ΔP = (1 − x_solvent) × P° = x_solute × P° — directly proportional to solute concentration. The basis of all colligative properties.
How do I use Clausius-Clapeyron to find ΔH_vap?
ΔH_vap = −R · ln(P₂/P₁) / (1/T₂ − 1/T₁). Where R = 8.314 J/(mol·K), and both temperatures must be in Kelvin (the calculator handles unit conversion). Worked example for water: T₁ = 80 °C = 353.15 K, P₁ = 47373 Pa. T₂ = 100 °C = 373.15 K, P₂ = 101325 Pa. ΔH = −8.314 × ln(101325/47373) / (1/373.15 − 1/353.15) = −8.314 × 0.7603 / (−0.000152) = 41,584 J/mol = 41.58 kJ/mol — close to reference 40.65 kJ/mol for water.
What's a typical ΔH_vap value?
20-80 kJ/mol for most molecular liquids. Specific reference values: helium 0.083 (BP 4.22 K, lowest); hydrogen 0.904; methane 8.19; ammonia 23.4; methanol 35.3; ethanol 38.6; water 40.65 (high because of H-bonding); benzene 30.72; mercury 59.1; iron 340; tungsten 800 (highest of common metals). Trouton's rule: ΔH_vap / T_BP ≈ 88 J/(mol·K) for most non-associated liquids; H-bonded liquids (water, alcohols) are higher (~100-120).
Why does my calculation give a negative ΔH_vap?
Almost always because P₁ and T₁ are paired with T₂ and P₂ swapped. P₁ MUST correspond to T₁ (lower T → lower vapor pressure for normal liquids); P₂ MUST correspond to T₂. If you swap them, ln(P₂/P₁) and (1/T₂ − 1/T₁) have the same sign instead of opposite signs, giving negative ΔH (unphysical — vaporization is always endothermic). Action: double-check your T-P pairings against the natural physical relationship (cooler liquid has lower vapor pressure).
How does Raoult's law relate to colligative properties?
Vapor-pressure lowering is one of four colligative properties; the other three (boiling-point elevation, freezing-point depression, osmotic pressure) all derive from it. Math chain: non-volatile solute lowers vapor pressure → boiling point rises (because ambient P now exceeds the lowered vapor pressure at the original BP) → freezing point falls (vapor-pressure curve shifted down intersects ice-vapor curve at lower T) → osmotic pressure builds (chemical-potential gradient). All four scale with mole fraction of solute (or molality × van't Hoff factor i). K_b(water) = 0.512 °C·kg/mol; K_f(water) = 1.86 °C·kg/mol; osmotic pressure π = M·R·T·i.
When does Raoult's law fail?
For non-ideal solutions. Strong positive deviations (γ > 1, P higher than Raoult): mismatched polarity (ethanol/hexane), broken H-bonding networks. Strong negative deviations (γ < 1, P lower than Raoult): enhanced attractions (acetone/chloroform via new H-bond formation, HCl/water via dissociation). For concentrated solutions (x_solvent < 0.5), even mildly non-ideal mixtures show 5-20% deviations from Raoult. Use activity coefficients: P = γ · x · P°, with γ from Margules, Wilson, NRTL, or UNIFAC models. For ionic solutes apply the van't Hoff factor i directly (NaCl i = 2, CaCl₂ i = 3 for dilute).
What's the boiling point of water at altitude?
Decreases with altitude due to lower atmospheric pressure. Reference table: sea level (760 mmHg): 100 °C; Denver 1600 m (~630 mmHg): 95 °C; La Paz 3650 m (~490 mmHg): 88 °C; Everest base camp 5300 m (~395 mmHg): 82 °C; Everest summit 8849 m (~240 mmHg): 70 °C. Rule of thumb: ~1 °C BP drop per 280 m (920 ft) altitude gain. Computed via Clausius-Clapeyron with ΔH_vap(water) = 40.65 kJ/mol.
How accurate is the Clausius-Clapeyron equation?
Within ~1-3% across a 50 K T range for most molecular liquids. Sources of error: (1) Constant-ΔH assumption — ΔH_vap actually decreases with T (vanishes at the critical point); for water, ΔH drops from 45.05 kJ/mol at 0 °C to 40.65 at 100 °C to 0 at 374 °C. Across 50 K the change is ~5%. (2) Non-ideal vapor behavior — the assumption V_liquid << V_vapor and ideal gas breaks down near the critical point (above ~50 bar) or with strongly polar vapors. For research-grade precision (NIST-traceable thermophysical work), use the integrated Antoine equation (3-parameter empirical fit) or the full Wagner / IAPWS equations of state.
What's the difference between this and the Antoine equation?
Both describe vapor-pressure-vs-temperature, but at different precision levels. Clausius-Clapeyron is theoretical (derived from thermodynamics); requires only ΔH_vap; assumes constant ΔH; accurate over ~50 K. Use for: deriving ΔH_vap from data, quick estimates with one data point. Antoine equation log P = A − B/(C + T) is empirical (3-parameter fit to experimental data over a specific T range); accurate to ~0.5% within its range; requires substance-specific A, B, C constants from CRC Handbook or NIST. Use for: high-precision vapor-pressure lookup, distillation column design. The calculator implements Clausius-Clapeyron for ΔH calculation; for the water-specific Antoine equation see our Vapour Pressure of Water Calculator.

Author Spotlight

The ToolsACE Team - ToolsACE.io Team

The ToolsACE Team

Our ToolsACE chemistry team built this calculator to handle the two most-used vapor-pressure relationships in physical chemistry: <strong>Clausius-Clapeyron</strong> (1834, for the temperature dependence of pure-substance vapor pressure) and <strong>Raoult's Law</strong> (1887, for vapor pressure lowering in ideal solutions). <strong>Mode 1 (Clausius-Clapeyron):</strong> enter initial and final temperatures and pressures; the calculator returns the enthalpy of vaporization ΔH_vap via ΔH = −R · ln(P₂/P₁) / (1/T₂ − 1/T₁). <strong>Mode 2 (Raoult's Law):</strong> enter solvent mole fraction and pure-solvent vapor pressure; the calculator returns the solution vapor pressure via P_solution = x_solvent × P°_solvent. Multi-unit support: temperature in °C / °F / K; pressure in Pa / kPa / bar / atm / mmHg / torr / psi (7 units, auto-converted). Smart warnings flag negative ΔH_vap (sign error in T/P pair assignment), unrealistic ΔH_vap (outside 5-200 kJ/mol typical range), and Raoult's-law non-ideality at low solvent mole fractions.

Rudolf Clausius (1834) and Émile Clapeyron — Clausius-Clapeyron equationFrançois-Marie Raoult (1887) — Raoult's Law of vapor-pressure loweringAtkins' Physical Chemistry; Levine's Physical Chemistry

Disclaimer

Clausius-Clapeyron mode assumes ΔH_vap is constant over the T₁→T₂ range; this is accurate for narrow ranges (~50 K) but breaks down for wide ranges where ΔH_vap decreases with T (vanishes at the critical point). For high-precision wide-range work use the integrated Antoine equation or full Wagner equation of state. P₁ MUST correspond to T₁ and P₂ to T₂; getting the pairing wrong gives a negative ΔH_vap (unphysical). Raoult's Law mode assumes ideal-solution behavior — accurate for dilute non-electrolyte solutions. For ionic solutes apply the van't Hoff factor i (NaCl ≈ 2, CaCl₂ ≈ 3). For non-ideal solutions use activity coefficients γ from Margules, Wilson, or NRTL models. References: Clausius (1834); Clapeyron; Raoult (1887); Atkins' Physical Chemistry (12th ed.); Levine's Physical Chemistry (7th ed.); CRC Handbook of Chemistry and Physics.