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Clausius Clapeyron Calculator

Compute clausius clapeyron using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.

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Chemistry

Clausius Clapeyron Calculator

Calculate vapor pressure at different temperatures using the Clausius-Clapeyron equation. Find P2, T2, or enthalpy of vaporization from known phase transition data.

Last updated: December 2025

Calculator

Adjust values & calculate
101.325 kPa
373.15 K
40660 J/mol
393.15
Vapor Pressure at T2
197.3653 kPa
Change: 96.0403 kPa (94.78%)
ln(P2/P1)
0.666723
Temp Difference
20.00 K
Pressure Change
94.78%
Note: The Clausius-Clapeyron equation assumes constant enthalpy of vaporization and ideal gas behavior. Results are most accurate for moderate temperature ranges near the normal boiling point.
Your Result
P2 = 197.3653 kPa | Change: 94.78%
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Formula

ln(P2/P1) = (deltaH_vap / R) * (1/T1 - 1/T2)

Where P1 and P2 are vapor pressures at temperatures T1 and T2 (in Kelvin), deltaH_vap is the molar enthalpy of vaporization (J/mol), and R is the universal gas constant (8.314 J/mol-K). The equation relates how vapor pressure changes with temperature during a phase transition.

Last reviewed: December 2025

Worked Examples

Example 1: Vapor Pressure of Water at 120 C

Water boils at 100 C (373.15 K) at 101.325 kPa. What is its vapor pressure at 120 C (393.15 K)? deltaH_vap = 40,660 J/mol.
Solution:
ln(P2/101.325) = (40660/8.314) * (1/373.15 - 1/393.15) ln(P2/101.325) = 4890.34 * (0.002680 - 0.002544) ln(P2/101.325) = 4890.34 * 0.000136 = 0.6651 P2 = 101.325 * e^0.6651 = 101.325 * 1.9448 = 197.05 kPa
Result: Vapor pressure at 120 C: 197.05 kPa (almost double atmospheric pressure)

Example 2: Boiling Point at Reduced Pressure

At what temperature does water boil under a vacuum of 50 kPa? Normal BP = 373.15 K, deltaH = 40,660 J/mol.
Solution:
ln(50/101.325) = (40660/8.314) * (1/373.15 - 1/T2) -0.7065 = 4890.34 * (1/373.15 - 1/T2) 1/T2 = 1/373.15 + 0.7065/4890.34 = 0.002680 + 0.000144 = 0.002824 T2 = 354.14 K = 80.99 C
Result: Water boils at 81.0 C under 50 kPa vacuum
Expert Insights

Background & Theory

The Clausius Clapeyron Calculator applies the following established principles and formulas. Chemistry is the science of matter's composition, structure, properties, and transformations. At the heart of quantitative chemistry lies the mole concept. One mole of any substance contains exactly 6.022ร—10ยฒยณ entities (Avogadro's number, Nโ‚), and the molar mass of an element or compound in grams per mole is numerically equal to its atomic or molecular mass in atomic mass units. This allows chemists to convert between measurable mass and the number of reacting particles. Stoichiometry uses balanced chemical equations to relate the amounts of reactants and products. A balanced equation conserves both mass and charge. Molarity, the most common concentration unit, is defined as M = n/V, where n is moles of solute and V is volume of solution in liters, giving units of mol/L. Acidity and basicity are quantified by the pH scale, defined as pH = โˆ’logโ‚โ‚€[Hโบ], where [Hโบ] is the molar concentration of hydrogen ions. Pure water at 25ยฐC has pH 7.00; acids have lower values and bases higher values. Each unit change represents a tenfold change in hydrogen ion concentration. Gas behavior is described by the ideal gas law PV = nRT, where P is pressure in pascals, V is volume in cubic meters, n is moles, R = 8.314 J/(molยทK), and T is temperature in kelvin. Special cases include Boyle's Law (Pโ‚Vโ‚ = Pโ‚‚Vโ‚‚ at constant temperature) and Charles's Law (Vโ‚/Tโ‚ = Vโ‚‚/Tโ‚‚ at constant pressure). Thermochemistry quantifies heat changes in reactions through enthalpy, H. Hess's Law states that the total enthalpy change for a reaction is the sum of enthalpy changes for any sequence of steps leading to the same overall reaction, making it possible to calculate enthalpies for reactions that cannot be measured directly. Electron configuration describes the distribution of electrons in atomic orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule. Periodic trends including atomic radius, ionization energy, and electronegativity arise systematically from electron configuration and nuclear charge, enabling chemists to predict and rationalize chemical behavior across the periodic table.

History

The history behind the Clausius Clapeyron Calculator traces back through the following developments. Chemistry's roots lie in alchemy, the medieval practice combining proto-scientific experimentation with mystical aims. Alchemists developed practical techniques including distillation, calcination, and the preparation of acids, building a body of empirical knowledge despite their theoretical misunderstandings. Modern chemistry is conventionally dated to Antoine Lavoisier (1743โ€“1794), often called the father of modern chemistry. Lavoisier demonstrated the law of conservation of mass in 1789, showing that matter is neither created nor destroyed in chemical reactions. He identified oxygen's role in combustion, dismantling the phlogiston theory, and co-authored the first systematic chemical nomenclature, establishing the language still used today. John Dalton proposed the first modern atomic theory in 1803, asserting that all matter is composed of indivisible atoms, that atoms of the same element are identical in mass, and that compounds form from fixed ratios of different atoms. This provided a physical basis for Lavoisier's conservation law and Proust's law of definite proportions. Dmitri Mendeleev published his periodic table in 1869, arranging the 63 known elements by atomic mass and revealing repeating patterns of chemical behavior. He boldly left gaps for undiscovered elements and predicted their properties with remarkable accuracy, predictions confirmed by the subsequent discovery of gallium, scandium, and germanium. Ernest Rutherford's gold foil experiment in 1911 revealed the nuclear model of the atom: a tiny, dense, positively charged nucleus surrounded by electrons. Niels Bohr refined this in 1913 with a quantized model of electron orbits that explained the hydrogen emission spectrum. Quantum chemistry and molecular orbital theory, developed through the 1920s and 1930s, provided the full quantum mechanical description of chemical bonding. The latter 20th century saw the rise of computational chemistry, enabling molecular simulation at unprecedented scale. The green chemistry movement, articulated in the 12 Principles of Green Chemistry in 1998, reoriented the field toward sustainability, waste reduction, and benign chemical design, reflecting chemistry's growing awareness of its environmental responsibilities.

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Frequently Asked Questions

The Clausius-Clapeyron equation describes the relationship between vapor pressure and temperature for a substance undergoing a phase transition, such as liquid to gas. The equation states that ln(P2/P1) = (deltaH_vap/R) * (1/T1 - 1/T2), where P1 and P2 are vapor pressures at temperatures T1 and T2 (in Kelvin), deltaH_vap is the molar enthalpy of vaporization, and R is the universal gas constant. This equation is derived from thermodynamic principles and assumes that the enthalpy of vaporization remains constant over the temperature range considered. It is one of the most important equations in physical chemistry for understanding phase equilibria.
The Clausius-Clapeyron equation relies on several simplifying assumptions. First, it assumes the enthalpy of vaporization (deltaH) is constant and does not change with temperature, which is approximately true over small temperature ranges but breaks down over large ones. Second, it assumes the vapor behaves as an ideal gas, following PV = nRT. Third, it assumes the molar volume of the liquid is negligible compared to the molar volume of the gas. These assumptions make the equation most accurate near the normal boiling point and for moderate temperature ranges. For high-precision work or near the critical point, the more general Clapeyron equation (dP/dT = deltaH / T*deltaV) should be used instead.
Yes, the general Clapeyron equation applies to any first-order phase transition, including solid-liquid (melting), solid-gas (sublimation), and liquid-gas (vaporization). For the solid-liquid transition, the equation becomes dP/dT = deltaH_fus / (T * deltaV_fus), where deltaH_fus is the enthalpy of fusion and deltaV_fus is the volume change upon melting. However, the simplified logarithmic form (Clausius-Clapeyron) is specifically derived for transitions involving a gas phase where volume changes are large. For melting, where volume changes are small and relatively constant, the simplified linear form dT/dP = T*deltaV/deltaH is often more appropriate and useful.
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
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Educational Note: This calculator is provided for educational and informational purposes. Results are based on the formulas and inputs provided. Always verify important calculations independently. NovaCalculator processes calculator inputs client-side; optional analytics follow visitor consent settings. ยฉ 2024โ€“2026 NovaCalculator.

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Formula

ln(P2/P1) = (deltaH_vap / R) * (1/T1 - 1/T2)

Where P1 and P2 are vapor pressures at temperatures T1 and T2 (in Kelvin), deltaH_vap is the molar enthalpy of vaporization (J/mol), and R is the universal gas constant (8.314 J/mol-K). The equation relates how vapor pressure changes with temperature during a phase transition.

Worked Examples

Example 1: Vapor Pressure of Water at 120 C

Problem: Water boils at 100 C (373.15 K) at 101.325 kPa. What is its vapor pressure at 120 C (393.15 K)? deltaH_vap = 40,660 J/mol.

Solution: ln(P2/101.325) = (40660/8.314) * (1/373.15 - 1/393.15)\nln(P2/101.325) = 4890.34 * (0.002680 - 0.002544)\nln(P2/101.325) = 4890.34 * 0.000136 = 0.6651\nP2 = 101.325 * e^0.6651 = 101.325 * 1.9448 = 197.05 kPa

Result: Vapor pressure at 120 C: 197.05 kPa (almost double atmospheric pressure)

Example 2: Boiling Point at Reduced Pressure

Problem: At what temperature does water boil under a vacuum of 50 kPa? Normal BP = 373.15 K, deltaH = 40,660 J/mol.

Solution: ln(50/101.325) = (40660/8.314) * (1/373.15 - 1/T2)\n-0.7065 = 4890.34 * (1/373.15 - 1/T2)\n1/T2 = 1/373.15 + 0.7065/4890.34 = 0.002680 + 0.000144 = 0.002824\nT2 = 354.14 K = 80.99 C

Result: Water boils at 81.0 C under 50 kPa vacuum

Frequently Asked Questions

What is the Clausius-Clapeyron equation?

The Clausius-Clapeyron equation describes the relationship between vapor pressure and temperature for a substance undergoing a phase transition, such as liquid to gas. The equation states that ln(P2/P1) = (deltaH_vap/R) * (1/T1 - 1/T2), where P1 and P2 are vapor pressures at temperatures T1 and T2 (in Kelvin), deltaH_vap is the molar enthalpy of vaporization, and R is the universal gas constant. This equation is derived from thermodynamic principles and assumes that the enthalpy of vaporization remains constant over the temperature range considered. It is one of the most important equations in physical chemistry for understanding phase equilibria.

What are the assumptions of the Clausius-Clapeyron equation?

The Clausius-Clapeyron equation relies on several simplifying assumptions. First, it assumes the enthalpy of vaporization (deltaH) is constant and does not change with temperature, which is approximately true over small temperature ranges but breaks down over large ones. Second, it assumes the vapor behaves as an ideal gas, following PV = nRT. Third, it assumes the molar volume of the liquid is negligible compared to the molar volume of the gas. These assumptions make the equation most accurate near the normal boiling point and for moderate temperature ranges. For high-precision work or near the critical point, the more general Clapeyron equation (dP/dT = deltaH / T*deltaV) should be used instead.

Can the Clausius-Clapeyron equation be used for solid-liquid transitions?

Yes, the general Clapeyron equation applies to any first-order phase transition, including solid-liquid (melting), solid-gas (sublimation), and liquid-gas (vaporization). For the solid-liquid transition, the equation becomes dP/dT = deltaH_fus / (T * deltaV_fus), where deltaH_fus is the enthalpy of fusion and deltaV_fus is the volume change upon melting. However, the simplified logarithmic form (Clausius-Clapeyron) is specifically derived for transitions involving a gas phase where volume changes are large. For melting, where volume changes are small and relatively constant, the simplified linear form dT/dP = T*deltaV/deltaH is often more appropriate and useful.

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No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.

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How do I verify Clausius Clapeyron Calculator's result independently?

The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.

References

Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy