Vapor Pressure Calculator - Clausius-Clapeyron Solver
Use this vapor pressure calculator to solve the Clausius-Clapeyron equation or Raoult's law. Enter temperature, enthalpy, or mole fraction to get results.
Vapor Pressure Calculator
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What Is a Vapor Pressure Calculator?
A vapor pressure calculator solves the two most common vapor pressure equations used in chemistry and thermodynamics: the Clausius-Clapeyron equation and Raoult's law. Enter your known temperature, pressure, and enthalpy values, and the calculator returns the vapor pressure at a new temperature or the vapor pressure of a solution from its mole fraction.
Students and engineers use this vapor pressure calculator for tasks like predicting how the vapor pressure of water changes with temperature, estimating the boiling point of a solvent at reduced pressure, or determining how a dissolved solute lowers the vapor pressure of a solution. The Clausius-Clapeyron mode handles pure-substance calculations, while Raoult's law mode handles ideal-solution calculations. You can use either mode depending on whether you are working with a single substance or a mixture.
Vapor pressure itself is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phase at a given temperature in a closed system. When the rate of molecules escaping the liquid surface equals the rate returning, the system is at equilibrium and the vapor has a definite pressure. Every liquid has a characteristic vapor pressure at each temperature, and this value determines whether the liquid will evaporate, boil, or remain stable under a given set of conditions. For more on how mixtures of gases contribute individual pressures, the partial pressure calculator covers partial pressures in gas mixtures.
How the Vapor Pressure Equations Work
ln(P₁/P₂) = (ΔH_vap / R) × (1/T₂ − 1/T₁)
P_solution = P_solvent × X_solvent
The Clausius-Clapeyron equation relates the natural logarithm of the pressure ratio to the enthalpy of vaporization divided by the gas constant, multiplied by the difference in reciprocal absolute temperatures. Raoult's law states that the vapor pressure of an ideal solution equals the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution. When working with Raoult's law, the mole fraction calculator helps you determine the solvent mole fraction from component masses or moles.
Variables: P₁ and P₂ are vapor pressures at temperatures T₁ and T₂ (in Kelvin). ΔH_vap is the molar enthalpy of vaporization in J/mol. R is the universal gas constant (8.3145 J/(mol·K)). P_solution is the vapor pressure of the solution, P_solvent is the vapor pressure of the pure solvent, and X_solvent is the mole fraction of the solvent.
According to the NIST Chemistry WebBook, the enthalpy of vaporization of water at its normal boiling point is 40,660 J/mol, the value used in Clausius-Clapeyron calculations. The NIST Chemistry WebBook provides thermodynamic data for hundreds of substances.
According to NIST, the universal gas constant R equals 8.314462618 J/(mol·K), the value used in the Clausius-Clapeyron equation.
Worked Example: Water at 25 °C
Given: Water at its normal boiling point has P₁ = 101,325 Pa at T₁ = 373.15 K. The enthalpy of vaporization of water is ΔH_vap = 40,660 J/mol.
Find: The vapor pressure at T₂ = 298.15 K (25 °C).
Step 1: Calculate the exponent: (40,660 / 8.3145) × (1/298.15 − 1/373.15) = 4,890.25 × 0.000674 = 3.297.
Step 2: P₂ = P₁ / e^3.297 = 101,325 / 27.03 = 3,749.69 Pa.
Result: The vapor pressure of water at 25 °C is approximately 3,749.69 Pa (3.75 kPa). The actual measured value is about 3,169 Pa; the Clausius-Clapeyron equation assumes constant ΔH_vap, which introduces a small approximation error over this temperature range.
Key Concepts Behind Vapor Pressure
Vapor-Liquid Equilibrium
At equilibrium in a closed container, molecules leave the liquid surface and return at equal rates. The pressure the vapor exerts at this balance point is the vapor pressure. Temperature shifts this balance: higher temperatures push more molecules into the vapor phase.
Enthalpy of Vaporization
The enthalpy of vaporization (ΔH_vap) is the energy needed to convert one mole of liquid to vapor at constant pressure. Substances with strong intermolecular forces, like water with hydrogen bonding, have high ΔH_vap values and lower vapor pressures at a given temperature.
Mole Fraction and Raoult's Law
Mole fraction is the ratio of moles of one component to total moles in a mixture. Raoult's law uses the solvent's mole fraction to predict how a dissolved solute lowers the vapor pressure of the solution compared to the pure solvent. The grams to moles calculator converts between grams and moles so you can compute mole fractions from mass data.
Clausius-Clapeyron Approximation
The integrated Clausius-Clapeyron equation assumes the enthalpy of vaporization stays constant over the temperature range and that the vapor behaves as an ideal gas. These assumptions work well over small temperature intervals but drift over wider ranges. For broader accuracy, use substance-specific Antoine equation constants.
How to Use This Vapor Pressure Calculator
- 1 Select the calculation mode. Choose Clausius-Clapeyron for pure-substance temperature-pressure problems or Raoult's law for solution vapor pressure.
- 2 Set your temperature and pressure units. The calculator converts internally, so pick the units your data uses.
- 3 Enter the known values. For Clausius-Clapeyron, provide initial temperature, initial pressure, final temperature, and enthalpy of vaporization. For Raoult's law, enter the pure solvent vapor pressure and the solvent mole fraction.
- 4 Read the result. The calculator displays the computed vapor pressure in your selected pressure unit.
- 5 Check the worked example above for a step-by-step walkthrough of the Clausius-Clapeyron calculation.
To find the vapor pressure of ethanol at 50 °C: set Clausius-Clapeyron mode, enter T₁ = 351.45 K (ethanol boiling point), P₁ = 101,325 Pa, T₂ = 323.15 K (50 °C), and ΔH_vap = 38,560 J/mol. The calculator returns the vapor pressure at 50 °C. This type of calculation is common when planning rotary evaporation in organic chemistry labs or when estimating solvent losses during storage.
The Clausius-Clapeyron derivation assumes ideal gas behavior for the vapor phase; the ideal gas calculator lets you check how closely a real vapor approximates ideal conditions.
Benefits of Using This Calculator
- • Solves both the Clausius-Clapeyron equation and Raoult's law in one tool, so you do not need separate calculators for pure substances and solutions.
- • Handles temperature and pressure unit conversions internally, which removes the most common source of manual calculation errors in thermodynamics problems.
- • Provides immediate results for homework and lab planning, letting you test how changing one variable affects vapor pressure without re-deriving the equation each time.
- • Works for any substance as long as you know the enthalpy of vaporization, making it useful for organic chemistry, physical chemistry, and chemical engineering problems.
- • Includes a worked example and formula breakdown so you can verify the calculator's output against your own hand calculations.
- • Supports five pressure units (Pa, kPa, atm, mmHg, torr) and three temperature units (K, °C, °F), which covers the unit systems you encounter in textbooks and lab manuals.
Factors That Affect Vapor Pressure Results
Temperature Range
The Clausius-Clapeyron equation assumes constant enthalpy of vaporization. Over small temperature intervals this is reasonable, but over large ranges the actual ΔH_vap changes. Keep your T₁ and T₂ within about 50 K for best accuracy.
Substance Properties
Different substances have different enthalpies of vaporization. Water (40,660 J/mol), ethanol (38,560 J/mol), and diethyl ether (26,520 J/mol) will give very different vapor pressures at the same temperature change.
Solution Composition
Raoult's law applies to ideal solutions where solute-solvent interactions match solvent-solvent interactions. Real solutions deviate from ideality, especially at high solute concentrations or with strongly interacting molecules.
Pressure Unit Consistency
The Clausius-Clapeyron equation uses a pressure ratio, so the absolute unit does not matter as long as P₁ and P₂ use the same unit. The calculator handles this internally but be aware when comparing with literature values. Published vapor pressure tables often report in mmHg or torr, while SI work uses pascals or kilopascals.
Limitations
- • The Clausius-Clapeyron equation treats the vapor as an ideal gas and assumes constant ΔH_vap. For high-precision work over wide temperature ranges, use the Antoine equation with substance-specific constants instead.
- • Raoult's law is accurate only for ideal or dilute solutions. Concentrated solutions, electrolytes, and mixtures with strong intermolecular interactions deviate from Raoult's law and require activity coefficients.
According to the IUPAC Gold Book, vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phase at a given temperature in a closed system. The IUPAC Gold Book provides the standard definitions used across chemistry.
Since boiling occurs when vapor pressure equals external pressure, the boiling point calculator shows how pressure changes shift boiling temperatures for common solvents.
Frequently Asked Questions
Q: What is vapor pressure?
A: Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its liquid or solid phase at a given temperature in a closed system. It increases with temperature because more molecules have enough kinetic energy to escape the liquid surface.
Q: How does the Clausius-Clapeyron equation relate vapor pressure to temperature?
A: The Clausius-Clapeyron equation, ln(P1/P2) = (ΔH_vap/R)(1/T2 − 1/T1), shows that the natural log of the pressure ratio depends on the enthalpy of vaporization and the difference in reciprocal temperatures. Higher temperatures produce higher vapor pressures.
Q: What is Raoult's law and when do you use it?
A: Raoult's law states that the vapor pressure of an ideal solution equals the vapor pressure of the pure solvent multiplied by the solvent's mole fraction. Use it when you need to predict how a dissolved non-volatile solute lowers the vapor pressure of a solvent.
Q: How does vapor pressure affect boiling point?
A: A liquid boils when its vapor pressure equals the external atmospheric pressure. At higher altitudes where atmospheric pressure is lower, the liquid reaches that equilibrium at a lower temperature, which is why water boils below 100 °C on mountains.
Q: What is the enthalpy of vaporization?
A: The enthalpy of vaporization is the energy required to convert one mole of a liquid into vapor at constant pressure. For water it is 40,660 J/mol at the normal boiling point. This value appears directly in the Clausius-Clapeyron equation.
Q: Why does vapor pressure increase with temperature?
A: At higher temperatures, more molecules in the liquid have enough kinetic energy to overcome intermolecular forces and enter the vapor phase. This shifts the equilibrium toward more vapor, raising the vapor pressure above the liquid surface.