Vapor Pressure Calculator
Calculate vapor pressure using Raoult's Law (solution vapor pressure) or the Clausius-Clapeyron equation (temperature dependence). Determine vapor pressure lowering for solutions and predict boiling points at different pressures. See also our Gibbs Free Energy Calculator and Equilibrium Constant Calculator for related thermodynamics computations.
How to Calculate Vapor Pressure
Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phase (liquid or solid) at a given temperature. It is a fundamental physical property that determines evaporation rates, boiling points, and the behavior of solutions. Two key equations govern vapor pressure calculations: Raoult's Law for solutions and the Clausius-Clapeyron equation for temperature dependence.
Raoult's Law states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the pure solvent's vapor pressure. This law applies to ideal solutions where solute-solvent interactions are similar to solvent-solvent interactions. When a non-volatile solute is dissolved in a solvent, it reduces the vapor pressure because fewer solvent molecules are at the surface and available to escape into the gas phase. This vapor pressure lowering is a colligative property — it depends only on the number of solute particles, not their identity.
- For Raoult's Law: Identify the pure solvent vapor pressure P° and the mole fraction of solvent χ.
- Calculate solution vapor pressure: P = χ × P°.
- Vapor pressure lowering: ΔP = P° − P = P° × χ_solute.
- For Clausius-Clapeyron: Know ΔH_vap, a reference point (T₁, P₁), and target temperature T₂.
- Apply: ln(P₂/P₁) = (ΔH_vap/R)(1/T₁ − 1/T₂).
- Solve for P₂ = P₁ × exp[(ΔH_vap/R)(1/T₁ − 1/T₂)].
The Clausius-Clapeyron equation describes how vapor pressure changes with temperature. It is derived from the Clausius-Clapeyron relation (dP/dT = ΔH_vap/(TΔV)) with the assumptions that the vapor behaves ideally and that the molar volume of the liquid is negligible compared to the vapor. This equation is remarkably accurate over moderate temperature ranges and is widely used to predict boiling points at different pressures, estimate enthalpies of vaporization, and understand atmospheric phenomena.
Vapor Pressure Formulas
Raoult's Law: P = χ_solvent × P°
Vapor pressure lowering: ΔP = χ_solute × P°
Clausius-Clapeyron: ln(P₂/P₁) = (ΔH_vap/R)(1/T₁ − 1/T₂)
Solving for P₂: P₂ = P₁ × e^[(ΔH_vap/R)(1/T₁ − 1/T₂)]
Where:
P = solution vapor pressure
P° = pure solvent vapor pressure
χ = mole fraction
ΔH_vap = enthalpy of vaporization (J/mol)
R = 8.314 J/(mol·K)
T = absolute temperature (K)
For non-ideal solutions, Raoult's Law is modified using activity coefficients: P = γ × χ × P°. Positive deviations (γ > 1) occur when solute-solvent interactions are weaker than solvent-solvent interactions (e.g., ethanol-hexane), resulting in higher vapor pressure than predicted. Negative deviations (γ < 1) occur when solute-solvent interactions are stronger (e.g., acetone-chloroform), resulting in lower vapor pressure. These deviations are important in distillation design and can lead to azeotrope formation.
Example Calculation
Example 1 — Raoult's Law:
Pure water vapor pressure at 25°C: P° = 23.8 mmHg. A solution has solvent mole fraction χ = 0.98.
Solution:
P = χ × P° = 0.98 × 23.8 = 23.324 mmHg
ΔP = P° − P = 23.8 − 23.324 = 0.476 mmHg
Or: ΔP = χ_solute × P° = 0.02 × 23.8 = 0.476 mmHg ✓
Example 2 — Clausius-Clapeyron:
Water: ΔH_vap = 40.7 kJ/mol, boils at 373 K (760 mmHg). Find vapor pressure at 350 K.
Solution:
ln(P₂/760) = (40700/8.314)(1/373 − 1/350)
ln(P₂/760) = 4894.4 × (0.002681 − 0.002857)
ln(P₂/760) = 4894.4 × (−0.000176)
ln(P₂/760) = −0.8614
P₂/760 = e^(−0.8614) = 0.4225
P₂ = 321.1 mmHg
Answer: Water vapor pressure at 350 K (77°C) ≈ 321 mmHg (below atmospheric, so water does not boil at this temperature).
Vapor Pressure Reference Table
| Substance | VP at 25°C (mmHg) | ΔH_vap (kJ/mol) | Boiling Point (°C) |
|---|---|---|---|
| Water | 23.8 | 40.7 | 100.0 |
| Ethanol | 59.0 | 38.6 | 78.4 |
| Methanol | 127.0 | 35.2 | 64.7 |
| Acetone | 231.0 | 31.3 | 56.1 |
| Diethyl ether | 534.0 | 26.5 | 34.6 |
| Chloroform | 197.0 | 31.4 | 61.2 |
| Benzene | 95.2 | 30.7 | 80.1 |
| Toluene | 28.4 | 33.2 | 110.6 |
| Hexane | 151.0 | 28.9 | 69.0 |
| Acetic acid | 15.7 | 23.7 | 118.1 |
| Mercury | 0.0017 | 59.1 | 356.7 |
| Glycerol | 0.0001 | 91.7 | 290.0 |
Frequently Asked Questions
What is vapor pressure and why does it matter?
Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid (or solid) phase at a given temperature. It matters because it determines evaporation rates, boiling points, and the stability of liquids. High vapor pressure substances (like acetone or ether) evaporate quickly and are considered volatile. Low vapor pressure substances (like glycerol or mercury) evaporate slowly. Vapor pressure affects everything from perfume formulation to industrial distillation to atmospheric science and weather prediction.
When does Raoult's Law fail?
Raoult's Law assumes ideal solution behavior — that solute-solvent interactions equal solvent-solvent interactions. It fails for: (1) concentrated solutions where solute-solute interactions become significant, (2) solutions with strong specific interactions (hydrogen bonding, ion-dipole), (3) electrolyte solutions where dissociation increases the effective number of particles, and (4) solutions of very different molecules (polar + nonpolar). For electrolytes, the van't Hoff factor i corrects for dissociation: ΔP = i × χ_solute × P°.
How does altitude affect boiling point?
At higher altitudes, atmospheric pressure is lower, so liquids boil at lower temperatures. Water boils at 100°C at sea level (760 mmHg) but at about 95°C in Denver (630 mmHg) and 71°C on Mount Everest (253 mmHg). The Clausius-Clapeyron equation can calculate the exact boiling point at any pressure. This affects cooking (food takes longer at altitude because water boils at lower temperature), industrial processes, and even the design of pressure cookers (which raise the boiling point by increasing pressure).
What is the relationship between vapor pressure and boiling point?
A liquid boils when its vapor pressure equals the external (atmospheric) pressure. At sea level (760 mmHg), water boils at 100°C because that is the temperature where water's vapor pressure reaches 760 mmHg. Substances with high vapor pressures at room temperature have low boiling points (they are volatile), while substances with low vapor pressures have high boiling points. The Clausius-Clapeyron equation quantifies this relationship, allowing prediction of boiling points at any pressure.
How do colligative properties relate to vapor pressure?
All colligative properties (boiling point elevation, freezing point depression, osmotic pressure) stem from vapor pressure lowering. When a non-volatile solute lowers the vapor pressure, the liquid must be heated to a higher temperature to boil (boiling point elevation: ΔTb = Kb × m × i) and cooled to a lower temperature to freeze (freezing point depression: ΔTf = Kf × m × i). These effects depend only on the number of solute particles (molality × van't Hoff factor), not their chemical identity — hence "colligative" (depending on collection/number).
What is an azeotrope?
An azeotrope is a mixture that boils at a constant temperature and produces vapor with the same composition as the liquid — it cannot be separated by simple distillation. Azeotropes form when solutions show large deviations from Raoult's Law. Positive azeotropes (minimum boiling, like ethanol-water at 95.6% ethanol, 78.1°C) have vapor pressures higher than predicted. Negative azeotropes (maximum boiling, like HCl-water at 20.2% HCl, 108.6°C) have vapor pressures lower than predicted. Special techniques (pressure-swing distillation, extractive distillation, molecular sieves) are needed to break azeotropes.
Understanding Vapor Pressure in Science and Industry
Vapor pressure is one of the most important physical properties in chemistry and chemical engineering. It governs phase transitions, determines the volatility of chemicals, and plays a central role in distillation, evaporation, and atmospheric processes. Understanding vapor pressure is essential for anyone working with volatile chemicals, designing separation processes, or studying weather and climate phenomena.
In chemical engineering, vapor-liquid equilibrium (VLE) data based on vapor pressure relationships are the foundation of distillation column design. The relative volatility of components (α = P°A/P°B) determines how easily they can be separated. When α is close to 1, many theoretical stages are needed, making separation expensive. Modified Raoult's Law with activity coefficients (γ) is used for non-ideal mixtures, and equations of state (Peng-Robinson, Soave-Redlich-Kwong) provide more accurate predictions for high-pressure systems.
Environmental science uses vapor pressure to predict the fate of pollutants. Volatile organic compounds (VOCs) with high vapor pressures readily evaporate into the atmosphere, contributing to smog formation and ozone depletion. Henry's Law (a special case relating vapor pressure to solubility) predicts how chemicals partition between water and air. The vapor pressure of pesticides determines whether they will remain on crops or volatilize into the atmosphere. Environmental risk assessments routinely use vapor pressure data to model chemical transport and exposure pathways.
Pharmaceutical science considers vapor pressure in drug formulation and stability. Volatile excipients must be handled carefully during manufacturing. Lyophilization (freeze-drying) exploits the vapor pressure of ice to remove water from sensitive biological products under vacuum. The sublimation pressure of ice at various temperatures determines the optimal shelf temperature and chamber pressure for freeze-drying cycles. Understanding vapor pressure is also critical for designing metered-dose inhalers, where propellant vapor pressure drives drug delivery to the lungs.
Atmospheric science relies heavily on vapor pressure concepts. The saturation vapor pressure of water determines relative humidity, cloud formation, and precipitation. The Clausius-Clapeyron equation predicts that for every 1°C increase in temperature, the atmosphere can hold approximately 7% more water vapor — a relationship with profound implications for climate change. As global temperatures rise, increased atmospheric moisture leads to more intense precipitation events, even as some regions experience increased drought due to enhanced evaporation.
In food science, vapor pressure affects drying, cooking, and preservation. Water activity (aw), defined as the ratio of food vapor pressure to pure water vapor pressure, determines microbial growth potential and chemical stability. Foods with aw below 0.6 are generally safe from microbial spoilage. Understanding how temperature, solute concentration, and matrix effects influence water activity helps food scientists design stable products with appropriate shelf life. Vacuum drying and spray drying exploit reduced pressure to lower the boiling point of water, enabling gentle removal of moisture from heat-sensitive foods.