Free Vapor Pressure Calculator

Understanding Vapor Pressure Calculations

This vapor pressure calculator brings together two fundamental thermodynamic approaches—the Clausius‑Clapeyron equation and Raoult’s law—in a single online tool. It functions as an intuitive Clausius‑Clapeyron calculator and as a Raoult’s law vapor pressure solver, making it suitable for both pure substances and solutions. By entering known data, you can compute unknown pressures, temperatures, or molar enthalpies, and the tool automatically handles unit conversions between pascals, torr, atm, and more.

What Is Vapor Pressure?

Vapor pressure is the equilibrium pressure exerted by the vapor phase of a substance when it is in contact with its liquid (or solid) phase inside a closed system. At dynamic equilibrium, the rates of evaporation and condensation become equal. The magnitude of vapor pressure is influenced by temperature, molecular mass, and the strength of intermolecular forces. Materials with weak molecular attractions, low molecular weight, or high kinetic energy tend to exhibit higher vapor pressures and are therefore more volatile. As temperature rises, more molecules acquire enough energy to escape the liquid surface, causing the vapor pressure to increase.

The Clausius‑Clapeyron Equation

The Clausius‑Clapeyron equation is derived from the general Clapeyron relation, which describes the slope of a phase boundary on a pressure–temperature diagram. For vaporization (liquid → gas) or sublimation (solid → gas), the volume change between the condensed phase and the gas phase is large, allowing the equation to be simplified to a highly useful form:

$$\ln\left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{\text{vap}}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$

where:

• $P_1$ and $P_2$ are the vapor pressures at temperatures $T_1$ and $T_2$ (both temperatures must be in Kelvin),
• $\Delta H_{\text{vap}}$ is the molar enthalpy of vaporization (J/mol),
• $R = 8.3145\ \text{J/(mol·K)}$ is the universal gas constant.

When three of the four variables ($P_1$, $T_1$, $P_2$, $\Delta H$) are known, the fourth can be solved directly. Because the relationship is logarithmic, vapor pressure changes non‑linearly with temperature. This vapor pressure formula is the foundation for many practical applications, including predicting boiling points at different altitudes. The calculator can also serve as an enthalpy of vaporization calculator when you have two pressure‑temperature pairs.

Enthalpy of Vaporization

The enthalpy of vaporization (often called heat of vaporization) is the energy required to convert one mole of a liquid into a vapor at constant pressure and temperature. It reflects the strength of intermolecular forces within the liquid. For water, $\Delta H_{\text{vap}}$ is approximately 40,660 J/mol, which is relatively high and explains why water boils at a high temperature under standard pressure. A similar quantity for the direct solid‑gas transition is known as the enthalpy of sublimation.

Example: Using the Clausius‑Clapeyron Equation

Consider water with the following data:

• $\Delta H_{\text{vap}} = 40,660\ \text{J/mol}$
• At $T_1 = 280\ \text{K}$, the vapor pressure $P_1 = 102,325\ \text{Pa}$
• Find $P_2$ at $T_2 = 263\ \text{K}$.

Insert the values:

$$\ln\left(\frac{P_2}{102,325}\right) = \frac{40,660}{8.3145} \left(\frac{1}{280} - \frac{1}{263}\right)$$

First compute the right‑hand side:

$$\frac{40,660}{8.3145} \approx 4,887.9,\qquad \frac{1}{280} - \frac{1}{263} \approx -0.000231$$

Product: $4,887.9 \times (-0.000231) = -1.129$

Thus $\ln(P_2/102,325) = -1.129$. Exponentiating gives:

$$\frac{P_2}{102,325} = e^{-1.129} \approx 0.323,\qquad P_2 \approx 33,060\ \text{Pa}$$

This result shows that cooling from 280 K to 263 K reduces the vapor pressure by about two‑thirds. Rearranging the same equation allows you to determine the temperature at which a liquid boils under a given external pressure—a capability that effectively turns this tool into a boiling point pressure calculator.

Raoult’s Law for Solutions

While the Clausius‑Clapeyron equation applies to pure substances, Raoult’s law handles mixtures. It states that the vapor pressure of a solvent in an ideal solution is proportional to its mole fraction. For a solution containing one volatile solvent and one or more non‑volatile solutes, the total vapor pressure is:

$$P_{\text{solution}} = X_{\text{solvent}} \cdot P_{\text{solvent}}^{\circ}$$

• $X_{\text{solvent}}$ is the mole fraction of the solvent (moles of solvent divided by total moles),
• $P_{\text{solvent}}^{\circ}$ is the vapor pressure of the pure solvent at the same temperature.

Raoult’s law is most accurate when the intermolecular forces between different species are nearly identical to those in the pure components—so‑called ideal solutions. Real solutions deviate from ideality, but the law often provides a reliable first approximation. When multiple volatile components exist, Dalton’s law of partial pressures must be applied to sum their contributions.

Example with Raoult’s Law

Dissolve 100 g of glucose (C₆H₁₂O₆, molar mass 180.2 g/mol) in 500 g of water (18.0 g/mol). The vapor pressure of pure water at 37 °C is 47.1 torr.

1. Moles of water: $n_{\text{water}} = 500\ \text{g} \div 18.0\ \text{g/mol} = 27.70\ \text{mol}$
2. Moles of glucose: $n_{\text{glucose}} = 100\ \text{g} \div 180.2\ \text{g/mol} = 0.555\ \text{mol}$
3. Mole fraction of water: $X_{\text{water}} = \dfrac{27.70}{27.70 + 0.555} = 0.98$

Apply Raoult’s law:

$$P_{\text{solution}} = 0.98 \times 47.1\ \text{torr} = 46.16\ \text{torr}$$

The addition of a non‑volatile solute lowers the vapor pressure—a colligative effect that depends only on the number of solute particles.

About the Calculator

This Clausius‑Clapeyron calculator online not only solves the classic vapor pressure equation but also automates unit conversions for pressure and temperature, so you never have to worry about Kelvin‑Celsius conversions or inconsistent pressure units. It includes a dedicated mode for Raoult’s law, making it a comprehensive vapor pressure formula tool for both pure substances and solutions. Whether you are a student tackling thermodynamics problems or an engineer estimating process conditions, this vapor pressure calculator streamlines the calculations and reduces the risk of manual errors.