Free Raoult's Law Calculator

This tool serves as an online vapor pressure calculator that applies Raoult's law formula to evaluate the vapor pressure of an ideal solution. Beyond that, it also computes the mole fraction of the solvent or solute and the pure solvent vapor pressure, making it a versatile ideal solution calculator.

Defining Raoult's Law

Raoult's law describes the vapor‑pressure behavior of ideal solutions containing a non‑volatile solute. It states that the relative lowering of the solvent’s vapor pressure is equal to the mole fraction of the solute. Equivalently, the vapor pressure of the solution is directly proportional to the solvent’s mole fraction:

$$P_{\text{solution}} = x_{\text{solvent}} \cdot P^{\circ}_{\text{solvent}}$$

Where:

• $P_{\text{solution}}$ – vapor pressure of the solution
• $x_{\text{solvent}}$ – mole fraction of the solvent
• $P^{\circ}_{\text{solvent}}$ – vapor pressure of the pure solvent (also called partial pressure)

This relationship is the core of any mole fraction vapor pressure calculation.

How to Use the Vapor Pressure Calculator

The calculator offers two input pathways:

1. Using Moles

• Enter the partial pressure of the pure solvent (with its preferred unit).
• Provide the number of moles of the solute.
• Provide the number of moles of the solvent. The tool then computes the solution vapor pressure and displays a graph of vapor pressure versus solvent mole fraction.

2. Using Mole Fraction

• Input the pure solvent vapor pressure.
• Input the mole fraction of the solvent. The result is the solution vapor pressure, along with the same graphical plot.

Worked Example

Suppose the pure solvent has a vapor pressure of 16 mmHg and its mole fraction in the solution is 0.4. Applying Raoult's law:

$$P_{\text{solution}} = 0.4 \times 16\ \text{mmHg} = 6.4\ \text{mmHg}$$

The calculator can also reverse the calculation when one of the other values is unknown.

Deriving Other Quantities

The Raoult's law formula can be rearranged to solve for the missing variable:

• Mole fraction of the solvent:

  $$x_{\text{solvent}} = \frac{P_{\text{solution}}}{P^{\circ}_{\text{solvent}}}$$

  Divide the solution vapor pressure by the pure solvent vapor pressure.

• Pure solvent vapor pressure:

  $$P^{\circ}_{\text{solvent}} = \frac{P_{\text{solution}}}{x_{\text{solvent}}}$$

  Divide the solution vapor pressure by the mole fraction of the solvent.

These variations make the tool a comprehensive solution vapor pressure calculator.

Vapor Pressure vs. Mole Fraction Graph

The calculator automatically generates a plot of the solution vapor pressure against the mole fraction of the solvent. Under constant temperature, this graph is a straight line, verifying that the vapor pressure is proportional to the mole fraction as predicted by Raoult's law. The mole fraction appears on the x‑axis and vapor pressure on the y‑axis.

Key Applications

• Determining molecular mass: By measuring the vapor pressure lowering, one can estimate the molar mass of an unknown non‑volatile solute.
• Non‑ideal solutions: With corrections for intermolecular forces, Raoult's law can serve as a starting point for real‑solution behavior.
• Component contribution: In mixtures where the proportion of each component is known, the law helps calculate each component's contribution to the total vapor pressure.

This calculator integrates all these capabilities into a single, easy‑to‑use interface.