Clausius-Clapeyron Equation

Clausius-Clapeyron Equation - Calculator & Plotter

Introduction and Theory

The Clausius-Clapeyron equation is a fundamental relation in thermodynamics that describes the phase transition between two phases of a substance, specifically vaporization and condensation. It relates the pressure and temperature of a system undergoing a phase change, allowing us to understand how vapor pressure changes with temperature for a given substance.

The Clausius-Clapeyron equation is typically expressed in its logarithmic form:

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

Where:

$P_1$ and $P_{2}$ are the vapor pressures in Pa, atm or mmHg at two different temperatures $T_{1}$ and $T_{2}$ given in Celsius , Fahrenheit or Kelvin,
$Δ H_{vap}$ is the enthalpy (heat) of vaporization (J/mol),
$R$ is the universal gas constant ( $R = 8.314 J/(mol* K)$ ).

This equation enables the calculation of vapor pressure at a temperature $T_2$ , given a known vapor pressure at temperature $T_1$ and the enthalpy of vaporization for the compound. The equation is particularly useful for predicting the behavior of substances undergoing phase transitions, such as from liquid to vapor, and is foundational in understanding boiling points, sublimation, and condensation in a wide range of scientific applications.

Theoretical Significance

The Clausius-Clapeyron equation is essential in physical chemistry and engineering applications, especially for systems involving heat engines, refrigeration cycles, meteorology, and chemical reactions. It allows the prediction of how substances behave under various pressure and temperature conditions.

The equation assumes that the enthalpy of vaporization remains constant over the temperature range and that the vapor behaves ideally (follows the ideal gas law). Although these assumptions may introduce small errors at high pressures or very low temperatures, the equation is widely used due to its simplicity and reasonable accuracy.

Clausius-Clapeyron Equation - Calculator and Plotter Description

The Clausius-Clapeyron calculator and plotter offers a practical way to explore the relationship between temperature and vapor pressure. With an intuitive user interface, the tool enables the user to calculate vapor pressures and visualize these relationships for different compounds, making it a valuable resource in thermodynamics and physical chemistry. The ability to export data for further analysis ensures that this tool can be integrated into more complex workflows. The Plotter is a powerful feature of the calculator that graphically displays the relationship between vapor pressure $P_2$ (on the y-axis) and temperature $T_2$ (on the x-axis).
The Clausius-Clapeyron Calculator is an intuitive tool designed to perform calculations and generate plots based on the Clausius-Clapeyron equation. The calculator includes several key components and options for user interaction:

Main Components of the Calculator

Text Fields: The calculator has six text fields:
- P1: The reference vapor pressure at temperature $T_{1}$ (greyed out).
- T1: The reference temperature (greyed out).
- P2: The vapor pressure at the user-specified temperature $T_{2}$ .
- T2: The temperature at which the vapor pressure is calculated.
- $\Delta H_{\text{vap}}$ : The enthalpy of vaporization (greyed out).
- R: The universal gas constant (greyed out).
Editable Fields: Only P2 and T2 are user-editable, meaning the user can input these values for calculations.
Drop-down Lists:
- Behind the P2 field, a drop-down list allows the selection of pressure units: Pa, atm, or mmHg.
- Behind the T2 field, the user can select the temperature units: Kelvin (K), Celsius (°C), or Fahrenheit (°F).
- The Compound drop-down list is located next to the copy to clipboard button.

Constants and Variables

R: The universal gas constant, $R = 8.314 \, \text{J/mol·K}$ , is fixed and used in the equation.
$Δ H_{vap}$ : The enthalpy of vaporization, typically a known constant for each compound (in J/mol).
P1: The known vapor pressure at the boiling point temperature T1 (1atm).
T1: The boiling point temperature at 1atm.

Fig. CHEMIX School Gas Equations: Boiling-point of Water at 1atm (100°C) and boiling-point at 0.08atm (40°C)

Fig. Propane, Water and Glycerol Boiling point curves pasted into CHEMIX School - Binary Plot

Boiling point curves for Propane, Water and Glycerol

Features of the Plotter:

Compound Selection:
- Users can select a specific compound from a drop-down list. The selected compound determines the value of $Δ H_{vap}$ , $P_{1}$ , and $T_{1}$ , based on known thermodynamic properties.
Graphical Representation:
- The graph plots vapor pressure on the y-axis against temperature on the x-axis.
- As a reference, the intersection point of the curve at 25°C and 1 atm is highlighted by a circle, with straight lines extending from the circle to the x-axis and y-axis for easy visualization of the reference point.
Pressure Range:
- The user can manually set the maximum pressure for the plot via a text box, allowing the graph to scale according to the desired pressure range.
- By default, the maximum pressure is set to 2 atm or 202650 Pa so that the boiling points for selected compounds are conveniently located near the midpoint of the y-axis.
Data Set:
- The calculated numeric values (data points) for a plot is stored in a multi-line text field on the right side of the calculator.
- These data points represent the temperature-pressure relationship for the selected compound and can be copied by clicking the "Copy to Clipboard" button.
Advanced Plotting:
- Once copied, the data can be pasted using a more advanced plotting tool in CHEMIX School e.g Binary Plot for further analysis, custom visualizations, or additional processing and storing.

Using the Clausius-Clapeyron Calculator & Plotter

Select a Compound and Plot the Graph:
- Choose the compound from the drop-down list. This will automatically generate the graph of vapor pressure vs. temperature.

Input Parameter - Set Maximum Pressure:
- Set the temperature $T_2$ and pressure $P_2$ in the corresponding text fields.
- Select the appropriate units for both $T_{2}$ (Kelvin, °C, or °F) and $P_2$ (Pa, atm, or mmHg) from the drop-down lists.
- Enter the desired maximum pressure for the plot, or leave it at the default 2 atm to ensure that boiling points appear midway on the plot.
Copy Data:
- Simultaneously as the plot is generated, the data points will appear in the text field on the right.
- To use these data points in external applications, click the "Copy to Clipboard" button.
Advanced Plotting:
- Paste the copied data into an CHEMIX School advanced plotting tool such as CHEMIX School - Binary Plot to create more detailed or custom visualizations.

Clausius-Clapeyron Boiling Point Experiment.html

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