Van Hoff Plot Inputs
Use the responsive calculator grid below. It becomes three columns on large screens, two on smaller screens, and one on mobile.
Example Data Table
This example shows a typical increasing K trend with temperature for an endothermic equilibrium.
| Temperature (K) | Equilibrium Constant K | 1/T (K⁻¹) | ln(K) |
|---|---|---|---|
| 280 | 0.420 | 0.003571 | -0.8675 |
| 290 | 0.610 | 0.003448 | -0.4943 |
| 300 | 0.860 | 0.003333 | -0.1508 |
| 310 | 1.210 | 0.003226 | 0.1906 |
| 320 | 1.680 | 0.003125 | 0.5188 |
| 330 | 2.290 | 0.003030 | 0.8286 |
Formula Used
Van Hoff equation:
ln(K) = −ΔH / (R × T) + ΔS / R
Linear form: y = mx + b
y = ln(K), x = 1/T, slope m = −ΔH/R, intercept b = ΔS/R
Thermodynamic recovery:
ΔH = −mR
ΔS = bR
ΔG = −RT ln(K)
This tool assumes ΔH and ΔS remain approximately constant across the chosen temperature range.
How to Use This Calculator
- Enter a reaction label if you want clearer exported reports.
- Provide at least two temperature values in kelvin.
- Enter the corresponding dimensionless equilibrium constants for each temperature.
- Leave blank rows empty. They are ignored automatically.
- Set a target temperature to predict K and ΔG.
- Submit the form to generate regression outputs and the plot.
- Review R², residuals, and thermodynamic signs before drawing conclusions.
- Use CSV or PDF export for reporting or recordkeeping.
Frequently Asked Questions
1. What does a van Hoff plot show?
It shows how the natural logarithm of an equilibrium constant changes with inverse temperature. A near straight line suggests the reaction follows the constant enthalpy and entropy approximation over the selected temperature range.
2. Why does the plot use ln(K) versus 1/T?
That arrangement turns the thermodynamic relationship into a linear equation. The slope reveals enthalpy behavior, while the intercept reveals entropy behavior. It also makes regression analysis simple and interpretable.
3. Must equilibrium constants be dimensionless?
Yes. The thermodynamic form is most accurate when K is dimensionless. If you use concentration or pressure ratios directly, make sure they are defined consistently with the chosen equilibrium expression.
4. What does a positive ΔH mean here?
A positive ΔH indicates an endothermic equilibrium under the fitted model. In many cases, K increases with temperature for such systems, producing the expected negative slope in ln(K) versus 1/T coordinates.
5. How should I interpret R²?
R² measures how closely the data follow the fitted line. Values nearer to one suggest a stronger linear relation. Lower values can indicate noisy measurements, narrow temperature range, or changing thermodynamic parameters.
6. Can I predict K outside my temperature range?
You can, but extrapolation is less reliable. The constant ΔH and ΔS assumption may fail outside the measured range, especially across phase changes, broad temperature spans, or nonideal experimental conditions.
7. Why are residuals useful?
Residuals show the difference between observed and fitted ln(K) values. Large or patterned residuals may signal outliers, measurement issues, or model limitations that should be checked before using the fitted thermodynamic parameters.
8. What causes this model to become inaccurate?
Accuracy drops when enthalpy varies strongly with temperature, when K values are inconsistent, or when experiments span conditions where activity effects, side reactions, or phase changes become important.