Advanced Topic 416 of 1102 Thermodynamics & Energetics
Gibbs-Helmholtz Equation
Relates the temperature dependence of free energy to enthalpy.
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In-depth explanation of Gibbs-Helmholtz Equation
The Gibbs-Helmholtz equation describes how the Gibbs energy divided by temperature varies with temperature at constant pressure, in the form d(G/T) by dT equals minus H divided by T squared. It shows that the temperature dependence of free energy is determined by the enthalpy, which provides a useful link between the two quantities. Applying the equation between two temperatures allows the Gibbs energy change to be estimated at a new temperature when the enthalpy change is known. It is also the starting point for deriving the van't Hoff equation for equilibrium constants. The equation is essential for analyzing how spontaneity shifts with temperature.
Going deeper: Gibbs-Helmholtz Equation
Key ideas: Use it to find how delta G changes with T when delta H is known: the derivative of delta G over T with respect to T equals minus delta H over T squared. Over a short interval, assuming constant delta H, integrate to estimate delta G at a new temperature.
Common mistakes and connections: Be careful: the derivative applies to G over T, not G itself. Using wrong signs is common. Its integrated form gives the van't Hoff equation, and it demonstrates that temperature dependence of free energy is governed by enthalpy.
Visualization of Gibbs-Helmholtz Equation
With delta H = -100 kJ/mol, delta G over T changes with temperature at a rate set by minus delta H over T squared, falling in size as T rises. The interactive lesson shows this as a live animation or chart.
Worked example and use case
If the standard enthalpy of a reaction is known, the Gibbs energy at a new temperature can be estimated from this relation without needing a full table of values.
Frequently asked questions about Gibbs-Helmholtz Equation
What is Gibbs-Helmholtz Equation?
Relates the temperature dependence of free energy to enthalpy.
Is Gibbs-Helmholtz Equation a beginner, intermediate or advanced topic?
Gibbs-Helmholtz Equation is a advanced topic in Thermodynamics & Energetics. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Gibbs-Helmholtz Equation?
Study these earlier topics in Thermodynamics & Energetics first: Heat of Fusion of Ice, Heat of Vaporization of Water, Thermodynamics of Dissolution.
What comes after Gibbs-Helmholtz Equation?
The next topics in Thermodynamics & Energetics are Van't Hoff Equation and Maxwell Relations.
Can I practise Gibbs-Helmholtz Equation with quizzes?
Yes. The interactive lesson includes a self-check question on Gibbs-Helmholtz Equation, and the Thermodynamics & Energetics quiz draws on every topic in this area.
Where Gibbs-Helmholtz Equation fits in Thermodynamics & Energetics
Gibbs-Helmholtz Equation is topic 88 of 91 in Thermodynamics & Energetics.