Gibbs, Helmholtz & Isotherm Solver

Thermodynamic Potentials

Gibbs Free Energy ($G$): The maximum reversible work performable by a system at constant temperature and pressure. Helmholtz Energy ($A$): The maximum reversible work performable at constant temperature and volume.

$\Delta G = \Delta H - T\Delta S$ | $\Delta A = \Delta U - T\Delta S$

Calculate $\Delta G$

Enthalpy Change ($\Delta H$) in kJ/mol Temperature ($T$) in Kelvin Entropy Change ($\Delta S$) in J/mol·K

Calculate $\Delta A$

Internal Energy ($\Delta U$) in kJ/mol Temperature ($T$) in Kelvin Entropy Change ($\Delta S$) in J/mol·K

$\Delta G^0$ to $K_{eq}$ Converter

Standard Gibbs Energy ($\Delta G^0$) in kJ/mol Temperature ($T$) in Kelvin

Vapor Pressure Solver

Enthalpy of Vaporization ($\Delta H_{vap}$) kJ/mol

$T_1$ (K)

$P_1$ (atm)

Target Temperature $T_2$ (K)

Reaction Shift Predictor

Equilibrium Constant ($K$) Reaction Quotient ($Q$)

Reaction Isotherm ($\Delta G$)

$\Delta G^0$ (Standard) in kJ/mol Temperature ($T$) in Kelvin Reaction Quotient ($Q$)

Guide: Entering Values

Our calculators use a smartParser to handle scientific notation.

Exponent: 10^5 means 10⁵

Multiply: 10*1 means 10 multiplied by 1.

Scientific: 1.8e-5 means 1.8 × 10^-5

Practical Examples:

Positive: Enter 10^2 for 100.
Negative: Enter -5 for acidic values.
Complex: Enter 10^-7 for neutral pH.

Reaction Spontaneity Matrix

$\Delta H$	$\Delta S$	Spontaneity ($ \Delta G $)
Negative (-)	Positive (+)	Spontaneous at all $T$
Positive (+)	Negative (-)	Non-spontaneous at all $T$
Negative (-)	Negative (-)	Spontaneous at Low $T$
Positive (+)	Positive (+)	Spontaneous at High $T$

The Gibbs-Helmholtz Equation

This equation is critical for calculating how the Gibbs free energy of a system changes with temperature.

$\left( \frac{\partial (G/T)}{\partial T} \right)_P = -\frac{H}{T^2}$

Derivation & Logic

Starting from $G = H - TS$, we know $dG = VdP - SdT$. At constant pressure, $dG = -SdT$, meaning $(\partial G/\partial T)_P = -S$. Substituting this back into the original equation gives the functional relationship between $G$, $H$, and $T$.

Solved Example

Problem: A reaction has $\Delta H = -100$ kJ and $\Delta S = -200$ J/K at 300 K. Is it spontaneous?
Solution:
$\Delta G = -100 - (300 \times -0.200) = -100 + 60 = -40$ kJ.
Since $\Delta G < 0$, the reaction is spontaneous.

Application in Scientific Research

Drug Design: Predicting binding affinity between ligands and proteins.
Metallurgy: Using Ellingham diagrams to find the stability of oxides.
Phase Transitions: Determining the boiling and melting points of new materials.

16 Frequently Asked Questions

1. What does a negative $\Delta G$ mean?
It indicates a spontaneous process (exergonic) that can occur without external energy.

2. What is the difference between $G$ and $A$?
$G$ is for constant Pressure/Temp (lab conditions); $A$ is for constant Volume/Temp (closed containers).

3. Can $\Delta G$ be zero?
Yes, at equilibrium, the change in Gibbs free energy is exactly zero.

4. How does $T$ affect spontaneity?
If $\Delta H$ and $\Delta S$ have the same sign, temperature determines if $\Delta G$ is negative.

5. What is the unit of $S$ in calculations?
Entropy is usually J/K, but must be converted to kJ/K ($/1000$) for $\Delta G$ formulas.

6. What is the Gibbs-Helmholtz equation used for?
To calculate enthalpy changes from temperature-dependent EMF or equilibrium data.

7. Is Helmholtz energy used in explosives?
Yes, because explosions often happen at nearly constant volume.

8. What is the "Free" in Free Energy?
It represents the energy available to do work, as opposed to energy lost as heat.

9. How is $G$ related to $K$ (Equilibrium)?
$\Delta G^0 = -RT \ln K$.

10. Does $\Delta G$ indicate reaction rate?
No, it only indicates if a reaction *can* happen, not how fast it will go.

11. What is an endergonic reaction?
A reaction where $\Delta G$ is positive, requiring energy input.

12. Can I calculate $G$ at any temperature?
Yes, assuming $\Delta H$ and $\Delta S$ are relatively constant over that range.

13. What is the standard state for Gibbs Energy?
Usually 298.15 K and 1 bar pressure.

14. Is Helmholtz energy a state function?
Yes, it depends only on the current state of the system, not the path taken.

15. Why is $A$ called the work function?
From the German word "Arbeit" (Work), as it represents total work capacity.

16. Can entropy ever be zero?
Only for a perfect crystal at 0 K, according to the Third Law.