Gibbs Free Energy Calculator helps you compute ΔG using ΔG = ΔH − TΔS. If ΔG < 0, the process is spontaneous at the given temperature; if ΔG > 0, it is non-spontaneous.
What Gibbs Free Energy Means
Gibbs free energy (G) is a thermodynamic measure of how much useful work a system can do under constant temperature and pressure. In chemistry, you usually care about the change in Gibbs free energy, written as ΔG.
The sign of ΔG tells you the direction a reaction or process will naturally go:
- ΔG < 0: spontaneous (goes forward)
- ΔG = 0: equilibrium (no net driving force)
- ΔG > 0: non-spontaneous (needs input work)
The Core Formula Behind the Gibbs Free Energy Calculator
The calculator computes the Gibbs free energy change using the standard relationship:
ΔG = ΔH − TΔS
Where:
- ΔH is the enthalpy change (heat absorbed or released) at the temperature of interest
- T is absolute temperature in Kelvin (K)
- ΔS is the entropy change (how dispersed energy becomes)
Units must be consistent. If you enter ΔH and ΔG in kJ/mol, then ΔS must be in kJ/(mol·K) so that TΔS also lands in kJ/mol.
How Temperature and Unit Conversions Affect Results
Temperature in the formula is always absolute. That means:
- T(K) = T(°C) + 273.15
Entropy is the most common source of unit mistakes. Many textbooks report ΔS in J/(mol·K), while other problems use kJ/(mol·K). The calculator performs the conversion so your ΔG is computed correctly.
Typical conversions used:
| Quantity | Conversion |
|---|---|
| kJ ↔ J | 1 kJ = 1000 J |
| Entropy units | kJ/(mol·K) = J/(mol·K) ÷ 1000 |
Using the Gibbs Free Energy Calculator (Step-by-Step)
- Enter temperature and choose whether it is in °C or K.
- Enter ΔH (enthalpy change) and pick its units (kJ/mol or J/mol).
- Enter ΔS (entropy change) and pick its units (kJ/(mol·K) or J/(mol·K)).
- Click Calculate to compute ΔG and the spontaneity conclusion.
The calculator returns ΔG in your selected output unit (default: kJ/mol) and states whether the process is spontaneous at that temperature.
What the Sign of ΔG Tells You
Even without deep thermodynamics, you can interpret the result quickly:
- If ΔH is negative (exothermic) and ΔS is positive (more disorder), then ΔG is often negative at many temperatures.
- If ΔH is positive and ΔS is negative, then ΔG is often positive and the reaction is unlikely to proceed spontaneously.
- If ΔH and ΔS have opposite signs, temperature can flip the sign of ΔG.
Practical Examples: Real-World Use Cases
Example 1: Predicting spontaneity for a reaction
Suppose a reaction has ΔH = −120 kJ/mol and ΔS = +0.350 kJ/(mol·K). At T = 298 K:
ΔG = ΔH − TΔS = −120 − (298)(0.350) = −120 − 104.3 = −224.3 kJ/mol
Because ΔG < 0, the reaction is spontaneous at 298 K.
Example 2: Temperature decides the direction
Consider a process with ΔH = +40 kJ/mol and ΔS = +0.150 kJ/(mol·K). At T = 250 K:
ΔG = 40 − (250)(0.150) = 40 − 37.5 = +2.5 kJ/mol
Here ΔG > 0, so it is non-spontaneous at 250 K. At higher temperature, the TΔS term grows, and ΔG can become negative.
Frequently Asked Questions
What does a negative Gibbs free energy value mean?
A negative Gibbs free energy change (ΔG < 0) means the process can occur spontaneously under constant temperature and pressure. The system lowers its free energy by moving forward, so no external energy input is required for the reaction to proceed in that direction at that temperature.
How do I know what units to use for ΔH and ΔS?
Use units that make TΔS match the units of ΔH. If ΔH is in kJ/mol, then ΔS should be in kJ/(mol·K). If your ΔS is in J/(mol·K), convert to kJ/(mol·K) before applying the formula.
Is Gibbs free energy only for chemical reactions?
Gibbs free energy applies broadly to any process where temperature and pressure are controlled, including phase changes, mixing, and electrochemical reactions. In practice, you often compute ΔG for reactions, but the same thermodynamic idea holds for other spontaneous or equilibrium behavior.
Why must temperature be in Kelvin?
The equation ΔG = ΔH − TΔS uses absolute temperature. Using °C directly would be wrong because it shifts the temperature scale by 273.15. Convert to Kelvin first so the entropy term multiplies by the correct absolute temperature.
What is the relationship between ΔG and equilibrium?
At equilibrium, the system has no net driving force, so ΔG = 0. That does not mean nothing is happening; rather, forward and reverse rates balance. If you change temperature or conditions, ΔG changes and the system shifts away from equilibrium.
Common Mistakes to Avoid
- Mixing units: entering ΔH in kJ/mol but ΔS in J/(mol·K) without converting.
- Using °C instead of Kelvin: the formula needs absolute temperature.
- Forgetting sign conventions: ΔH and ΔS can be negative or positive depending on the process.
- Assuming spontaneity is constant: ΔG depends on temperature, so spontaneity can change.
Bottom Line
The Gibbs Free Energy Calculator gives you a fast, reliable way to compute ΔG from ΔH, ΔS, and T. Use the sign of ΔG to decide spontaneity at the temperature you care about, and rely on consistent units for accurate results.