Gibbs Free Energy Calculator – Reaction Spontaneity
Calculate the change in Gibbs free energy from enthalpy, temperature, and entropy to determine if a reaction is spontaneous.
AI Quick Summary
Definition & Purpose:
This calculator computes the change in Gibbs free energy for a reaction from its enthalpy change, temperature, and entropy change, and determines whether the reaction is spontaneous.
When to Use:
Use it to determine whether a reaction will proceed spontaneously under given conditions, or to see how temperature affects a reaction's spontaneity.
Key Takeaway Insights:
- A negative Delta G means the reaction is spontaneous (thermodynamically favorable) under the given conditions, while a positive Delta G means it's non-spontaneous and requires an external energy input to proceed.
- Temperature plays a direct role in spontaneity through the T x Delta S term — some reactions that are non-spontaneous at low temperature become spontaneous at higher temperature, and vice versa, depending on the signs of Delta H and Delta S.
- Spontaneous doesn't mean fast — Delta G describes whether a reaction is thermodynamically favorable, not how quickly it proceeds, which is instead governed by kinetics and activation energy.
Introduction
Gibbs Free Energy Calculator
Enter a reaction's enthalpy change, temperature, and entropy change, and this calculator computes the Gibbs free energy change and whether the reaction is spontaneous.
Formula
ΔG = ΔH − T × ΔS, with ΔS converted from J/(mol·K) to kJ/(mol·K) by dividing by 1000 to match ΔH's units.
For ΔH = -50 kJ/mol, T = 298 K, and ΔS = 100 J/(mol·K): ΔG = -50 − 298 × 0.1 = -50 − 29.8 = -79.8 kJ/mol — spontaneous.
Reading the sign of ΔG
A negative ΔG means the reaction is spontaneous, or thermodynamically favorable, under the given conditions. A positive ΔG means the opposite — the reaction won't proceed forward on its own and needs an external energy input. The magnitude of ΔG reflects how strongly favorable or unfavorable the reaction is, not how quickly it happens.
Spontaneous doesn't mean fast
This is a common point of confusion: spontaneity is purely a thermodynamic statement about whether a reaction is energetically favorable, completely separate from how fast it actually proceeds. The classic example is diamond converting to graphite — thermodynamically spontaneous, but so slow under normal conditions that it's effectively unnoticeable. Reaction speed is governed by kinetics and activation energy, not by ΔG.
How temperature can flip spontaneity
Because temperature directly scales the T × ΔS term, some reactions shift between spontaneous and non-spontaneous depending on temperature. A reaction with both positive ΔH and positive ΔS, for example, can be non-spontaneous at low temperatures but become spontaneous at higher ones, once the growing T × ΔS term outweighs the unfavorable ΔH — a pattern worth checking whenever a reaction's spontaneity seems temperature-sensitive.
Formula & Variables Explained
This tool utilizes standard equations formulated under standard rules.
Variables:
- Input parameter: Values supplied to resolve the output formula.
How to Calculate (Step-by-Step)
- Input the required parameters into the form.
- Click the calculate or auto-compute option.
- The outputs will refresh instantly with step-by-step variables.
Worked Examples Calculation
1dH = -50 kJ/mol, T = 298K, dS = 100 J/(mol*K)
Enthalpy change (ΔH) = -50 kJ/mol, Temperature = 298 K, Entropy change (ΔS) = 100 J/(mol·K)
Delta G = -50 - 298 x (100/1000) = -50 - 298 x 0.1 = -50 - 29.8 = -79.8 kJ/mol
ΔG = -79.8 kJ/mol (Spontaneous)
Real-World Applications
Widely used in student curriculum, professional projections, and quick estimations.
Limitations & Common Mistakes
- Entering incompatible unit formats (e.g. Mixing Metric and Imperial).
- Typographical mistakes in numeric entry fields.
A negative Delta G indicates a reaction is thermodynamically favorable, but it says nothing about reaction rate — a spontaneous reaction can still proceed extremely slowly without a catalyst or sufficient activation energy.
Frequently Asked Questions (FAQ)
Q:What does a negative Delta G mean?
A negative Delta G indicates the reaction is spontaneous, or thermodynamically favorable, under the given conditions — it will tend to proceed in the forward direction as written without requiring continuous energy input. A positive Delta G means the reverse: the reaction is non-spontaneous as written and would require energy input to proceed forward.
Q:Does spontaneous mean the reaction happens instantly?
No — this is a common misunderstanding. 'Spontaneous' in thermodynamics only describes whether a reaction is energetically favorable, not how fast it happens. A classic example is the conversion of diamond to graphite, which is thermodynamically spontaneous (favorable) but proceeds so slowly under normal conditions that it's effectively unnoticeable on any practical timescale. Reaction speed is governed separately by kinetics and activation energy.
Q:How does temperature affect whether a reaction is spontaneous?
Temperature directly scales the T x Delta S term in the equation, so its effect on spontaneity depends on the signs of Delta H and Delta S. A reaction with positive Delta H and positive Delta S (energy-absorbing but increasing disorder) can be non-spontaneous at low temperature but become spontaneous at high temperature, since the growing T x Delta S term eventually outweighs the unfavorable Delta H. The reverse pattern can happen for negative Delta H and negative Delta S reactions.
Q:Why is entropy divided by 1000 in this calculation?
Enthalpy is conventionally expressed in kJ/mol while entropy is conventionally expressed in J/(mol·K) — a thousand-fold unit difference. Dividing the entropy value by 1000 converts it to kJ/(mol·K), matching the units of enthalpy so the two terms can be combined correctly in the Delta G equation.
References & Citations
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