Gibbs Free Energy

students, imagine you are choosing whether a reaction will happen on its own. A burnable fuel may release lots of heat, but a dissolving salt may happen even without heating. So what decides whether a chemical change is energetically “allowed” in real life? The key idea is Gibbs free energy. 🔥❄️

In this lesson, you will learn how Gibbs free energy connects enthalpy, entropy, and spontaneity. By the end, you should be able to:

explain what Gibbs free energy means and why it matters,
use the equation $\Delta G = \Delta H - T\Delta S$ correctly,
decide whether a reaction is spontaneous at a given temperature,
connect Gibbs free energy to the bigger IB Chemistry HL theme of what drives reactivity,
use reaction examples to show how energy changes influence chemical behavior.

What Gibbs Free Energy Means

Gibbs free energy is a way to predict whether a reaction can happen spontaneously at constant temperature and pressure. In chemistry, spontaneous does not mean “fast.” It means the process is thermodynamically favorable and can proceed without continuous outside energy input once it starts.

The Gibbs free energy change is written as $\Delta G$. It combines two important factors:

enthalpy change $\Delta H$, which tells us whether heat is released or absorbed,
entropy change $\Delta S$, which tells us whether disorder or energy dispersal increases or decreases.

Temperature is written as $T$ and must be in kelvin when used in calculations. The central relationship is:

$$\Delta G = \Delta H - T\Delta S$$

This equation is powerful because it shows that a reaction is not controlled by heat alone. A reaction may be favorable because it releases heat, because it increases entropy, or because both happen together.

A useful interpretation is:

if $\Delta G < 0$, the reaction is spontaneous in the forward direction,
if $\Delta G = 0$, the system is at equilibrium,
if $\Delta G > 0$, the forward reaction is not spontaneous.

This helps explain why some reactions happen easily, some need energy input, and some only occur under special conditions.

Linking Gibbs Free Energy to Enthalpy and Entropy

To understand Gibbs free energy, students, it helps to revisit the two parts inside the formula.

Enthalpy $$\Delta H$$

Enthalpy is closely related to heat change at constant pressure. A reaction with $\Delta H < 0$ is exothermic, meaning it releases heat to the surroundings. A reaction with $\Delta H > 0$ is endothermic, meaning it absorbs heat.

Exothermic reactions often seem more likely to happen, but that is not always true. For example, some reactions absorb heat and still happen spontaneously because the entropy term is large enough to compensate.

Entropy $$\Delta S$$

Entropy is often described as disorder, but a more accurate IB-friendly idea is energy dispersal or the number of possible ways particles and energy can be arranged. A positive $\Delta S$ means the system becomes more spread out or more random in an energy sense.

Examples of positive entropy change include:

a solid melting into a liquid,
a liquid evaporating into a gas,
one molecule breaking into several smaller particles,
mixing substances so they become more dispersed.

Because gases have much higher entropy than liquids and solids, reactions that produce gases often have favorable entropy changes.

Temperature $T$ matters

The term $T\Delta S$ shows why temperature changes the outcome. If $\Delta S$ is positive, increasing $T$ makes the entropy term more important, which can make $\Delta G$ more negative. If $\Delta S$ is negative, higher temperature can make $\Delta G$ less favorable.

This means some reactions are spontaneous only at certain temperatures. That is a major reason Gibbs free energy is such a useful concept in chemistry.

Predicting Spontaneity with $$\Delta G = \Delta H - T\Delta S$$

IB Chemistry HL often asks you to reason through the sign of $\Delta G$ instead of only memorizing the formula. There are four common sign combinations:

1. $\Delta H < 0$ and $$\Delta S > 0$$

This is the most favorable case. Since both terms help make $\Delta G$ negative, the reaction is spontaneous at all temperatures.

Example idea: a process that releases heat and produces more dispersed particles.

2. $\Delta H < 0$ and $$\Delta S < 0$$

Here, heat release favors spontaneity, but entropy opposes it. The reaction may be spontaneous at low temperatures, when the $T\Delta S$ term is smaller.

Example idea: some crystallization or condensation processes.

3. $\Delta H > 0$ and $$\Delta S > 0$$

In this case, heat input is unfavorable, but entropy favors the reaction. The reaction may be spontaneous at high temperatures, because the $T\Delta S$ term becomes large enough to overcome the positive enthalpy.

Example idea: thermal decomposition reactions that produce gases.

4. $\Delta H > 0$ and $$\Delta S < 0$$

This is the least favorable combination. Both terms make $\Delta G$ positive, so the reaction is non-spontaneous at all temperatures.

These sign patterns are very useful in exams because they let you judge behavior quickly without doing a full calculation.

Worked Example: Using the Equation

Suppose a reaction has $\Delta H = -85\,\text{kJ mol}^{-1}$ and $\Delta S = -120\,\text{J K}^{-1}\text{ mol}^{-1}$ at $298\,\text{K}$.

First, make the units match. Convert entropy to kilojoules:

$$-120\,\text{J K}^{-1}\text{ mol}^{-1} = -0.120\,\text{kJ K}^{-1}\text{ mol}^{-1}$$

Now calculate:

$$\Delta G = \Delta H - T\Delta S$$

$$\Delta G = -85 - (298)(-0.120)$$

$$\Delta G = -85 + 35.76$$

$$\Delta G = -49.24\,\text{kJ mol}^{-1}$$

Because $\Delta G < 0$, the reaction is spontaneous at $298\,\text{K}$.

This example shows an important idea: even when entropy is negative, a strongly exothermic reaction can still be spontaneous because the enthalpy term dominates.

Gibbs Free Energy, Equilibrium, and Reactivity

Gibbs free energy is closely linked to equilibrium. At equilibrium, the forward and reverse reactions occur at the same rate, and the overall composition stays constant. Thermodynamically, this corresponds to $\Delta G = 0$ for the system.

That means a reaction with a negative $\Delta G$ is not “finished” in a simple sense. It is simply driven in the forward direction until equilibrium is reached. This is why reaction feasibility and reaction rate are different ideas.

A reaction may have $\Delta G < 0$ but still happen very slowly if the activation energy is high. For example, diamond can convert to graphite because graphite is thermodynamically more stable, but the change happens extremely slowly because the activation energy barrier is very large.

This is a key IB point: thermodynamics tells you whether a reaction is favorable; kinetics tells you how fast it happens.

Gibbs Free Energy in Fuel Chemistry and Real Life

Fuel chemistry is a strong real-world application of Gibbs free energy. Fuels such as methane, ethanol, and gasoline release energy when they burn. Their combustion reactions usually have negative $\Delta H$ and often produce gases and heat, which can also support a favorable entropy change in some cases.

For a fuel to be useful, a combustion reaction should have a negative $\Delta G$ under normal conditions. That means it can release usable energy. This is why fuels are linked to reactivity and energy changes in the IB syllabus.

Examples in everyday life:

a car engine using gasoline combustion,
a camping stove using propane,
cellular respiration in biology, which releases energy from glucose oxidation.

In all of these, the reaction’s Gibbs free energy determines whether the process can deliver energy in a useful way.

Conclusion

Gibbs free energy brings together the two big ideas behind chemical reactivity: heat changes and disorder changes. students, the equation $\Delta G = \Delta H - T\Delta S$ helps you judge whether a reaction is spontaneous, whether temperature matters, and how equilibrium fits into the picture.

In IB Chemistry HL, this topic matters because it explains why some reactions happen readily, why others need heating, and why favorable reactions may still be slow. Gibbs free energy is not just a formula to memorize; it is a framework for understanding what drives chemical change. 🌟

Study Notes

Gibbs free energy change is written as $\Delta G$.
The key equation is $\Delta G = \Delta H - T\Delta S$.
Use temperature in kelvin when calculating $T\Delta S$.
If $\Delta G < 0$, the reaction is spontaneous.
If $\Delta G = 0$, the system is at equilibrium.
If $\Delta G > 0$, the forward reaction is not spontaneous.
$\Delta H < 0$ means exothermic; $\Delta H > 0$ means endothermic.
$\Delta S > 0$ means entropy increases; $\Delta S < 0$ means entropy decreases.
High temperature makes the entropy term $T\Delta S$ more important.
A reaction can be spontaneous and still be slow if the activation energy is high.
Gibbs free energy links thermodynamics, entropy, enthalpy, equilibrium, and fuel chemistry in Reactivity 1.