Graphs of Gibbs free energy

Master Thermodynamics! Will a chemical reaction happen on its own? Gibbs Free Energy (ΔG) is the ultimate thermodynamic master key. It combines enthalpy and entropy into a single equation to predict whether a reaction is spontaneous or non-spontaneous.

Gibbs Free Energy and Spontaneity of a Reaction

Whether a chemical reaction is product-favored (spontaneous) or reactant-favored (non-spontaneous) under standard-state conditions is perfectly reflected in the sign of its Standard Gibbs Free Energy change (Δ_rG°).

Josiah Willard Gibbs introduced this concept to measure the maximum amount of "useful work" a closed thermodynamic system can perform at a constant temperature and pressure. It is defined by the fundamental equation:

The Gibbs Equation

Δ_rG° = Δ_rH° - TΔ_rS°

Where:
Δ_rH° = Change in Standard Enthalpy
Δ_rS° = Change in Standard Entropy
T = Absolute Temperature (in Kelvin)

Thermodynamics Physical Chemistry Class 11 Chemistry

Predicting Spontaneity: The 4 Cases

The equation clearly shows that the sign of Δ_rG° depends entirely on the mathematical signs of Δ_rH° and Δ_rS°, and the absolute temperature (T), which can only be positive. For a reaction to be spontaneous, ΔG must be negative.

Let's analyze the four possible combinations:

Case 1: Both ΔH and ΔS are Positive (+)

This represents an endothermic process (ΔH > 0) that results in an increase in system disorder (ΔS > 0). Examples include melting ice or boiling water.

• ΔG becomes negative only if the temperature term (TΔS) is larger than ΔH.
• Result: The process is Spontaneous (product-favored) only at HIGH temperatures, and non-spontaneous at low temperatures.

Case 2: Both ΔH and ΔS are Negative (-)

This represents an exothermic process (ΔH < 0) that results in a decrease in system disorder (ΔS < 0). Examples include freezing water or condensation.

• ΔG becomes negative only if the magnitude of ΔH is greater than the magnitude of TΔS.
• Result: The process is Spontaneous (product-favored) only at LOW temperatures, and non-spontaneous at high temperatures.

Case 3: ΔH is Positive (+) and ΔS is Negative (-)

This is the worst-case scenario for a reaction. It requires heat (endothermic) and creates more order (decreases entropy). In the equation, subtracting a negative number makes it positive, so ΔG will always be a positive number plus a positive number.

• Result: ΔG is strictly positive regardless of temperature. The process is Non-spontaneous (reactant-favored) at ALL temperatures.

Case 4: ΔH is Negative (-) and ΔS is Positive (+)

This is the ideal scenario for a reaction. It releases heat (exothermic) and increases system disorder. In the equation, you are taking a negative number and subtracting a positive number, ensuring ΔG is heavily negative.

• Result: ΔG is strictly negative regardless of temperature. The process is Spontaneous (product-favored) at ALL temperatures.

Figure 1: Summary table predicting reaction spontaneity based on ΔH and ΔS signs.

Graphical Analysis 1: Gibbs Free Energy vs. Temperature

In JEE and NEET, you will often encounter straight-line graphs plotting ΔG on the y-axis against Absolute Temperature (T) on the x-axis. Using the line equation y = mx + c, the Gibbs equation becomes ΔG = (-ΔS)T + ΔH.

• The slope of the line is equal to -ΔS.
• The y-intercept is equal to ΔH.
• The temperature at which the line crosses the x-axis (ΔG = 0) is the equilibrium temperature ($T_{eq} = \Delta H / \Delta S$).

Figure 2: Plot of ΔG vs T for the four cases of reaction spontaneity.

Graphical Analysis 2: Gibbs Free Energy vs. Extent of Reaction

As a chemical reaction progresses from pure reactants to pure products, the total free energy of the system changes. The system will naturally evolve towards the state with the lowest possible free energy.

Figure 3: Free energy curves showing the difference between exergonic (spontaneous) and endergonic (non-spontaneous) reactions.

In any reversible reaction, the free energy curve dips down and reaches a minimum point before rising again. This absolute minimum point represents Chemical Equilibrium.

• At the minimum point, the slope of the curve is zero ($dG/dx = 0$).
• Therefore, ΔG = 0 at equilibrium. The system can no longer perform any useful work.

Figure 4: The system naturally falls into the free energy "valley" known as Chemical Equilibrium (ΔG = 0).

Frequently Asked Questions (FAQs)

What does a negative Gibbs Free Energy (ΔG) indicate?

A negative ΔG indicates that a reaction is spontaneous (or product-favored) under standard conditions. It means the system releases free energy as it progresses, which theoretically can be harnessed to do useful work.

How does temperature affect reaction spontaneity?

Temperature only dictates spontaneity when Enthalpy (ΔH) and Entropy (ΔS) have the same mathematical sign. If both are positive, the reaction is spontaneous only at high temperatures. If both are negative, the reaction is spontaneous only at low temperatures.

Why does Gibbs Free Energy reach a minimum at equilibrium?

At equilibrium, the thermodynamic system has reached its most stable state, meaning its capacity to do useful, non-expansion work is completely exhausted. Therefore, the free energy of the system is at an absolute minimum, and any further change in either direction would require an input of energy (making ΔG = 0).

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