Chemical Thermodynamics: Enthalpy, Entropy and Gibbs Energy

Chemical thermodynamics studies energy changes in chemical reactions — how much heat is released or absorbed, how disorder changes, and whether a reaction will happen on its own. Three quantities run the show: enthalpy (H), entropy (S) and Gibbs free energy (G). Together they predict the direction of every chemical change.

It matters because energy bookkeeping decides what is possible: how much power a battery can deliver, why some reactions need constant heating, why ice melts above 0°C. Thermodynamics sets the destination; how fast you get there is kinetics, a separate question.

Key Concepts

• System and surroundings: the system is the reaction under study; everything else is the surroundings. Energy crossing between them is what we track.
• First law: energy is conserved — it changes form but the total never changes.
• Enthalpy (H): heat absorbed or released at constant pressure. Negative ΔH = exothermic; positive ΔH = endothermic. Unit: kJ/mol.
• Entropy (S): disorder, precisely the number of ways energy can spread out. Unit: J/(mol·K).
• Second law: the entropy of the universe (system + surroundings) always increases in a spontaneous process.
• Gibbs free energy (G): the combined spontaneity criterion at constant T and pressure. Negative ΔG = spontaneous; positive ΔG = needs driving.

Formulas

• ΔG = ΔH − T·ΔS, with T in kelvin. Convert ΔS to kJ/(mol·K) before combining with ΔH in kJ/mol.
• ΔG° = −R·T·ln K, linking standard free energy to the equilibrium constant K (R = 8.314 J/(mol·K)). Large negative ΔG° means products dominate.
• Assumes constant temperature and pressure. The sign of ΔG predicts direction, never speed.

Worked Example

A reaction has ΔH = −120 kJ/mol and ΔS = −200 J/(mol·K). Is it spontaneous at T = 300 K?

1. Convert entropy: ΔS = −0.2 kJ/(mol·K).
2. ΔG = −120 − (300 × −0.2) = −120 + 60 = −60 kJ/mol.
3. ΔG is negative, so the reaction is spontaneous — the heat release outweighs the entropy decrease.

Note the temperature dependence: at high enough T, the −T·ΔS term grows and eventually flips ΔG positive — which is why some reactions reverse when heated.

Common Misconceptions

• "Exothermic reactions are always spontaneous." Not if the entropy decrease is large — at high temperatures the T·ΔS term can dominate and stop the reaction.
• "Entropy always increases." Only the universe's entropy must increase; a system's own entropy can fall (freezing water) if the surroundings gain more.
• "Negative ΔG means a fast reaction." Spontaneity says nothing about rate — a very negative ΔG reaction can take centuries without a catalyst.

Real-World Applications

• Batteries and fuel cells: cell voltage comes directly from ΔG of the redox reaction.
• Haber process: ammonia synthesis is tuned with temperature and pressure using ΔG trade-offs.
• Refrigeration: heat pumps cycle refrigerant through compression and expansion under the same laws.

Enthalpy tracks heat, entropy tracks disorder, and Gibbs free energy combines them: ΔG = ΔH − T·ΔS, negative means go. Thermodynamics promises the destination; kinetics decides how long the journey takes.