Chemistry · General chemistry II · Concept
Gibbs free energy, entropy and spontaneity
A process is spontaneous when it can proceed without continuous outside help. At constant temperature and pressure, the Gibbs free energy change ΔG = ΔH − TΔS decides: a negative ΔG means spontaneous as written. ΔG° also fixes the equilibrium constant through ΔG° = −RT ln K, and for a nonstandard mixture ΔG = ΔG° + RT ln Q.
Spontaneous does not mean fast
A spontaneous process can keep going on its own once started, but thermodynamics says nothing about its rate. Diamond turning into graphite is spontaneous and immeasurably slow; hydrogen and oxygen need a spark before they react.
Entropy
Entropy measures how many ways a system’s energy can be spread out. It rises from solid to liquid to gas, when a solid dissolves, and when a reaction makes more moles of gas. The second law says the entropy of the universe increases in every spontaneous process. A reaction’s ΔS° comes from standard molar entropies the way ΔH° comes from enthalpies of formation, except that elements have nonzero entropies.
Gibbs free energy
At constant temperature and pressure, ΔG, read “delta G”, combines the energy and entropy changes of the system. ΔG < 0: spontaneous as written; ΔG > 0: the reverse is spontaneous; ΔG = 0: at equilibrium.
The four sign cases
Because the entropy term −TΔS grows with temperature, the signs of ΔH and ΔS decide how temperature matters.
| ΔH | ΔS | Spontaneous |
|---|---|---|
| − | + | At every temperature |
| + | − | At no temperature |
| − | − | Below T = ΔH/ΔS |
| + | + | Above T = ΔH/ΔS |
Free energy and equilibrium
ΔG° refers to standard states. It sets the equilibrium constant: a negative ΔG° gives K > 1 and a positive one K < 1. For a mixture with reaction quotient Q, ΔG = ΔG° + RT ln Q, which is zero exactly when Q = K.
Common mistakes
- Mixing kJ and J: ΔH is usually in kJ and ΔS in J/K, so convert one before combining them.
- Using a Celsius temperature in ΔG = ΔH − TΔS.
- Reading a negative ΔG as a fast reaction: ΔG says whether, not how fast.
- Using ΔG° for a mixture that is not in its standard states: use ΔG = ΔG° + RT ln Q.
- Leaving out elements when summing entropies: unlike enthalpies of formation, their standard entropies are not zero.
Key terms
- Gibbs energy
- G = H − TS. At constant temperature and pressure, a reaction with ΔG < 0 is spontaneous in the forward direction, and ΔG > 0 means the reverse is favored.
- Entropy
- S, a measure of how spread out a system’s energy and particles are, often described as disorder. It usually increases from solid to liquid to gas.
- Thermodynamic spontaneity
- A spontaneous process happens on its own once started, without continued outside energy. Spontaneous doesn’t mean fast: diamond turning into graphite is spontaneous but extremely slow.
- Second law of thermodynamics
- In any spontaneous process, the total entropy of the universe increases: ΔS(universe) = ΔS(system) + ΔS(surroundings) > 0. The system’s own entropy can fall if the surroundings gain more.
- Standard state
- The reference conditions behind tabulated thermodynamic values: a pure gas at 1 atm (1 bar in newer tables), a solute at 1 M, and a pure liquid or solid in its most stable form. Temperature isn’t fixed by it, though tables usually use 25 °C.
- Standard free energy of formation
- The Gibbs energy change for making one mole of a compound from its elements, with everything in standard states. Elements in their standard states have ΔG°f = 0.
Work through an example
Use the data in the table to find ΔH°, ΔS° and ΔG° at 298.15 K for 2H₂(g) + O₂(g) → 2H₂O(l).
Find ΔG° from enthalpies and entropies →Sources and scope
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