Entropy and spontaneity
Why do some reactions happen on their own while others need a push? Entropy and free energy answer that question.
Spontaneous processes
A spontaneous process happens without continuous outside intervention: ice melts at room temperature, iron rusts, and gases spread out. Spontaneous does not mean fast: diamond turning into graphite is spontaneous but takes millions of years.
Entropy
Entropy \(S\) measures the number of ways energy and particles can be arranged, often described as disorder. Gases have higher entropy than liquids, which have more than solids. Dissolving, melting, and reactions that produce more gas molecules generally increase entropy.
The second law
The second law of thermodynamics states that the total entropy of the universe increases in any spontaneous process. A system's entropy can decrease, as when water freezes, but only if the surroundings gain more entropy, for example from heat released into them.
Gibbs free energy
For processes at constant temperature and pressure, the Gibbs free energy change \(\Delta G = \Delta H - T\Delta S\) decides spontaneity. If \(\Delta G < 0\), the process is spontaneous; if \(\Delta G > 0\), it is not; if \(\Delta G = 0\), the system is at equilibrium.
\Delta G = \Delta H - T\Delta SThe role of temperature
If \(\Delta H < 0\) and \(\Delta S > 0\), \(\Delta G\) is always negative: spontaneous at all temperatures. If \(\Delta H > 0\) and \(\Delta S < 0\), never spontaneous. In the mixed cases, temperature decides. Ice melting has \(\Delta H > 0\) and \(\Delta S > 0\), so it is spontaneous above \(0^\circ\)C, where the \(T\Delta S\) term wins.
Worked example
For a reaction with \(\Delta H = +40\) kJ and \(\Delta S = +0.10\) kJ/K, \(\Delta G = 40 - T(0.10)\). It becomes spontaneous when \(T > \frac{40}{0.10} = 400\) K. Below 400 K the reaction will not proceed on its own.
Free energy and equilibrium
\(\Delta G^\circ\) is related to the equilibrium constant by \(\Delta G^\circ = -RT\ln K\). A large negative \(\Delta G^\circ\) means \(K \gg 1\), so products are strongly favoured. This links thermodynamics to the equilibrium unit.
\Delta G^\circ = -RT\ln KFree energy in living things
Cells drive non-spontaneous reactions, such as building proteins, by coupling them to strongly spontaneous ones, mainly the hydrolysis of ATP (\(\Delta G^\circ \approx -30.5\) kJ/mol). The overall coupled process has negative \(\Delta G\).
Key takeaways
Spontaneous processes need no ongoing push but may be slow. Entropy measures dispersal; the second law says the universe's entropy rises. \(\Delta G = \Delta H - T\Delta S\) decides spontaneity at constant \(T\) and \(P\). Temperature can switch spontaneity when \(\Delta H\) and \(\Delta S\) share a sign. \(\Delta G^\circ = -RT\ln K\) links free energy to equilibrium.
Flashcard
Occurs without continuous intervention
Check your understanding
A reaction has Delta H = -100 kJ and Delta S = +50 J/K. It is: