A reaction is spontaneous if the overall transformation leads to an increase in total entropy (system plus surroundings). The direction of spontaneous change always increases the total entropy of the universe at the expense of energy available to so useful work. This is known as the second law of thermodynamics.

  • Entropy $\rm (S)$ is a property which quantifies the degree of disorder or randomness in a system.
  • Ordered states have low $\rm S$, disordered states have high $\rm S$: $\rm S(s) < S(l) < S(g)$.
  • Generally matter and energy become more disordered, and the $\rm S_{universe}$ increases.
  • $\rm\Delta S^o_{reaction} = \sum S^{\theta}_{\boxed{}} (products)$ $–$ $\rm \sum S^{\theta}_{\boxed{}} (reactants)$
  • Gibb’s free energy $\rm (G)$ is the criterion for predicting the spontaneity of a reaction or process: it is related to $\rm\Delta S^o_{total}$. It gives the energy available to do useful work and is related to the enthalpy and entropy changes of reaction and the temperature $\rm T$ in kelvin: $\rm\Delta G_{reaction} = \Delta H_{reaction} - T\Delta S_{reaction}$
  • $\rm\Delta G_{sys} <0$ for a spontaneous process. $\rm\Delta G_{sys} = 0$ at equilibrium.
    Calculating $\rm \Delta G_{reaction}$ (when $\rm T = 298~K$)
    $\rm\Delta G_{reaction} = \sum \Delta G^o_{form} (products)$ $–$ $\rm \sum \Delta G^o_{form} (reactants)$
    Calculating $\rm\Delta G_{reaction}$ (for all $\rm T$).
    $\rm \Delta G_{reaction} = \Delta H_{reaction} - T\Delta S_{reaction}$
    $\rm T$ is in $\rm K$. As the units of $\rm S$ are generally $\rm J~mol^{-1}~K^{-1}$ and $\rm H$ are $\rm kJ~mol^{-1}$ they may need to be changed to be consistent.
  • $\rm\Delta G_{sys}$ and thus the direction of change varies with temperature.
    At low temp: $\rm\Delta G^o_{reaction} \approx \Delta H^o_{reaction}$ : exothermic reactions are spontaneous.    
    At high temp: $\rm \rm\Delta G^o_{reaction} = - T \Delta S^o_{reaction}$ : this allows some endothermic reactions if $\rm \Delta S^o_{reaction} > 0$.