223 Chemical Equilibrium
A balanced state of a reacting system that is used to predict the final amounts of reactants and products.
Minimum Gibbs energy at equilibrium. A reaction mixture reaches equilibrium when the Gibbs energy of the mixture is at a minimum. Gibbs energy is the energy available for non-expansion work at fixed temperature and pressure. This principle is used to locate the composition at which the net amounts stop changing.
The equilibrium condition is
\[ \Delta_{r}G = 0 \]
where
- \(\Delta_{r}G\) is the Gibbs energy of reaction.
Dynamic balance of rates. The reaction has not stopped: the forward and reverse rates are equal. This principle is used to treat equilibrium as a dynamic balance rather than a halt.
The reaction Gibbs energy. The reaction Gibbs energy is fixed by the standard value and by the composition through the reaction quotient. The reaction quotient is the same combination of activities as the equilibrium constant, written for the present composition. This principle is used to decide which way a mixture will shift.
The reaction Gibbs energy is
\[ \Delta_{r}G = \Delta_{r}G^{\circ} + RT\ln Q \]
where
- \(\Delta_{r}G\) is the Gibbs energy of reaction.
- \(\Delta_{r}G^{\circ}\) is the standard Gibbs energy of reaction.
- \(R\) is the gas constant.
- \(T\) is the absolute temperature.
- \(Q\) is the reaction quotient.
The equilibrium constant. The equilibrium constant is fixed by the standard Gibbs energy of reaction. This principle is used to compute the greatest possible yield from tabulated data.
The equilibrium constant is
\[ K = e^{-\Delta_{r}G^{\circ}/RT} \]
where
- \(K\) is the equilibrium constant.
- \(\Delta_{r}G^{\circ}\) is the standard Gibbs energy of reaction.
- \(R\) is the gas constant.
- \(T\) is the absolute temperature.
The van’t Hoff equation. Raising the temperature shifts the equilibrium of an endothermic reaction toward products. An endothermic reaction is a reaction that absorbs heat. This principle is used to predict how \(K\) changes with temperature.
The van’t Hoff equation is
\[ \dfrac{d\ln K}{dT} = \dfrac{\Delta_{r}H^{\circ}}{RT^{2}} \]
where
- \(K\) is the equilibrium constant.
- \(T\) is the absolute temperature.
- \(\Delta_{r}H^{\circ}\) is the standard enthalpy of reaction.
- \(R\) is the gas constant.
Note: Atkins identifies the balance with the mixture at its lowest Gibbs energy.