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The change in Gibbs free energy is associated with changes in energy as a function of enthalpy, entropy, and temperature: `\Delta G = \Delta H - T\Delta S` , where H is the enthalpy, T the temperature, and S the entropy.
In general, exothermic reactions are more favorable then endothermic reactions. That is, it is more likely that a reaction would be spontaneous if it releases energy rather than when one needs an input of energy to get it going. However, this is not the only criteria. Enthalpy mainly concerns the system and not the surroundings, and for a reaction to be favorable, the entropy of the entire system must increase (2nd law of thermodynamics). An exothermic reactions is deemed favorable since it releases heat to the environment, and heat is the most disordered form of energy. Another factor then to consider to account for the disorder of the environment is the change in entropy of the system - and this is accounted for by S.
Since the Gibbs free energy takes care of both these factors, H and S, it can be used to determine whether a reaction is thermodynamically favored or not. When `\Delta G` is negative, the reactions is favorable - and it becomes increasingly favorable as change in enthalpy becomes more negative and change in entropy becomes more positive. As can be seen from the equation, it is also affected by temperature as temperature affects the entropy of the system. It is however, not related to the amount of reactants and products, and not associated with equilibrium constants.
Amounts of reactants and products as well as equilibrium constants are associated with the kinetics of the reaction and not the thermodynamics. (final reference would be a starting point for more on this).
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