Gibbs free energy decrease

The combined first and second laws state that, at constant T and V, a system seeks to minimize A until dA for any subsequent change is zero (Equation 4.14), and likewise, at constant T and P, the Gibbs free energy decreases until dG for any subsequent change equals zero (Equation 4.20). One then recognizes that the condition for equilibrium is exactly the same at constant T and V as it is at constant T, P. 

Arguments based on the second law which are given in standard text books [3,4] lead to the conclusion that, on its own, a chemical reaction will proceed in the direction in which the Gibbs free energy decreases and, when equilibrium is reached, this quantity has a minimum value. More precisely, for a system undergoing some small change... 

Equation (12-2) leads to the following criterion for spontaneity for a process occurring at constant temperature and pressure, but with the system in thermal and mechanical contact with the surroundings The Gibbs free energy decreases for a spontaneous (irreversible) process and remains constant for an equilibrium (reversible) process. 

This result states that during the process the Gibbs free energy decreases (AG is negative) until equilibrium is reached, at which point G does not change any more (AG is zero). In other words, the Gibbs free energy at equilibrium is at a minimum. Mathematically,... 

In the above equation AGe is the Gibbs free energy of formation of an embryo of size Te Since AG approaches zero as the bubble radius, r, approaches zero or infinity, the Gibbs free energy decreases (the free energy is consumed because... 

During the course of a reaction at constant volume and temperature, in line with the second law of thermodynamics, the Gibbs free energy decreases monotonously. 

However, we also noted that in the case of hydrogen the absolute value of the Gibbs free energy decreases with temperatnre. It is the same for carbon monoxide, and so we can say that for all practical fuels this is so. It is impractical to operate a fuel cell at below ambient temperature, and so the highest possible efficiency limit will occur at ambient temperature, Ta. At this temperature the Gibbs free energy is maximum and is equal to AGt. So, in practice, we can refine our formula for the maximum efficiency to... 

Ta is the work of adhesion, which is equivalent to the Gibbs free energy decrease (per unit area) when an interface is formed from two pure component surfaces. The work of adhesion increases as the interfacial attraction increases, leading to a decrease in interfacial tension. It is apparent from (18) that, if the two compmients are identical, an expression can be obtained that relates the surface tensimi (7,- to the work of cohesion (Wed for component i ... 

As a systam reaches equilibrium the Gibbs free energy decreases, attaining a minimum at the point of equiUbrium. 

For a reaction to be spontaneous, AS must be positive. The value of T is always positive on the absolute (kelvin) temperature scale. So applying these signs to the relationship AG = -TAS j j, the value of AG must be negative for a reaction to be spontaneous. So, when a spontaneous reaction occurs at constant temperature and pressure, the Gibbs free energy decreases. If the value of AG is positive, the reaction is not spontaneous. 

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