Spontaneity and reaction equilibrium

In Sec. 5.8, we found that the spontaneous direction of a process taking place in a closed system at constant T and p, with expansion work only, is the direction of decreasing G. In the case of a chemical process occurring at constant T and p, AjG is the rate at which G changes with Thus if AfG is positive, spontaneously decreases if ArG is negative, spontaneously increases. During a spontaneous process d and AjG have opposite signs.  

Note how the equality of Eq. 11.7.3 agrees with the inequality dG —S dT + V dp, a criterion of spontaneity in a closed system with expansion work only (Eq. 5.8.6 on page 145). When d and ArG have opposite signs, AjGd is negative and dG = 

If the system is closed and contains at least one phase that is a mixture, a state of reaction equilibrium can be approached spontaneously at constant T and p in either direction of the reaction that is, by both positive and negative changes of In this equilibrium state, therefore, G has its minimum value for the given T and p. Since G is a smooth function 

Thermodynamics and Chemistry, second edition, version 3 2011 by Howard DeVoe. Latest version www.chem.umd.edu/thermobook 

It is important to realize that this condition is independent of whether or not reaction equilibrium is approached at constant temperature and pressure. It is a universal criterion of reaction equilibrium. The value of A G is equal to iVifii and depends on the state of the system. If the state is such that A G is positive, the direction of spontaneous change is one that, under the existing constraints, allows ArG to decrease. If ArG is negative, the spontaneous change increases the value of A G. When the system reaches reaction equilibrium, whatever the path of the spontaneous process, the value of ArG becomes zero. 

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