Spontaneous change nonstandard conditions

SECTIONS 19.6 AND 19.7 The values of AH and AS generally do not vary much with temperature. Therefore, the dependence of AG with temperature is governed mainly by the value of T in the expression AG = AH — TAS. The entropy term —TAS has the greater effect on the temperature dependence of AG and, hence, on the spontaneity of the process. For example, a process for which AH > 0 and As > 0, such as the melting of ice, can be nonspontaneous (AG > 0) at low temperatures and spontaneous (AG < 0) at higher temperatures. Under nonstandard conditions AG is related to AG° and the value of the reaction quotient, Q AG = AG" + RT In Q. At equilibrium (AG = 0, Q = K), AG = —RT InkT. Thus, the standard free-energy change is directly related to the equilibrium constant for the reaction. This relationship expresses the temperature dependence of equilibrium constants. 

Two ways of predicting reaction direction are from the value of AG and from the relation of Q to K. These variables represent different aspects of the same phenomenon and are related to each other by AG = RT In Q/K. When Q = K, the system can release no more free energy. Beginning with Q at the standard state, the free energy change is AG°, and it is related to the equilibrium constant by AG° = -RT In K. For nonstandard conditions, AG has two components AG° and RT In O. Any nonequilibrium mixture of reactants and products moves spontaneously (AG < 0) toward the equilibrium mixture. A product-favored reaction has K > 1 and, thus, AG° < 0. 

In Section 19-3, we developed a criterion for spontaneous change (Ecdi > 0), but we used the criterion only with E° data from Table 19.1 Qualitative conclusions reached with E eU values often hold over a broad range of nonstandard conditions as well. However, when E eii is within a few hundredths of a volt of zero, it is sometimes necessary to determine E eii for nonstandard conditions in order to apply the criterion for spontaneity of redox reactions, as illustrated in Example 19-10. 

The sign of the standard free-energy change AG° tells the direction of spontaneous reaction when both reactants and products are present at standard-state conditions. In actual reactions, however, the composition of the reaction mixture seldom corresponds to standard-state pressures and concentrations. Moreover, the partial pressures and concentrations change as a reaction proceeds. How, then, do we calculate the free-energy change AG for a reaction when the reactants and products are present at nonstandard-state pressures and concentrations ... 

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