ArG and K as Functions of Temperature

In this section, we will describe how to use the value of AfG or K at one temperature to obtain their values at another temperature. In the method illustrated in Example 13-11, we assume that AjH and AfS° are independent of temperature. Even with this assumption, AfG = AjH — TA S° is strongly temperature-dependent because the temperature factor, T, multiplies Aj.S°. 

Determining the Relationship Between an Equilibrium Constant and Temperature by Using Equations for Gibbs Energy of Reaction 

At what temperature will the equilibrium constant for the formation of NOClfg) be X = 1.00 X 10 Data for this reaction at 25 °C are 

To determine an unknown temperature from a known equilibrium constant, we need an equation in which both of these terms appear. The required equation is A G = —RT In K. However, to solve for the unknown temperature, we need the value of Afi° at that temperature. We know the value of Afi° at 25 °C (-40.9 kJ moP ), but we also know that this value will be different at other temperatures. We can assume, however, that the values of AjH and A S will not change much with temperature. This means that we can obtain a value of AjG from the equation A G = ArH - TAjS , where T is the unknown temperature and the values of ArH and A S are those at 25 C. Now we have two equations that we can set equal to each other. 

Although the answer shows three significant figures, the final result should probably be rounded to just two significant figures. The assumption we made about the constancy of AjH and AfS is probably no more valid than that. 

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