Free Energy and Nonstandard Conditions

To obtain a mathematical relationship between AG° and the equilibrium constant, K, first we must realize that the equilibrium state does not correspond to standard conditions. We cannot expect all reactants and products to be present at one atmosphere pressure and one molar concentration for every equilibrium reaction The derivation of the mathematical relationship that adjusts for nonstandard conditions is one you will learn if you continue to study chemistry. For now, we simply offer the expression itself  

Here R is the universal gas constant, T is the temperature, and Q is the reaction quotient. Recall from Section 12.3, however, that Q approaches K as the system 

With this equation, we can calculate an equilibrium constant if we know the standard free energy change for the desired reaction. As we learned in Section 10.7, we can often obtain that from tabulated data. Example Problem 12.15 applies Equation 12.7 to the conversion of methane to methanol. 

The conversion of methane gas (CH4) to methanol (CH3OH), which is a liquid at room temperature, is an area in which considerable research is being done. Still, this process is not yet economically viable. Using tabulated thermodynamic data, calculate the equilibrium constant for the following reaction at 25°C  

Comment on whether or not the equilibrium position of this reaction is the likely source of the problem for commercialization of the process. 

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