The Law of Mass Action and Equilibrium Constants

Equation 12.14 is the law of mass action, which appears in elementary chemistry books, written for Reaction 12.B. The term at the right is the familiar equilibrium constant, AT, which has the following characteristics  

Its form follows directly from the definition of the fugacity and the observation that at equihbrium a differential chemical change produces zero change in Gibbs energy. 

The individual species fugacities appear only in the form of the activity 

In Chapter 7, where we introduced the activity, we said little about it here we say a little more. Equation 7.26 and the definition of the fugacity can be combined to 

This equilibrium constant is dimensionless, as are all equilibrium constants expressed in terms of activities, because the equilibrium constant is a ratio of products of activities to various powers (+ and —), and activities are all dimensionless. That was one of the reasons for defining the activity, to make all equilibrium constants dimensionless. However, the numerical value of the activity depends on the choice of standard states. If we change standard states we will change the computed numerical value of the equilibrium constant, but in a way that will not change the computed concentrations at equilibrium (if we pay careful attention to standard states ). As we will see later, we often use modified equilibrium constants that have built-in dimensions however, the basic equilibrium constant, which is defined by Eqs. 12.14and 12.15,is always dimensionless. 

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