What Happens to the Units in Equilibrium Constants

We have said that it is common to disregard units and write equilibrium constants as dimensionless quantities. The reason is as follows Prior to being used in an equilibrium expression, each molar concentration is divided by a reference concentration of IM, and each partial pressure is divided by a reference pressure of 1 atm. The reference concentration (1 M) and reference pressure (1 atm) are known as the standard states for aqueous and gaseous species, respectively. This cancels the units without changing the value of the concentration or pressure in question. The dimensionless result of dividing a concentration by a reference value is called the activity. Activities commonly are used by chemists in place of concentrations, but a detailed discussion of activities is beyond the scope of this book. Using as an example the equilibrium between N2O4 and NO2, 

We can then convert the molar concentrations to partial pressures using the ideal gas equation  

In each case, dividing by the reference value eliminates the units without changing the numerical value of the result. We will not show the division by reference values explicitly, but you should realize that this is the reason why there are no units associated with equilibrium constants. 

Division of each entry in an equilibrium expression by a reference value actually enables us to use molar concentrations and partial pressures in the same equilibrium expression. For example, we can write the equilibrium expression for the reaction 

Each of the entries in the expression is divided by the appropriate reference value, making the result dimensionless. Note that this equihbrimn constant is neither a nor a Kp.lt is referred to simply as AT or as where the subscripted eq denotes equilibrium. We will encounter the use of mixed equilibrium constants such as this in Chapters 19 and 20. 

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