Conventions activity dimensionless

Formerly [H20] = 1 was by convention (though pre-1950 Bjernun used the actual [H20]), but the current expression of equilibrium constants in dimensionless form by using ratios of concentrations (activities) to standard states results in the water term being unity since solvent water is, to a very close approximation, in its standard state. 

Figure 9.6 Total conversion for inert membrane reactor with catalyst on the feed side (IMRCF), catalytic membrane reactor (CMR) and conventional fixed-bed reactor (FBR) with uniform and Dirac delta catalyst activity distributions as a function of the dimensionless residence time [Yeung et al., 1994]...

Thermodynamic equilibrium constants are dimensionless because they are expressed in terms of activities rather than partial pressure or concentration. The convention in chemical kinetics is to use concentrations rather than activities, even for gaseous species. Therefore, the equilibrium constants Ki, K2, and introduced here are the empirical equilibrium constants described briefly in Section 14.2. These constants are not dimensionless and must be multiplied by the concentration of the reference state, = l T/Pref, raised to the appropriate power to be made equal to the thermodynamic equilibrium constant. Nevertheless, to maintain consistency with the conventions of chemical kinetics, such constants as Ki, K2, and are referred to as equilibrium constants in this section and are written without the subscript c. 

Given the definition of from Eq. 4.2, we find that the binding constant has units of M Other equilibria can have different units. Putting units on values is the most common convention used by chemists. Yet, we must remember that all equilibrium constants are really defined by ratios of activities, which are dimensionless values (see Section 3.1.5). True binding constants are therefore dimensionless. This should not come as a surprise, because the... 

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