Overall Plate Height Expression

If we add to Eq. 11.37 the longitudinal diffusion and stationary phase terms, Eqs. 11.8 and 11.18, we get the overall plate height expression 

This can be condensed to highlight only the velocity dependence 

The last two equations provide a good summary of how the various plate height terms are assembled into an overall plate height equation for chromatography. Whether or not all the constants (y, qy A,) of the equations are known, these expressions show the nature of the dependence of H on the controllable system parameters vy dp, d, Ry Dmy and Ds. The expressions consequently have profound consequences for guiding practical chromatography. These consequences will be discussed in the next chapter. 

Performance Liquid Chromatography, Wiley, New York, 1989, Chapter 1. 

1( ) A solute has a capacity factor of 9. What is the probability that a 

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Although the above listing of contributions to the colunn plate height is not coq>rehensive, it encompasses the major bandbroadening factors and the overall plate height can be expressed as their sun, equation (1.30). 

When the terms contributing to band broadening are collected and equilibrium spreading is assumed to be negligible, the following general expression for overall plate height is obtained ... 

This effect of Eddy diffusion on the overall plate height can be expressed as the A term... 

There is also an analogous contribution to the overall plate height due to diffusive spreading in the stationary phase and using similar reasoning as above this may be expressed as... 

The factors affecting the contribution of this effect to the overall plate height are as those experienced for the mobile phase mass transfer term. Thus, the mobile phase mass transfer term may be expressed as... 

Giddings [3,4] has shown that the overall plate height arising from these kinetic factors can be expressed mathematically as... 

The coupling equations shown above are applicable to one kind of velocity bias, such as that between adjacent channels. However, the theory is more or less the same for the other kinds of velocity biases listed previously, but the constants (a>fi9 a>A, (oa) are different, yielding different a> and A in the foregoing coupling expressions. Each kind of velocity bias generates its own independent random walk, leading to an additive plate height term H,. The overall mobile phase term is therefore the sum... 

Discussion—It is expressed in kilopascals (mm Hg) per meter of packed height for packed columns, or kilo-pascals (mm Hg) overall for real plate columns. It is higher for aromatics than for paraffins, and for higher molecular weights than for lighter molecules, at a given boilup rate. 

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