Van Deemter derived an expression for the variance from the resistance to mass transfer in the stationary phase, (), which is as follows:

(7)

where (k') is the capacity ratio of the solute,

(df) is the effective film thickness of the stationary

phase,

(DS) is the diffusivity of the solute in the stationary

phase,

and the other symbols have the meaning previously ascribed to them.

Now, applying the law of Summation of Variances,

(8)

where () is the total variance/unit length of the column.

Thus substituting for (), (), () and () from equations (4), (5), (6) and (7), respectively,

(9)

Equation (9) is the Van Deemter equation that describes the variance per unit length of a column in terms of the physical properties of the column contents, the distribution system and the linear velocity of the mobile phase. Alternatively the Van Deemter equation can be expressed in the form,

(10)

where (H) is the Height of the Theoretical Plate. The relationship between (H) and (sx) is explained in Book 6.

Hence the term "HETP equation" for equation (10). This form of the Van Deemter equation is very nearly correct for LC but, due to the compressibility of the gaseous mobile phase in GC, neither the linear velocity nor the pressure is constant along the column. Furthermore, as the diffusivity, (Dm), is a function of pressure, the above form of the equation can only be approximate. However, equation (10) generally gives the correct form of the relationship between (H) and the linear velocity (u). It also predicts that there will be an optimum velocity that gives a minimum value for (H) and, thus, a maximum efficiency. Pressure corrections for retention volume and the height of the theoretical plate are derived in Books 6 and 7.