The Mechanism of Chromatographic Retention - The Association of Methanol with Water > Page 31

The molar concentration, in these circumstances, can be defined as the moles per milliliter before mixing. As there is a volume change on mixing, to be precise, equation (7) should be expressed in moles per milliliter after mixing. At the maximum, however, there is a 3% change in volume on mixing and, thus, (k) will, also, only be changed by approximately 3%. Thus, to simplify the algebra (but, nevertheless, maintain a precision of 3% or better) molar concentrations before mixing are used.

If (a) is the volume fraction of methanol in the original mixture, then the volume fraction of water will be (1-a). Now, the molar volume of a substance is the ratio of the molecular weight to the density, consequently, the molar concentrations of methanol and water will be() and () respectively (where (VM) and (VW) are the molar volumes of methanol and water respectively.

Thus, (8)

and (9)

Solving for [W] using equations (7), (8) and (9),

(10)

where

and

In addition, (11)

and (12)

As [M], [W] and [MW] were defined in moles per milliliter then the volume (vi) after mixing will be