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
