1. Error Due to the Volume Change
2. Effectiveness of an Extraction

**THEORY**

The behavioural pattern of two immiscible solvents, say ‘*a*’ and ‘*b*’, is essentially nonideal with respect to one another. Now, if a
third substance is made to dissolve in a two-phase mixture of the solvents (*i.e.,* ‘*a*’ and ‘*b*’), it may
behave ideally in either phases provided its concentration in each individual
phase is approximately small. Therefore, under these prevailing experimental
parameters the ratio of the mole fractions of the solute in the two respective
immiscible phases (‘*a*’ and ‘*b*’) is found to be a constant which is
absolutely independent of the quantity of solute present. It is termed as the **Nernst Distribution Law** or the **Partition Law **and may be expressed as
follows :

where, [A]* _{a}* = Mole
fraction of solute A in Phase ‘

[B]* _{b}*
= Mole fraction of solute B in Phase ‘

K* _{p}* =
A constant.

The constant (K* _{p}*)
is also known as the

(*a*) It is not
thermodynamically rigorous *i.e.,* it
takes no cognizance of the activities of the different species. In other words,
it is solely applicable to very dilute solutions in which case the ratio of the
activities almost approaches unity, and

(*b*) It does not
hold good when the distributing substances encounters association or
distribution in either phases (*i.e.,*
‘*a*’ and ‘*b*’).

Consequently, a more rigorous treatment particularly
specifies K* _{p}* as the ratio
of the activities of the substance (A) in the two solvents instead of their
concentrations. Hence, for dilute solutions, at a specified constant pressure
and temperature, the mole fraction of a solute is directly proportional to its
concentration in molarity or mass per unit volume ; which implies that these
may be employed instead of mole-fraction in Eq. (

Thus, the **Partition
Coefficient** K* _{p}* is also
given by the following expression :

..............................(b)

where, S_{1} = Solubility of substance A in
solvent ‘*a*’, and

S_{2} = Solubility of substance A in solvent ‘*b*’.

Adequate precaution and care must be exercised in
determining partition coefficients based on the solubility data as S_{1}
is not the solubility of substance ‘A’ in pure Solvent ‘*a*’, but rather the solubility in Solvent ‘*a*’ saturated with Solvent ‘*b*’.

*Example ***: **In
order to determine the exact partition coefficient of substance ‘A’ between
water and

Likewise, the following Table 27.1, records the mutual
solubilities of a few typical solvent pairs that are used frequently for **liquid-liquid extraction** procedures.

In liquid-liquid extractions the following *two* aspects are very crucial and
important, namely :

(*a*) Error due
to the Volume Change, and

(*b*)
Effectiveness of an Extraction.

These *two*
aspects shall be discussed briefly at this juncture.

In a situation wherein two immiscible solvents are
employed in an extraction, the volumes of the two individual phases after
attainment of equilibrium may be appreciably different in comparison to the
initial volumes of the solvents used. Therefore, a number of procedures have
been adopted to avoid **‘error due to** **the volume change’ **incurred thereby,
namely :

(*i*) Measure the
volume of the phase employed for the analysis and incorporate this volume in
the calculations,

(*ii*) Separate
the phase quantitatively and subsequently dilute to a known volume,

(*iii*) Separate
the phase quantitatively and make use of the entire volume in the remaining
steps of the ongoing analysis, and

(*iv*) Carry a
marker substance through the extraction to automatically compensate for volume
changes.

However, the latter procedure finds its abundant use in
chromatographic methods of analysis.

Based on the appropriate partition coefficient of an
immiscible solvent pair it is possible to calculate the ‘effectiveness of an
extraction’.

Let us assume that ‘*x*’
moles of solute present initially in a volume V_{2} of Solvent ‘*b*’. Now, this particular sample
undergoes extraction with a volume V_{1} of Solvent ‘*a*’ and subsequently ‘*y*’ moles of com-pound are left in V_{2}
at equilibrium.

Substituting these values in Eq. (*a*) and using molarity instead of mole fraction, we have :

after simplifying and rearranging :

where, *f *= Fraction not
extracted.

Figure 27.1, represents the nomogram from which the
unextracted fraction for various values of V_{2}/V_{1} and K
may be obtained.

From Eqs. (*d*)
it is quite evident that the fraction extracted is absolutely independent of
the initial solute concentration. Hence, the fraction left unextracted after ‘*n*’ extraction may be given by the
following expression:

..................................(e)

assuming that the same volumes of solvents have been used
for each extraction.

Form Eq. (*e*) it
is distinctly obvious that a series of several extractions would definitely
prove to be more efficacious than one single extraction using the same total
volume of solvent.

From figure 27.1, the following steps may be adopted in
order to determine the percentage of the analyte left in the sample after a
single extraction :

*(i)
*Hold a straight edge in such a manner that it is made to
pass though the point on the ‘left scale’ which exactly corresponds to that
ratio of extracting solvent to sample solvent volume and through the point
representing the partition coefficient (K* _{p}*)
on the

*(ii)
*The percentage of the ‘**analyte**’, left behind in the sample solvent after a single
extraction is given by the intersection of the straight-edge with the **‘right scale’**.

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Pharmaceutical Drug Analysis: Liquid-Liquid Extraction : Liquid-Liquid Extraction: Theory |

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