Chemistry Reference
In-Depth Information
dependent on drug (e.g., p
K
a
, lipophilicity, and intermolecular forces in the solid state)
and solvent properties (e.g., pH, polarity, and solvent interactions) [1
-
3]. Due to these
multifactorial dependencies, it is dif
cult to describe solubility accurately in a mathe-
matical fashion across a broad class of compounds and solvents. The reader is
encouraged to consult comprehensive texts on the topic such as Refs [2,4,5]. One
equation that has been used to describe solubility in nonideal solutions is based on the
Hildebrand solubility approach and is shown in Equation 6.1:
Δ
H
f
T
0
T
T
0
V
2
Φ
1
2
log
X
2
303
RT
δ
1
δ
2
;
(6.1)
2
:
303
RT
2
:
2
2
2
P
2
δ
Total
δ
D
δ
δ
H
D
nonpolar effects
P
polar effects
H
hydrogen bonding effects
;
:
;
:
;
:
where
X
2
is the solubility expressed in mole fraction,
Δ
H
f
is the heat of fusion,
R
is the gas constant,
T
0
is the melting point,
T
is the temperature of the solution,
Φ
is the volume fraction occupied by the solid,
V
2
is the molar volume of the liquid solute, and
δ
1
is the solubility parameter of the solvent and
δ
2
of the solute.
Although the equation cannot be applied to predict solubility for all solutes in all
solvents, it gives us valuable insight into what factors in
uence solubility. Accordingly,
factors such as higher melting point, higher heat of fusion, and lower solution
temperature will translate into lower solubility. The solubility parameters (
δ
) are energy
contributions re
solvent interactions and how these
relate to solubility is also reflected in Equation 6.1.
An inference from Equation 6.1 is that solubility is dif
ecting intermolecular and solute
-
cult to accurately model
without experimentation. According to Ref. [6], one of the main challenges in early
development is collecting high-quality, accurate drug-relevant solubility data. Solubility
measurement methodology must cover the wide diversity of chemical space and account
for the relevant parameters. Obtaining high-quality solubility data experimentally
requires careful attention to experimental details and may require several iterations.
Dissolution is solubility
first theories describing dissolution
in a quantitative sense were published in 1897 by Noyes and Whitney [7]. These now
classical equations have since been modi
'
is kinetic cousin and the
ed to include elements of Fick
'
s law of
diffusion [8], as well as other parameters, leading to the most extant modi
ed Noyes
-
Whitney equation [9,10]:
d
X
d
d
t
A
D
δ
C
S
X
d
V
DR
;
(6.2)
