Geology Reference
In-Depth Information
K is therefore a function of temperature through the term RT, where R is
the gas constant, 8.314 J mol
1
K and T is the temperature expressed in
Kelvin (K). The value of the constant given in Equation 6.13 depends on
how the abundance of the solute or chemical is expressed i.e. partial
pressure, mole fraction or molar concentration. For mole fraction the
constant has a value of 1, whereby ln 1
¼
0 and can therefore be ignored.
Rearranging Equation 6.13 to solve for DG, and then combining with
the Gibbs-Helmholz equation results in
RT lnK
¼
DH
TDS
ð
6
:
14
Þ
Hence
;
lnK
¼
DH
RT
þ
DS
ð
6
:
15
Þ
R
It therefore follows that an experimentally determined plot of ln K
against 1/T (1/K) will yield a slope of
DH/R, and an intercept of DS/R
(DH and DS are considered to be constant over a small temperature
range). In laboratories measuring partition coefficients for environmen-
tal fate, then
10 to 45 1C is a typical temperature range. Equation 6.15
is usually expressed in the form:
lnK
¼
m
T
þ
b
ð
6
:
16
Þ
where m is the slope of the line and hence Rm
¼
DH. Once DH is
established then K can be adjusted to any environmentally relevant
temperature according to the integrated form of the van't Hoff equation
lnK
ð
T
2
Þ¼
lnK
ð
T
1
Þ
DH
R
T
2
1
1
ð
6
:
17
Þ
T
1
where T
1
is the reference temperature (298 K) at which K(T
1
)andDH have
been measured and T
2
is the temperature of interest. For many organic
chemicals that persist in the environment, careful laboratory measurements
of a particular partitioning coefficient over a range of temperatures may
not exist, therefore DH
0
(the enthalpy for the partitioning process at stand-
ard state, 101 kPa and 298 K) is often used in Equation 6.17.
Case study and worked example - Calculating water concentrations of
Lindane
To illustrate the effect that temperature has on a partition coefficient
and use some of the equations above, it is worth examining the
