Applications of Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 161

relationship φ oc . Karickhoff, Brown, and Scott (1979) demonstrated that the

linear isotherm described above was valid for several organic compounds over a wide
range of aqueous concentrations. The linear isotherm was found to be valid up to
approximately 50% of the aqueous solubility of the compound. The isotherms were
reversible and showed only a 15% decrease in K sw at an ion (NaCl) concentration
of 20 mg/mL. They also demonstrated the linear relationship between K sw and f oc
for a polyaromatic hydrocarbon (pyrene). Further, Means et al. (1980) extended this
relationship to several PAHs on sediments and soils. The slope of the plot of K sw
(kg sorbate/kg sorbent) versus f oc is a constant for a given compound on various soils
and sediments. Thus, we have

φ om .2

K sw = K oc f oc . (4.76)

The slope K oc is therefore a convenient way of characterizing the sorption of a
particular hydrophobic compound.

E XAMPLE 4.19 O BTAINING K oc FROM E XPERIMENTAL D ATA
One gram of soil in 500 mL of aqueous solution was spiked with 10 mg/L of an organic
compound. After equilibration for 48 h, the aqueous concentration of the compound
was 1 mg/L. If the soil organic carbon content was 0.02, obtain K sw and K oc for the
compound.

w s = 1g, V w = 500 mL, C w, i = 10 mg / mL C i w = 1mg / L, f oc = 0.02.
W i /w s = ( 0.01 − 0.001 ) 0.5 / 1 = 0.0045 g / g. K sw = (W i /w s )/C i w = 4.5 L / kg.
K oc = K sw /f oc = 225 L / g = 2.25 × 10 5 L / kg.

The partitioning of a solute from water to soil organic carbon is similar to the
partitioning to octanol. This leads to an LFER between K oc and K ow . As discussed
earlier, the octanol-water partition constant is given by

γ i w
γ i o

V w
V o

.

K ow = (4.77)

Since the partitioning into the organic fraction of the mineral matter can be described
similarly, we can write

γ i wc
γ i cw

V w
V c

1
ρ c

K oc = , (4.78)

where γ i cw aretherespectiveactivitycoefficientsofsolute i inwatersaturated

with organic matter (humus) and humic saturated with water, V w and V c are the
respective molar volumes, and

γ i wc and

ρ c is the density of the organic matter so that K oc is
expressed in L/kg. Using the equation for K ow to substitute for V w , we obtain

C 1 K ow γ i o
γ i cw

γ i wc
γ i w

.

K oc = (4.79)