Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 295

where β = (K w C a /HK aw ) + (K s W/HK sw ) and α = (K w /H) + (K s /H) + k r . Note

that α is a composite rate constant that characterizes the loss mechanism within the

water.

E XAMPLE 6.9 L OSS OF C HLOROFORM FROM A S HALLOW S TREAM

For the Amite River near Baton Rouge, Louisiana, the depth is 2 m, f oc is 0.02 for the
sediment and has an average flow velocity of 1 m/s. For an episodic spill of chloroform
in the river, determine its concentration 20 miles downstream of Baton Rouge.
Assume that the background concentration of chloroform in air is negligible. Since
chloroform is highly water soluble, and its hydrophobicity is small, we can assume
that its concentration in the sediment will be low. Thus β is negligible. Because of
the high stream velocity and low sorption to sediment, the water-to-air mass trans-
fer is likely to dominate over water-to-sediment mass transfer. Hence α = (K w /h) +
k r . The reaction in water is hydrolysis and its rate is given by 4.2 10 − 8 h − 1 .

Clearly, this is low and chloroform is a refractory compound. From Table 4.12,
1 /K w = ( 1 / 4.2 × 10 − 5 ) + ( 1 /( 3.2 × 10 − 3 )( 0.183 )) . Hence K w is 3.9 × 10 − 5 m/s =
0.14 m/h. Since t = x/u = (20 miles)(1609 m/mile)/(1 m/s)(3600 s/h) = 8.9 h. Hence
α = 0.14 / 2 = 0.07 h − 1 . C w /C 0 = exp [− ( 0.07 )( 8.9 ) ]= 0.53. Hence, the concentra-
tion at the monitoring station will be 53% of its concentration at the spill point.

×

6.2.1.3 Biochemical Oxygen Demand in Natural Streams

Bacteria and microorganisms decompose organic matter in wastewater via enzyme
catalysis. The amount of oxygen that the bacteria need to decompose a given organic
compound to products (CO 2 and H 2 O), and in the process produce new cells, is called
the biochemical oxygen demand (BOD). The reaction is represented as

organic matter + O 2 → CO 2 + H 2 O + new cells.

BOD is used to characterize the extent of pollution in rivers, streams, lakes, and in
wastewater under aerobic conditions. BOD is measured using a five-day test, that is,
the oxygen demand in five days of a batch laboratory experiment. It is represented
as BOD 5 . The BOD 5 test is a wet oxidation experiment whereby the organisms are
allowed to break down organic matter under aerobic conditions. It is a convenient
method, but does not represent the total BOD. A 20-day test (BOD 20 ) is consid-
ered the ultimate BOD of a water body. BOD measurements are used to define the
strength of municipal wastewater, determine the treatment efficiency by observing the
oxygendemandremaininginaneffluentwastestream,determinetheorganicpollution
strength in surface waters, and determine the reactor size and oxygen concentration
required for aerobic treatment processes.
The oxygen demand , L , in water is given by a first-order reaction rate

d L
d t =

− k 1 L . (6.80)