Question

a) The water in a lake is found to have a toluene concentration of 1 µg/L. Calculate the concentration at equilibrium in the air above the lake (µg/L) and the sediment in the lake (µg/kg). Assume that the sediment has an organic carbon fraction of 0.05.

b) Perform the same calculation for a phenanthrene concentration in water of 1 µg/L.

c) For each chemical, comment on whether you would be more concerned about its release to the air or sediment.

Assume a temperature of 25°C.

Compound log Kow KH (atm·L/mol)

Toluene 2.69 6.61

Phenanthrene 4.57 0.0423

Answer 1

(A)Henry’s law definition: At a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

Considering the definition the equation can be stated as : K = p_x / C_x

where:

k              = the equilibrium constant for the solvation process

p_x            = partial pressure of gas x in equilibrium with a solution containing some of the gas

C_x            = the concentration of gas x in the liquid solution

So, the partial pressure of toluene is will be:

K x C_x = p_x

6.61 x 1 = 6.61 atm

So, the concentration at equilibrium in the air will be calculated using the formula: C_x’ = p_x / K

Thus, C_x’ = p_x / K

               = 6.61/6.61

                = 1 µg/L

Now, for concentration in sediment the formula would be : C_m = k_d x C_w

Where K_d is calculated using the formula =

K_d = KOC (partition coefficient organic carbon to water) x OC (organic carbon content)

     = [log KOC = 0.81 x log KOW + 0.1] x 0.05

     = [log KOC = 0.81 x 2.26 + 0.1] x 0.05

     = 1.9306 x 0.05

    = 0.09653

Thus, C_m = k_d x C_w

                = 0.09653 x 1

                = 0.09653 µg/kg (sediment concentration)

(B) So, for phenanthrene the calculation would be as follows.

Air: K x C_x = p_x

      0.0423 x 1 = 0.0423 atm

So, the concentration at equilibrium in the air will be calculated using the formula: C_x’ = p_x / K

Thus, C_x’ = p_x / K

               = 0.0423/0.0423

                = 1 µg/L

Sediment: C_m = k_d x C_w

Where K_d is calculated using the formula =

K_d = KOC (partition coefficient organic carbon to water) x OC (organic carbon content)

     = [log KOC = 0.81 x log KOW + 0.1] x 0.05

     = [log KOC = 0.81 x 4.57 + 0.1] x 0.05

     = 3.8017 x 0.05

    = 0.190085

Thus, C_m = k_d x C_w

                = 0.190085x 1

                = 0.190085µg/kg (sediment concentration)

(C) Comment on concerned about its release to the air or sediment for both chemicals:

Since the concentration of toluene and phenanthrene is greater in air than sediment as seen above, the concern should be more when the two chemicals are released in air.