1. In their study of on the temperature effects of 17a-estradiol biodegradation, Zheng et al. (2012) reported the following pseudo-1^st - order rate constants as a  function of temperature.

Use these data to estimate the activation energy and the frequency factor for this reaction over the temperature range up to the optimum temperature.

2. Imagine a single polyethelyne (PE) block 2.5x10^-4 m thick. At t = 0, one edge of the block is exposed to a solution that contains trans-chlordane, which begins diffusing into the PE block. Assume the solution next to the PE block is well-mixed and maintained at a constant transchlordane concentration. Using concepts from our course, create a mathematical model describing this diffusion process.

Use your model to create a figure showing the relative concentration (C(x)/C(x = 0)) as a function of distance into the block after t = 12 h of exposure. Assume that for trans-chlordane the water-PE partition coefficient is log(KpE (L_w/kg_pE)) = 5.17 and the diffusivity is log (Dpa (m²/s)) = -13.51.

3. Six chemicals (Table 1) were added to a diesel fuel (average MW = 159 g/mol, density = 990 g/L) to explore partitioning behavior of these chemicals among the NAPL and its surrounding phases. Fifty-mL of the resulting mixed NAPL were added to a 1.0-L beaker containing 500-g of soil (organic carbon content = 5.2%), 500-mL of water, and the remaining volume was atmospheric air. Assume the NAPL behaves as an ideal liquid and the properties in Table 1 apply for the test temperatures, and answer the following questions about the equilibrium composition of the system.

Table 1. Chemicals found in the NAPL, their respective concentrations in that NAPL, and some potentially useful properties of those chemicals.

a. Which of the six chemicals is present at the greatest concentration in the aqueous phase, and what is that concentration (mg/L)?

b. Which of the six chemicals is present at the greatest concentration in the gas phase, and what is that concentration (atm)?

c. Which of the six chemicals is present at the greatest concentration in the solid phase, and what is that concentration (mg/kg)?

4. In their study of N₂O emissions from the Ohio River, Beaulieu et al. (2010) used a floating acrylic chamber to measure the flux at the air-water interface. The chamber had a volume of 20-L and the area at the air-water interface was 0.164 m². During the 20-min monitoring process, the chamber was supported with floats on the water surface, and every 5-min a small sample volume was removed from the chamber and reserved for later analysis to determine the concentration of N2O in the air in the chamber. (Beaulieu et al. (2010) "Nitrous oxide emissions form a large, impounded river: The Ohio River" Environ. Sci. Technol. Vol 44:7527-7533.)

a. Assume the chamber can be treated as a well-mixed volume, and write a material balance expression describing the accumulation of N₂O within the chamber as a function of time.

b. Solve the partial differential equation you developed to obtain an equation describing the N₂O concentration in the chamber as a function of time.

c. Use appropriate information from the table below and from our text to define parameters for your model, and create a figure showing the N₂O concentration (14/L_air) in the chamber as a function of time over the range 0 ≤ t (h) ≤ 10.

d. Beaulieu et al. (2010) estimated the flux at the air-water interface from the following equation, where V_chamber is the chamber volume, A_chamber is the chamber area at the air-water interface, and ΔC/Δt is the slope of the N₂O concentration versus time curve developed from their first 20 min of sampling. Briefly describe how their approach compares with your model.

emission rate = Vchamber ΔC / A_chamber Δt

Table 1. Potentially helpful parameters for describing the flux of N₂O across the air-water interface.