In a chemical reaction mechanism that involves a reactive intermediate, how long do we have to wait to make a steady state approximation?
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CE 5333 Aquatic Geochemistry Homework 1 Due: February 7, 2020
1. In a chemical reaction mechanism that involves a reactive intermediate, how long do we have
to wait to make a steady state approximation? Let’s consider the example of a consecutive
reaction for the degradation of the pesticide: ethylene dibromide (EDB).
a. Use the steady-state approximation to predict the concentration of products as a function of time assuming an initial EDB concentration of 1 mM. Plot your results for up to 150 minutes.
b. Compare your results from (a) with the exact solution for the time-dependent product concentration. Plot this exact solution on your graph from part (a).
c. How long do you have to wait until the steady state approximation for VB yields results that are within 1% of the exact solution?
d. For a general case of a consecutive reaction like the one depicted above, derive an
expression that relates the rate constants to the characteristic time needed to reach steady
state. (You may simplify your expression for cases when k2>>k1).
2. Hexavalent chromium, Cr(VI) , is a metal that is used for metal plating, wood preservation
and corrosion inhibition. The improper disposal of industrial wastes in recent decades has led
to Cr(VI) contamination in drinking water aquifers.
At the pH of natural waters, Cr(VI) can exist in two major forms: the chromate anion CrO4
2-
and the dimer compound Cr2O7
2-
.
(a) A groundwater sample contains 10 µM CrO4 2- and 10 µM Cr2O7 2- at pH 8, 25°C. What is the total molar concentration of chromium in the water?
(b) Write a balanced chemical equation describing the transformation from CrO4
2- to the
dimer compound Cr2O7
2-
. Choose the reactants and products of your equation from the
table below:
