I need all parts to this question answered please. Chromium is a toxic metal and

Question

I need all parts to this question answered please.

Chromium is a toxic metal and an essential nutrient. This is why chemistry is great. When it is Cr(VI) it is highly toxic and we make movies about it (see Erin Brockovich). When it is Cr(III) it is both easily removed from water and a trace nutrient. Microbes can reduce Cr(VI) to Cr(III) and we know it follows M-M kinetics. Unfortunately, Cr(III) can reduce Mn(III) to Mn(II) producing Cr(VI) again. Mn(III) is readily sourced in nature from the mineral birnessite. Birnessite will dissolve to Mn(III) and Mn(IV) compounds. Let’s use the approximate formula of NaMn2O4 for birnessite. Let’s assume the speciation of all the dissolved phases are Mn3+, Mn2+, CrO42-, Cr3+. Let’s say the OM substrate for the microbial reaction is acetate. The residual Mn(IV) becomes the solid MnO2.

a. There are three chemical equations discussed above. Birnessite dissolution to Mn3+ and MnO2(s), Microbial reduction of CrO42- with acetate to Cr3+ and bicarbonate, and Mn3+ oxidation of Cr3+ to CrO42- and Mn2+. Write all three balanced equations.
b. What are the three kinetic expressions?
c. Let’s say your big concern is Cr(VI). Generate a function for CrO42- at any time t.
d. Now if Na+, pH, and acetate are all constant , and Mn3+ is always at
equilibrium with birnessite (less likely but not impossible), what type of kinetic
expression can you write for CrO42-?
e. What is that simplified expression?

Explanation / Answer

a) Cr (VI) to Cr (III)

on from +6 to +3:

For the reduction from +6 to +3:

Cr2O7 -2 + 14 H+ + 6e- --------------------> 2 Cr+3 + 7 H2O

CrO4 -2 + CH3COOH -------------------------> 2H2CO3- + Cr+3

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