Homework answers / question archive / 1) (a) Calculate the free metal concentration and the concentration of significant inorganic complexes of nickel (Ni2+) and mercury (Hg2+) in freshwater at pH = 8

1) (a) Calculate the free metal concentration and the concentration of significant inorganic complexes of nickel (Ni2+) and mercury (Hg2+) in freshwater at pH = 8

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1) (a) Calculate the free metal concentration and the concentration of significant inorganic complexes of nickel (Ni²⁺) and mercury (Hg²⁺) in freshwater at pH = 8.1 with the following composition:

pH = 8.1

`               [SO₄^2-] = 10^-5 M

[Cl^-] = 10^-3 M

[Ni²⁺]_total = 10^-7 M

[Hg²⁺]_total = 10^-7 M

In your answer, consider the following species:

Ni(OH)^- logK₁ = 4.1

                Ni(OH)₂⁰                      logβ₂  = 9.0

                        Ni(SO₄) ⁰                      logK₁ = 2.3

Ni(Cl)^-                              logK₁ = 0.6

                       

                        Hg(OH)^-                        logK₁  = 10.6

                Hg(OH)₂⁰                     logβ₂  = 21.8

                Hg(SO₄)⁰              logK₁  = 2.5

Hg(Cl)^-                            logK₁  = 7.2

                Hg(Cl)₂⁰ logβ₂  =  14.0

(b) What properties characterize a soft metal? Which metal is softer, Ni²⁺ or Hg?

2) Citrate is a common metabolite produced by aquatic organisms that binds to divalent cations. Both Ca²⁺ and Fe²⁺ can form strong complexes with the citrate anion (C₆H₈O₇^3-).

Ca²⁺ + Cit^3- = CaCit^-; K₁ = 10^4.7

Fe²⁺ + Cit^3- = FeCit^-; K₁ = 10^13.5

Note that:

HCit^2- = H⁺ + Cit^3-; pK_a,3 = 6.3

Knowing that the rate constant for water exchange (k_-w) is 6e8 s^-1 for Ca²⁺ and 4e6 s^-1 for Fe²⁺, and that the stability constant for outer-sphere complexes (K_os) of a trivalent ligand with a divalent metal  (z_mz_l = -6) is 10^3.22,

a) Calculate the overall rate of formation (k_f) of the Ca²⁺ complex and Fe²⁺ complex in freshwater at a pH of 8.2 and 25°C.

b) Calculate the overall rate of dissociation (k_d) of the FeCit^- and CaCit^- complexes.

c) The overall rate of forming the metal-citrate complex is equal to the rate of formation minus the rate of dissociation:

dML/dt = kf[M²⁺][L^3-] – kd[ML^-]

You add 1e-4 M citrate to a solution containing 1e-7 M of Ca²⁺ and 1e-7 M of Fe²⁺. The solution has a pH of 8.2, so you can assume that all of the citrate starts out as the trivalent anion.

Make two separate plots of the concentration of [CaCit^-] and [FeCit^-] over time (an easy way to do this is to set up an excel sheet that iteratively calculates the change in [ML^-] and [M²⁺] given initial concentrations and a short time step. A good estimate of appropriate time step is one tenth of the half-life of the free metal). About how long does each reaction take to come to equili

3) A chemical dye manufacturing company buried a drum containing methanol waste in the ground next to the factory. After decades, the drum has now been breeched and methanol is leaking into the surrounding watershed, reaching concentrations of 10 mM. The groundwater next to the drum is at pH= 7, Pco₂ = 10^-1.5 atm, is anoxic, contains amorphous iron hydroxide (Fe(OH)_3(s)) as a major mineral, and is inhabited by the soil bacteria Shewanella putrefaciens, an iron reducing bacteria that can oxidize organic carbon into CO₂ by converting Fe³⁺ into Fe²⁺. The concentration of dissolved Fe²⁺ is limited by the precipitation of FeCO₃(s) (Ksp = 10^-10.7), and can be estimated to be 9e-6 M in this system. You want to determine whether Shewanella can naturally remediate the methanol spill.

The relevant half reactions are:

1/6 CO_2(g) + H⁺ + e^- = 1/6 CH₃OH_(aq) + 1/6 H₂O                        pe⁰ = +0.5

Fe(OH)_3(s) + 3H⁺ + e^- = Fe²⁺ + 3H₂O                                            pe⁰ = +16.0

a) Calculate the pe of each half reaction.

b) Write a balanced equation for the overall reaction

c) Calculate the ΔG of the overall whole reaction

d) Is it thermodynamically favorable for Shewanella to oxidize methanol under these conditions?

e) There are similar tanks buried around the watershed, some of which are within soils containing alkaline minerals that significantly raise the groundwater pH. At what pH is it no longer thermodynamically favorable for Shewanella to degrade the methanol?