|
CEE
680 |
|
Fall
2011 |
Water
Chemistry
Homework Set #7
Problem #1 (1 point)
1.
Nickel forms a series of complexes with aqueous ammonia. Draw a set of alpha curves (vs log[ NH3
]) for the Nickel Ammonia system. Use
the following stability constants (determined from Smith & Martel; Vol.4,
pg.40). Include also an n-bar curve.
|
|
Log K1 = 2.72 |
|
|
|
Log |
|
|
|
Log K3 = 1.66 |
|
|
|
Log K4 = 1.12 |
|
|
|
Log K5 = 0.67 |
|
|
|
Log K6 = -0.03 |
|
Solution to #1
I
would use a spreadsheet program to develop alpha curves, and plot them using
the same spreadsheet or some other graphics software (I used SigmaPlot). Probably the first step is to determine the
various overall beta constants:
|
Constants |
Log(Step-wise
"K") |
Log(Overall
"Beta") |
|
1st |
2.72 |
2.72 |
|
2nd |
2.17 |
4.89 |
|
3rd |
1.66 |
6.55 |
|
4th |
1.12 |
7.67 |
|
5th |
0.67 |
8.34 |
|
6th |
-0.03 |
8.31 |
Next
we can apply the complexation equations that are based on the beta's and the
free ligand concentration.
and
and
where
"M" is Nickel (Ni), and "L" is ammonia (NH3).
Problem #2 (2 points)
2.
Determine the species composition of a solution containing 10 mM total nickel
and 30 mM total ammonia. Assume that the
solution is buffered at pH 10.3. Then
discuss the assumptions you might have made, and how changes in pH might affect
this system.
Solution to #2
To
solve this specific problem, we need to use the general alpha graph prepared in
#1. In addition we have to calculate the
mass-balance-based n-bar curve that is specific to these concentration
constraints.
This
line has been plotted in the graph for problem #1. The intersection with this n-bar curve with
the original n-bar curve (the one based only on the equilibrium constants)
gives the equilibrium condition. This is
indicated by a vertical line. The
intersection of this line with all alpha's and with the x-axis gives us the
concentration of the various species.
Careful inspection of the spreadsheet reveals:
intersection |
value |
species |
concentration (M) |
|
x-axis |
-1.965 |
NH3 |
0.0108 |
|
alpha-0 |
0.0476 |
Ni |
4.7E-04 |
|
alpha-1 |
0.2708 |
NiNH3 |
2.7E-03 |
|
alpha-2 |
0.4342 |
Ni(NH3)2 |
4.3E-03 |
|
alpha-3 |
0.2151 |
Ni(NH3)3 |
2.2E-03 |
|
alpha-4 |
0.0307 |
Ni(NH3)4 |
3.1E-04 |
|
alpha-5 |
0.00156 |
Ni(NH3)5 |
1.6E-05 |
|
alpha-6 |
1.57E-05 |
Ni(NH3)6 |
1.6E-07 |
The
pH is important, because it will affect the ammonia speciation, and possibly
the formation of Nickel hydroxides. Since
ammonia has a pKa of 9.3, nearly all of the unbound (by Nickel) ammonia will be
in the uncharged form. This is the form
that complexes with Nickel. As a result,
protonation of ammonia does not appreciably affect the accuracy of our
calculations. However, if we had tried
to solve this problem for a lower pH, say 8.3, then we would have had to
consider the NH4+ species explicitly. This becomes a more complex problem, which is
probably best solved with a program such as MINEQL. Nevertheless, we can be certain that at lower
pH, there would be a lower equilibrium concentration of NH3, and
less complexation of Ni by ammonia. Its
also clear that there would be more free Ni as the pH dropped.
Problem #3 (2 points)
3.
Using MINEQL prepare a Log Concentration vs pH graph for the copper NTA problem
solved in class. But this time assume a
total concentration of 10-3 M for copper and 10-2.7 M for
NTA. Show the same three species I
plotted on my graph, and use the same axis range. Are there differences between your graph and
mine? Explain. Prepare a second graph, but this time show
other important soluble species and label them.
(Note: for this problem, I would refer you to your earlier notes on MINEQL as well as pages 4-12 through 4-14 in the Version 3.0 MINEQL manual, and similar sections in the v 4.5 manual. Treat this as a pH titration of a system containing Cu and NTA. Note that since we’re imposing a pH, it will remain as a Type III species. MINEQL treats a pH variable run as a “titration” where the “logK of pH” is allowed to vary over a fixed range (0-14). Allow MINEQL to form all of the species for which it has equilibrium constants. You may want to save the “Multi”, and “S2” files so that you can import them into your favorite graphics or spreadsheet package. I used Sigmaplot.)
Solution #3
The
following graphs are from a "titration" multiple run with
MINEQL. The LogK for pH was varied from
0 to 14, with 70 points collected. These
were saved and entered into a SigmaPlot file for graphing.
Small
differences are evident in comparing these graphs with those presented in
class. Evidently, the higher total NTA
in this problem depresses the free copper concentration. For example, the copper and copper-NTA lines
intersect nearly a pH unit lower with this example. Furthermore, at pH 7, the free copper is
about 3 orders of magnitude below where it was in the problem solved in
class. This is due to the thousand-fold
higher concentration of trivalent NTA at this pH.
In
general, all copper species without NTA are depressed in concentration. The copper species with two NTA's is at a
substantially elevated concentration.
Another
observation is the unusual and changing slopes of many of these lines. This underscores the complexity of a system
with so many soluble and insoluble species.
Systems with a few species are easy to solve by hand, and easy to
visualize. Those with larger numbers of
species really require a computer.
