EGC 2nd Homework
1.
Due: Feb 24, 2012
Temperature can have an effect on equilibrium constants. This can be an important consideration for deep
groundwaters or industrial waste streams that have elevated temperatures. The relationship between T and K is
described by the following equation:
d ln K ΔH°
=
dT
RT2
A.
Integrate this differential so that you can calculate K2 given T2, K1, and T1.
B.
Using the thermodynamic data given below, graph the pH of pure water for temperatures between 10˚C and
75˚C, using the reaction given below. Assume that the activity of H2O(l) is 1 at both temperatures and that
∆H˚ is constant over this temperature range.
H2O(l) = H
∆Hf˚ (H2O) = -285.83 kJ mol
C.
-1
-
+ OH (aq)
∆Hf˚
Kw = 1x10
+
(H (aq))
= 0 kJ mol
-1
-14
at STP
-
∆Hf˚ (OH (aq)) = -230.0 kJ mol
-1
Using the thermodynamic data given below, graph the log Keq for the dissolution of lead carbonate, PbCO3
for temperatures between 10˚C and 75˚C, using the reaction given below. Assume that the activity of
PbCO3(s) is 1 at all temperatures.
PbCO3(s) = Pb
∆Hf˚ (PbCO3) = -1207.4 kJ mol
2.
+
(aq)
2+
(aq)
-1
+ CO3
2-
-9
K = 3.80 x 10 at STP
(aq)
2+
-1
2-
∆Hf˚ (Pb ) = -542.83 kJ mol ∆Hf˚ (CO3 ) = -677.1 kJ mol
2-
-5
-1
-3
A typical activity range for oxalate anion (C2O4 ) is 5x10 to 1x10 in soils and aquifers with high microbial
activity. Given the reaction:
+
2-
1/4 O2(g) + H (aq) + 1/2 C2O4 (aq) = CO2(g) + 1/2 H2O(l) log K = 31.5
calculate the oxalate activity in equilibrium with PO2 = 0.02 atm, PCO2 = 0.032 atm, and pH 6. Compare the
results of the calculation and the representative numbers given above. In a few sentences describe why these
numbers are different.
3.
The cation exchange capacity (CEC) of vermiculite or smectite is largely a result of their layer charge (permanent
-1
charge). In units of cmol kg :
CEC = (x/Mr) * 10
5
where x is the layer charge, and Mr is the relative molecular mass of the clay mineral. Using this equation,
calculate the CEC for vermiculite and smectite. Include in your answer the chemical formula you are using for
each of the phyllosilicates.
4.
Through a titration experiment, it is found that the net proton surface charge density (σH) of a soil humus sample
can be described mathematically by the equation:
σH =
-1
-1
Β1Κ110 −pH
Β Κ 10 −pH
+ 2 2
−C
1 + Κ110 − pH 1 + Κ 2 10 −pH
-1
4.7
9.2
where C= 8.0 molckg , B1= 6.0 molckg , B2= 2 molckg , K1=10 , and K2=10 .
A.
Construct a graph that shows the variation in σH with pH.
B. Comment on the following statement (do you think its is true or not, and why): the titration curve of soil
humus (such as humic or fulvic acid) resembles the titration curve of a polyprotic acid. This indicates that
soil humus is a polyelectrolyte and has multiple acidic functional groups of varying pKa.
EGC 2nd Homework
5.
Due: Feb 24, 2012
Acid soils and groundwater systems often are toxic due to high available Al. One possible remediation scheme
.
is to treat the soils or aquifer system with gypsum (CaSO4 2H2O). Assume a soil contains beidellite (a smectite)
with Al adsorbed to all of its exchange sites (Al-saturated beidellite):
Al0.3[Si7.5Al0.5][Al3.6Mg0.4]O20(OH)4
Develop a chemical equation that describes the reaction of gypsum and beidellite to form Ca-saturated beidellite
.
and jurbanite (AlOHSO4 5H2O). Make sure the equation you write is balanced. [Hint, you will need to include
0.45 moles of gypsum. You may also include water, H+, or OH- as needed.)
6.
The weathering of potassium feldspar to form kaolinite clay is an important weathering reaction, particularly in
humid climate soils. The reaction may be written:
KAlSi3O8 + H+ +
7.
9
1
H O = Al2Si2O5 (OH)5 + K + + 2H4SiO4
2 2
2
-0.9
A.
The equilibrium constant at 25C and 1 bar pressure is Keq = 10
constant expression.
B.
Assuming the concentration of potassium is [K ] = 2 x 10 mol/kg and the dissolved silica is [H4SiO4] = 2 x
-4
10 mol/kg in soil water, at what pH would feldspar be in equilibrium with the kaolinite, and, therefore, not
weather? Given that the pH of soil water in most humid climates is below 6.0, discuss the significance of
your answer.
+
. Write the corresponding equilibrium
-4
Calculate or find the ionic potentials of the metals in the following groups:
+
+
2+
2+
+
+
Cs > Rb > K > Na > Li
Ba > Sr > Ca
2+
> Mg
+
2+
The sequence of metals above show their adsorption selectivity, that is the ones that sorb the strongest to
minerals and organic matter to the ones which sorb the weakest. Comparing the metals within each group to
each other, provide an explanation for the sequence.
Plot the atomic number (x axis) versus ionic potential (y axis) of the elements K through Zn in row 4 and Rb
through Cd in row 5 of the periodic table. Describe any trends you observe. Use IP of the most oxidized cation
that the element forms. For instance, use the IP of K+ not K.
EGC 2nd Homework
Due: Feb 24, 2012
8. The following data were collected for the chemical analyses of four soil solutions after 10-6 M CuSO4 was added
to the soils during an experiment. Using the data below (which is given in pConc. (pC = -log [ ]), except for DOM
which is given in ppm), calculate the speciation for each soil using a geochemical speciation program with the
conditions given below. (Hint: molar site density of DOM = equivalents of charge / L)
•
•
•
•
•
•
•
soil temperature = 25 degrees Celsius
compute the ionic strength
fix the pH at the values given
there are no adsorption reactions (not too realistic for Cu)
the values given in the table are for total concentrations in molar units
allow solids to precipitate
DOM has a charge density of 10 meq/g OM. [Enter in DOM as the specie: DOM. Minteq will ask you
for the molar charge concentration which can be calculated by multiplying the charge density (in eq/g)
times the concentration in g/L].
Soil
Altamont clay loam
Arizo sandy loam
Domino silt loam
Redding sandy loam
pH
6.9
8.2
7.6
5.6
Ca
2.60
2.68
2.23
3.15
Mg
3.10
3.40
2.87
2.82
Na
3.00
2.96
2.72
2.55
K
3.22
3.22
2.89
3.40
Soil
Altamont clay loam
Arizo sandy loam
Domino silt loam
Redding sandy loam
DOM
27.1
12.3
15.9
32.1
Cu
6.00
6.00
6.00
6.00
CO3
2.70
3.00
2.52
2.68
SO4
2.60
2.54
2.82
2.17
Cl
3.00
2.68
3.22
2.92
A. What are the dominate species of Cu in each soil? Using the HSAB concept, explain the speciation results.
B. What Cu mineral(s) would precipitate from each of these solutions? Which soil precipitates the most Cu
solid?
C. In which soil would you predict the highest mobility for Cu, based on your speciation results?
9.
The solvation complexes, Fe(H2O)63+ and Hg(H2O)62+ can form complexes with halide ions. Below is
thermodynamic data at 298 K for the formation of these complexes.
Metal
Ligand
Fe(III)
F-
Fe(III)
Hg(II)
ClClBrI-
Hg(II)
Hg(II)
ΔG° (kJ mol-1)
-29.5
ΔS° (J mol-1K-1)
+131.5
-2.6
-38.5
+67.8
+52.0
-51.5
-73.2
+29.5
-7.0
A.
Use these data to calculate ΔH° for each of the complexes.
B.
Explain the differences in ΔH° based on the HSAB principles.