ENVIRONMENTAL GEOCHEMISTRY,
Α. ΑRGΥRAKI, UNIVERSITY OF ATHENS 2013
EXERSISE 2: OPEN SYSTEMS AND KINETICS
1. Consider an element X exchanging between two geochemical reservoirs A and B.
Let Ma and Mb be the masses of X in reservoirs A and B, respectivel y; let ta and tb
be the residence times of X in reservoirs A and B, respectively. Further let M
=Ma+Mb be the total mass of X in the two reservoirs combined.
(a) Show that at steady state, Ma = M/ (1 + [ta/tb])
(b) In the limit ta>> tb what controls the value of Ma?
2. A stream (5000 m 3 /day) enters a pond (1000m 3 ) situated above a mine -tailings
pile. The tailings pile contains the mineral cerussite (PbCO 3 ) which is found to
dissolve with a rate law: Rdiss= kA(Cs -C) with k = 0.2/ m 2 -day. Cs is the saturation
concentration of PbCO 3 which at the pH of the pond, is 15.0 mole/ m 3 . A is the
surface area of exposed cerussite which is estimated to be at total of 1 m 2 in the
pond. The outflow stream from the pond has a flow rate of 5000 m 3 / day.
Set up a simple box model for the situatio n and calculate the steady-state
concentration of Pb 2 + in the pond. How does it compare with the equilibrium
saturation concentration? What is the residence time of dissolved Pb in the pond?
3. A sewage inflow with total dissolved organic carbon of 25 mg C/ kg-water enters
a pond that contains 10000 kg water. The inflow rate of the sewer is 100 kg -water/
day. Respiration in the lake occurs with a rate constant of 0.02/ hour. Water leaves
the lake at a rate of 300 kg/ day (the volume of the lake is constant , however due to
input by rain and other streams). What will be the steady state concentration of
dissolved organic carbon in the water?
1
ENVIRONMENTAL GEOCHEMISTRY,
Α. ΑRGΥRAKI, UNIVERSITY OF ATHENS 2013
EXERCISE 3: AQUEOUS GEOCHEMISTRY – pH AS CONTROLLING
FACTOR OF CARBON SPECIATION IN WATER
Carbon dissolved in natural waters can occur as three possible species H 2 CO 3 ,
HCO 3 - and CO 3 2 - . The specie that is present has a strong effect on how carbon
behaves in the carbon cycle, and affects such issues as the greenhouse effect. The
acidit y of natural waters can affect the speciation of carbon. For example between
1930 and 1975 the median pH of the lakes in the Adirondack Mountains in NE USA
decreased from 6.7 to 5.1.
Draw a diagram showing the % variation of each carbon specie (y axis) with
changing pH (x axis). Use the equilibrium constants for the dissociation of
carbonic acid: K a 1 =4.2x10 - 7 and K a 2 = 5.0x10 - 1 1 .
Answer the questions:
1. Write the equation for the first dissociation constant (Ka1). What does the value of Ka1 indicate about
the strength of carbonic acid?
2. Write the equation for the second dissociation constant (Ka2). What does this value indicate about
how easily the second proton is lost from carbonic acid?
3. From the drawn diagram what is the proportion of the carbon species at the pH of the lakes in 1930
and 1975?
4. Comment on the change in proportions over this time. What is the percentage change for HCO3-?
5. What would you predict that dominant form of dissolved carbon would be in sea water?
6. What are the assumptions upon which the use of these calculations depend?
2
ENVIRONMENTAL GEOCHEMISTRY,
Α. ΑRGΥRAKI, UNIVERSITY OF ATHENS 2013
EXERCISE 4: STATISTICAL TREATMENT OF GEOCHEMICAL DATA
1.
Arsenic concentration (ppm) was measured in n = 22 soil samples. Calculate
the descriptive statistics of the data set (mean, median, range, standard
deviation, variance ) and plot a histogram of the data. Is the statistical
distribution of As normal in the study area? 17.7, 17.4, 22.8, 35.5, 28.6, 17.2,
19.1, <4, 7.2, <4, 15.2, 14.7, 14.9, 10.9, 12.4, 12.4. 11.6, 14.7, 10.2, 5.2, 16.5,
8.9.
2.
Test the hypothesis that n = 14 concentration data of As in soil have a normal
distribution, by creating a probabilit y plot (x: concentration, y: (%) cumulative
frequency). As (ppm): 5, 6, 7, 7.5, 8, 8.5, 9, 9.5, 10, 10.5, 11, 11.5, 12, 13.
3.
Comment on the statistical data given below for Pb (ppm) in soil from an area
in SE Chalkidiki. Mention t ype of distribution and geochemical background
concentration of Pb. Given the global mean Pb concentration in soil is 17 ppm
(Levinson, 1980), explain the reason of the wide discrepancy between this
value and the calculated local geochemical background. In addition to
geochemical data what other information would be useful in order to
Statistics
discriminate between naturalDescriptive
and anthrop
ogenic soil contamination?
Variable: Pb
Anderson-Darling Normality Test
A-Squared:
P-Value:
0
1000
2000
3000
4000
5000
Descriptive Statistics
95% Confidence Interval for Mu
9.899
0.000
Mean
StDev
Variance
Skewness
Kurtosis
N
526.382
815.331
664765
4.03662
18.5532
65
Minimum
1st Quartile
Median
3rd Quartile
Maximum
37.70
161.50
295.00
495.50
5060.00
95% Confidence Interval for Mu
Variable:
324.35
200
300
400
500
600
700
log_Pb
728.41
95% Confidence Interval for Sigma
695.30
985.84
Anderson-Darling
Normality
Test
95% Confidence Interval for Median
A-Squared:
230.21
P-Value:
95% Confidence Interval for Median
1.5
1.9
2.3
2.7
3.1
3.5
95% Confidence Interval for Mu
0.454
359.69
0.262
Mean
StDev
Variance
Skewness
Kurtosis
N
2.48038
0.42384
0.179636
0.527636
0.678002
65
Minimum
1st Quartile
Median
3rd Quartile
Maximum
1.57634
2.20807
2.46982
2.69504
3.70415
95% Confidence Interval for Mu
2.37536
2.4
2.5
2.6
2.58540
95% Confidence Interval for Sigma
3
ENVIRONMENTAL GEOCHEMISTRY,
Α. ΑRGΥRAKI, UNIVERSITY OF ATHENS 2013
EXERCISE 5: EVALUATION OF STATISTICAL DATA OF
ENVIRONMENTAL GEOCHEMISTRY – THE IMPORTANCE OF SAMPLING
In the frame of an environmental geochemical research aiming at the determination
of suitabilit y of land use in relation to the content of heavy metals in soil, sampling
and anal ysis of surface soil samples (0 -15 cm) took place in a field of dimensions
180x170m. The geology of the area includes sandstones and clay schists. In the
area, primitive installations of lead smelting w ere operated during the past (1300 1550 a.C.) which constitute potential source of soil pollution. At the recent
history, the field is used as pasture land, without any other anthropogenic activities
(e.g cultivation).
The research focused on the determ ination of concentrations of lead and copper in
the soil. Information deriving from the bibliography concerning the normal and
toxic levels of concentrations of the two elements is given in Table 1. Two
sampling trials were conducted in which soil samples were collected as below:
based on a regular grid 20x20m with collection of bulk samples of mass 500g at
each point of the grid
based on a regular grid 20x20m with collection of bulk samples of mass 2500g at
each point of the grid (composite bulk sample fro m surface of area 1m2 around
each point of the sampling grid).
In both cases, duplicate samples were collected at some of the sampling points and
in distance 2m away from the initial points. These samples were chemicall y
anal ysed in duplicate aiming at th e statistical anal ysis of variance of the values
(ANOVA) and the separation of geochemical variance from the variance that is due
to random errors during the sampling and chemical anal ysis. The anal ytical
methodology was common for all the samples and the anal ytical technique that was
used was ICP -AES. The descriptive statistics for the populations of Cu and Pb in
the soil samples as well as the results of ANOVA are given in Table 2.
Questions
1. Do you observe any differences in the geochemical distributio n of Cu and Pb
in the soil? How would you characterize the field in regard to pollution by
the two heavy metals?
2. Calculate the uncertaint y of measurements (smeas) for each metal and each
sampling protocol, as well as the relevant reliabilit y (U%). How do y ou
evaluate the qualit y of the results for each metal concerning the random
errors during the collection of samples and the chemical anal ysis?
3. Comment on how the increase of mass of the bulk sample influenced the
reliabilit y of the measurements for each m etal. Where do the differences that
you observed come from?
4. Which of the two sampling protocols would you propose for further research
of determination of the concentrations for each metal in this particular field
and why?
4
ENVIRONMENTAL GEOCHEMISTRY,
Α. ΑRGΥRAKI, UNIVERSITY OF ATHENS 2013
5.5
5.7
Limit of
toxicity in
gardens/cultur
es
Limit of
toxicity in
In parks/open
spaces
13
24
Clay
Schists
90
3
Sandstones
Granitic
rocks
42
14
Limestones
Βαsic
rocks
Cu 50
Pb 14
Ultrabasic
rocks
Earth’ s crust
Element
Table 1: Typical concentrations in rocks and limits of toxicit y of concentrations in
soil for the elements Cu and Pb in μg g -1 (Sources: Alloway, 1990; UK
Department of the Environment, 1987).
30
10
39
23
130
500
130
2000
Table 2: Descriptive statistics for Cu and Pb and results of ANOVA from duplicate
samples and duplicate anal yses in the study area (Source: Argyraki, A., PhD
Thesis, 1997).
Statistical Parameter
Cu
Pb
First way of sampling (bulk sample 500 g)
Number of samples
40
40
Mean (μg g-1)
26.9
6046
Median (μg g-1)
25.7
3915
Standard Deviation (μg 5.3
5321
g-1)
ANOVA
Number of duplicate
Number of duplicate
samples: 7
samples: 7
Mean: 26.1
Mean: 7515.9
Sgeochem = 2.343
Sgeochem = 7968.633
Ssamp = 3.339
Ssamp = 1864.781
Sanal = 0.613
Sanal = 157.621
Stotal = 4.124
Stotal = 8185.436
Second way of sampling (bulk sample 2500 g)
Number of samples
40
40
Mean (μg g-1)
27.4
6322
Median (μg g-1)
26.1
4320
Standard Deviation(μg
4.9
5633
g-1)
ANOVA
Number of duplicate
Number of duplicate
samples: 9
samples: 9
Mean: 26.5
Mean: 6093.2
Sgeochem = 2.947
Sgeochem = 5520.622
Ssamp = 2.392
Ssamp = 930.843
Sanal = 0.696
Sanal = 134.599
Stotal = 3.859
Stotal = 5600.165
5
ENVIRONMENTAL GEOCHEMISTRY,
Α. ΑRGΥRAKI, UNIVERSITY OF ATHENS 2013
EXERCISE 6: EVALUATION OF STATISTICAL DATA –
GEOCHEMICAL MAPPING
Garden soil and house dust samples were collected during an environmental
geochemical research aiming at assessing the health risks due to Pb exposure in a
mining village. An ore mill factory is operating in the village for processing mixed
sulfide ore to produce finel y grained (< 200 μm) galena and sphalerite
concentrates. The concentrates are piled within the factory area before they are
shipped to a smelter. The soil and dust sampling locations are presented in the
attached maps and the Pb concentrations in soil and dust are presented in Table 1.
Questions
1. Calculate the descriptive statistics of Pb in the two sampling media (mean,
median, minimum, maximum, standard deviation).
2. Draw the appropriate graphs to help you describe the geochemical population
of Pb in soil and house dust.
3. Based on your answers in 1, 2, split the Pb data values in categories (low,
medium, high) and show them on the maps.
4. Draw two graphs showing the Pb concentration as a function of distance from
the ore mill factory for the two sam pling media. From these graphs and your
maps in question 3 can you indicate a possible source of Pb? Comment on
your results with respect to health risks from exposure to Pb bearing in mind
that concentrations above 500 ppm are considered toxic. Which of t he two
sampling media do you think is the most significant hazard for the people
living in the village?
Table 1: Concentrations of Pb in soil and dust samples.
Soil
Pb
Dust
Pb
Soil
Pb
Dust
Pb
sample (mg/kg) sample (mg/kg) sample (mg/kg) sample (mg/kg)
SD4
1224
DD4
988
SJ4
1353
DJ4
3606
SD6
1240
DD6
986
SJ5
959
DJ5
1155
SE4
765
DE4
798
SJ6
2042
DJ6
973
SE5
858
DE5
1145
SK2
1313
DK2
2115
SE6
988
DE6
922
SK3
1614
DK3
847
SE7
753
DE7
458
SK4
1714
DK4
1669
SF5
1305
DF5
737
SK5
1415
DK5
2699
SF6
1058
DF6
721
SK6
927
DK6
3062
SG2
1346
DG2
1028
SB10
180
SG3
124
DG3
390
SB3
942
SG4
797
DG4
1108
SB4
215
SG4-1 1179
DG4-1 660
SB9
499
SG5
1037
DG5
661
SD10
830
SH3
1036
DH3
873
SE10
799
SH4
1167
DH4
708
SF2
1794
SH5
977
DH5
643
SF8
867
SH7
1083
DH7
632
SH10
1267
SI2
1386
DI2
4524
SH2
982
SI5
814
DI5
6917
SI3
1386
SI6
776
DI6
2524
SJ10
1209
SJ2
1512
DJ2
1253
SJ3
1435
SJ3-1
1407
DJ3-1 5014
SJ9
1848
6
ENVIRONMENTAL GEOCHEMISTRY,
Α. ΑRGΥRAKI, UNIVERSITY OF ATHENS 2013
7