CEE 572 |
1 November 2000 |
Open book, open notes
Answer all three (3) sets of
questions:
I. (20%) Choose the piece of
laboratory glassware, equipment, apparatus, or component that is the best
choice, and place the letter from below in the appropriate box:
1 |
Container for weighing 0.1
mg of a chemical |
V. |
2 |
Glassware for starting and
stopping the flow of a titrant solution in a burette |
T |
3 |
Measurement of exactly 1
liter |
U |
4 |
Vessel for dissolving a
sparingly soluble solid in water |
B |
5 |
Labware for measurement of
exactly 1.00 mL |
O |
6 |
Labware for fast
measurement of 42 mL |
M |
7 |
Glassware used for adding
a titrant during volumetric analysis |
C |
8 |
Equipment for comparison
of standard with sample based on a gravimetric analytical procedure |
A |
9 |
Component on a specific
ion electrode that is most often responsible for errors |
Q |
10 |
Labware for storage of a
volatile or corrosive sample |
K |
A. Analytical balance
B. Beaker with graduations
C. Buret
D. Buret stand
E. Coaxial cable
F. Erlenmeyer flask
G. Evaporating dish
H. Filling Solution
I. Filter flask
J. Glass membrane
K. Glass-stoppered reagent bottle
L. Glass fiber filter
M. Graduated cylinder
N. Incubator
O. Pipet
P. Pipet bulb
Q. Porous plug
R. Reference electrode
S. Spectrophotometer
T. Stopcock
U. Volumetric flask
V. Weighing paper
W. Weighting tray
X. Vacuum pump
II.
(45%) You've just prepared a solution by dissolving 20 mg sodium sulfide (Na2S),
and 30 mg potassium sulfate tetrahydrate (K2SO42H2O) in 1 Liter of distilled water.
1.
What is the theoretical TDS of this solution?
2.
What is the concentration of total sulfur in this solution in mg/L?
3.
What is the concentration of reduced sulfur (i.e., S(-II)) in this solution in
mg/L?
4.
What is the ionic strength of this solution?
5. If
your analytical balance is accurate to 0.001 g (i.e., this is the standard
deviation of a single measurement), what is the 95% confidence interval for
your estimate of the total sulfur concentration?
6.
Calculate the expected specific conductance of a solution containing only the
30 mg/L potassium sulfate tetrahydrate based on ideal behavior (i.e., no effect
of ionic strength).
Assemble essential data:
|
Atomic Wt |
ionic cond. |
Na |
22.99 |
50.1 |
S |
32.06 |
|
K |
39.1 |
73.5 |
O |
16 |
|
H |
1.01 |
|
OH |
|
198 |
SO4 |
|
79.8 |
Calculate molar quantities
and percentages
|
|
Amount Added |
|
|
|
|
|
|
GFW |
|
mg |
s.d. |
mMoles |
s.d. |
%water |
%Sulfur |
%S(-II) |
78.04 |
Na2S |
20 |
1 |
0.256279 |
0.013 |
0.00% |
41.08% |
41.08% |
210.3 |
K2SO4 2H2O |
30 |
1 |
0.142653 |
0.005 |
17.14% |
15.24% |
0.00% |
Answers:
1) |
TDS = |
44.86 |
mg/L |
|
|
2) |
Tot S = |
12.79 |
mg-S/L |
|
|
3) |
Tot S(II) = |
8.22 |
mg-S/L |
|
For problem #4, it is by far
most accurate to use the known ionic composition along with the defining
equation for ionic strength:
4) |
I = |
1.197E-03 |
|
|
|
For question #5 we can treat
the cited standard deviation as a know property of the entire population of
replicate measurements. This is because
it was probably determined after comparing very large numbers of repeated
weighings (possibly by the balance manufacturer or by a QC group). For this reason, the appropriate t statistic
would be selected from those with an infinite number of degrees of freedom.
5) |
s.d. for Tot S |
0.0137 |
M |
|
|
|
s.d.*t95% |
0.0268 |
M |
|
|
|
range = |
0.3721 |
to |
0.4257 |
M |
|
range = |
11.93 |
to |
13.65 |
mg-S/L |
For problem #6, it is
important to use the known ionic composition along with the equivalent ionic
conductances:
6) |
K = |
43.74 |
umho/cm |
|
III.
(35%) Imagine that you've been asked to
measure nickel concentrations in a contaminated groundwater. Your laboratory is poorly equipped, however
you do have some simple glassware, an analytical balance, and a burette. You decide that you can used EDTA as a
titrant and determine nickel concentrations using a volumetric method. You also have some dimethylglyoxime which
specifically complexes nickel giving a bright red compound. Describe how you would measure nickel using
these compounds and equipment. Comment
on the EDTA titrant concentration you would use, if you’re trying to measure
nickel in the 0-10 mg/L range. Also
discuss possible interferents, why they would cause interference, how you might
determine which species interfere and how you might overcome this problem. This discussion should include anticipated
sources of error.
Use dimethylglyoxime as an indicator for your EDTA
titration of nickel. This should be
done at high pH so that the fully deprotonated EDTA is substantial
inconcentration, but no so high as to cause excessive nickel hydroxide
precipitation. When the bright red
color disappears, you can be sure that all of the Ni has been complexed by the
EDTA. If the Ni concentration ranges
from 0-10 mg/L (e.g., 0-0.17 mM) and your titrating a 100 mL volume, a good
concentration for the titrant would be about 0.5 mM. This would require titrant volmes from 0 to 34 mL, which is
conventient for a 50 mL buret.
Standards would be prepared from pure nickel salts (e.g., nickel chloride) that were weighed and dissolved in high-purity water. These could be titrated in the same manner as the samples and an empirical standard curve could be prepared.
Interference will result from any metals that bind
with EDTA as strongely or more strongly than Ni. You could overcome this problem by removing these metals prior to
analysis. Options for this include:
Alternatively, you could analyze for these interfering metals separately, and then subtract their molar concentrations from the measurement for nickel plus interferents. This would require that you know what the interfering metals are and that you have an independent method for estimating the concentration of these interfering metals.
Interference will also result from metals which bind with methylglyoxime to produce a red color. These will also have to be removed prior to analysis.
Sources of error would include the following:
Properties of the Stable Elements[1]
Element |
Symbol |
Atomic # |
Atomic Wt. |
Valence |
Electronegativity |
Aluminum |
Al |
13 |
26.98 |
3 |
1.47 |
Antimony |
Sb |
51 |
121.75 |
3,5 |
1.82 |
Argon |
Ar |
18 |
39.95 |
0 |
|
Arsenic |
As |
33 |
74.92 |
3,5 |
2.20 |
Barium |
Ba |
56 |
137.34 |
2 |
0.97 |
Beryllium |
Be |
4 |
9.01 |
2 |
1.47 |
Bismuth |
Bi |
83 |
208.98 |
3,5 |
1.67 |
Boron |
B |
5 |
10.81 |
3 |
2.01 |
Bromine |
Br |
35 |
79.91 |
1,3,5,7 |
2.74 |
Cadmium |
Cd |
48 |
112.40 |
2 |
1.46 |
Calcium |
Ca |
20 |
40.08 |
2 |
1.04 |
Carbon |
C |
6 |
12.01 |
2,4 |
2.50 |
Cerium |
Ce |
58 |
140.12 |
3,4 |
1.06 |
Cesium |
Cs |
55 |
132.91 |
1 |
0.86 |
Chlorine |
Cl |
17 |
35.45 |
1,3,5,7 |
2.83 |
Chromium |
Cr |
24 |
52.00 |
2,3,6 |
1.56 |
Cobalt |
Co |
27 |
58.93 |
2,3 |
1.70 |
Copper |
Cu |
29 |
63.54 |
1,2 |
1.75 |
Dysprosium |
Cy |
66 |
162.50 |
3 |
1.10 |
Erbium |
Er |
68 |
167.26 |
3 |
1.11 |
Europium |
Eu |
63 |
151.96 |
2,3 |
1.01 |
Fluorine |
F |
9 |
19.00 |
1 |
4.10 |
Gadolinium |
Gd |
64 |
157.25 |
3 |
1.11 |
Gallium |
Ga |
31 |
69.72 |
2,3 |
1.82 |
Germanium |
Ge |
32 |
72.59 |
4 |
2.02 |
Gold |
Au |
79 |
196.97 |
1,3 |
1.42 |
Hafnium |
Hf |
72 |
178.49 |
4 |
1.23 |
Helium |
He |
2 |
4.00 |
0 |
|
Holmiuum |
Ho |
67 |
164.93 |
3 |
1.10 |
Hydrogen |
H |
1 |
1.01 |
1 |
2.20 |
Indium |
In |
49 |
114.82 |
3 |
1.49 |
Iodine |
I |
53 |
126.90 |
1,3,5,7 |
2.21 |
Iron |
Fe |
26 |
55.85 |
2,3 |
1.64 |
Krypton |
Kr |
36 |
83.80 |
0 |
|
Lanthanium |
La |
57 |
138.91 |
3 |
1.08 |
Lead |
Pb |
82 |
207.19 |
2,4 |
1.55 |
Lithium |
Li |
3 |
6.94 |
1 |
0.97 |
Lutetium |
Lu |
71 |
174.97 |
3 |
1.14 |
Magnesium |
Mg |
12 |
24.31 |
2 |
1.23 |
Manganese |
Mn |
25 |
54.94 |
2,3,4,6,7 |
1.60 |
Properties of the Stable Elements
Element |
Symbol |
Atomic # |
Atomic Wt. |
Valence |
Electronegativity |
Mercury |
Hg |
80 |
200.59 |
1,2 |
1.44 |
Molybdenum |
Mo |
42 |
95.94 |
3,4,6 |
1.30 |
Neodymium |
Nd |
60 |
144.24 |
3 |
1.30 |
Neon |
Ne |
10 |
20.18 |
0 |
1.07 |
Nickel |
Ni |
28 |
58.71 |
2,3 |
1.75 |
Niobium |
Nb |
41 |
92.91 |
3,5 |
1.23 |
Nitrogen |
N |
7 |
14.01 |
3,5 |
3.07 |
Osmium |
Os |
76 |
190.2 |
2,3,4,8 |
1.52 |
Oxygen |
O |
8 |
16.00 |
2 |
3.50 |
Palladium |
Pd |
46 |
106.4 |
2,4,6 |
1.39 |
Phosphorus |
P |
15 |
30.97 |
3,5 |
2.06 |
Platinum |
Pt |
78 |
195.09 |
2,4 |
1.44 |
Potassium |
K |
19 |
39.10 |
1 |
0.91 |
Praseodymium |
Pr |
59 |
140.91 |
3 |
1.07 |
Rhenium |
Re |
75 |
186.2 |
|
1.46 |
Rhodium |
Rh |
45 |
102.91 |
3 |
1.45 |
Rubidium |
Rb |
37 |
85.47 |
1 |
0.89 |
Ruthenium |
Ru |
44 |
101.07 |
3,4,6,8 |
1.42 |
Samarium |
Sm |
62 |
150.35 |
2,3 |
1.07 |
Scandium |
Sc |
21 |
44.96 |
3 |
1.20 |
Selenium |
Se |
34 |
78.96 |
2,4,6 |
2.48 |
Silicon |
Si |
14 |
28.09 |
4 |
1.74 |
Silver |
Ag |
47 |
107.87 |
1 |
1.42 |
Sodium |
Na |
11 |
22.99 |
1 |
1.01 |
Strontium |
Sr |
38 |
87.62 |
2 |
0.99 |
Sulfur |
S |
16 |
32.06 |
2,4,6 |
2.44 |
Tantalum |
Ta |
73 |
180.95 |
5 |
1.33 |
Tellurium |
Te |
52 |
127.60 |
2,4,6 |
2.01 |
Terbium |
Tb |
65 |
158.92 |
3 |
1.10 |
Thallium |
Tl |
81 |
204.37 |
1,3 |
1.44 |
Thorium |
Th |
90 |
232.04 |
4 |
1.11 |
Thulium |
Tm |
69 |
168.93 |
3 |
1.11 |
Tin |
Sn |
50 |
118.69 |
2,4 |
1.72 |
Titanium |
Ti |
22 |
47.90 |
3,4 |
1.32 |
Tungsten |
W |
74 |
183.85 |
6 |
1.40 |
Uranium |
U |
92 |
238.03 |
4,6 |
1.22 |
Vanadium |
V |
23 |
50.94 |
3,5 |
1.45 |
Xenon |
Xe |
54 |
131.30 |
0 |
|
Ytterbium |
Y |
39 |
88.91 |
2,3 |
1.06 |
Zinc |
Zn |
30 |
65.37 |
2 |
1.66 |
Zirconium |
Zr |
40 |
91.22 |
4 |
1.22 |
Ionic Conductances, mho-cm2/equivalent
(I=0, 25oC)
Cation |
|
Anion |
|
H+ |
349.8 |
OH- |
198.0 |
Na+ |
50.1 |
HCO3- |
44.5 |
K+ |
73.5 |
F- |
55.4 |
Li+ |
38.7 |
Cl- |
76.3 |
NH4+ |
73.4 |
Br- |
78.4 |
Ca+2 |
59.5 |
CH3COO- |
40.9 |
Mg+2 |
53.1 |
NO3- |
71.4 |
|
|
SO4-2 |
79.8 |
Student's t Distribution
Degrees of |
Alpha Values |
||||
Freedom |
10% |
5% |
2.5% |
1% |
0.5% |
1 |
3.078 |
6.314 |
12.706 |
31.821 |
63.657 |
2 |
1.886 |
2.920 |
4.303 |
6.965 |
9.925 |
3 |
1.638 |
2.353 |
3.182 |
4.541 |
5.841 |
4 |
1.533 |
2.132 |
2.776 |
3.747 |
4.604 |
5 |
1.476 |
2.015 |
2.571 |
3.365 |
4.032 |
6 |
1.440 |
1.943 |
2.447 |
3.143 |
3.707 |
7 |
1.415 |
1.895 |
2.365 |
2.998 |
3.499 |
8 |
1.397 |
1.860 |
2.306 |
2.896 |
3.355 |
9 |
1.383 |
1.833 |
2.262 |
2.821 |
3.250 |
10 |
1.372 |
1.812 |
2.228 |
2.764 |
3.169 |
15 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
20 |
1.325 |
1.725 |
2.086 |
2.528 |
2.845 |
inf. |
1.282 |
1.645 |
1.960 |
2.326 |
2.576 |
Calculating Quotients for Dixon's Test
# Observations |
Statistic |
Test for High
Value, Xn |
Test for Low Value, X1 |
3-7 |
Q10 |
(Xn-Xn-1)/(Xn-X1) |
(X2-X1)/(Xn-X1) |
8-10 |
Q11 |
(Xn-Xn-1)/(Xn-X2) |
(X2-X1)/(Xn-1-X1) |
11-13 |
Q21 |
(Xn-Xn-2)/(Xn-X2) |
(X3-X1)/(Xn-1-X1) |
14-25 |
Q22 |
(Xn-Xn-2)/(Xn-X3) |
(X3-X1)/(Xn-2-X1) |
Values for Dixon's Quotient, Qs
|
|
Risk of False Rejection |
|||
Statistic |
# Observations |
0.5% |
1% |
5% |
10% |
Q10 |
3 |
0.994 |
0.988 |
0.941 |
0.886 |
|
4 |
0.926 |
0.889 |
0.765 |
0.697 |
|
5 |
0.821 |
0.780 |
0.642 |
0.557 |
|
6 |
0.740 |
0.698 |
0.560 |
0.482 |
|
7 |
0.680 |
0.637 |
0.507 |
0.434 |
Q11 |
8 |
0.725 |
0.683 |
0.554 |
0.479 |
|
9 |
0.677 |
0.635 |
0.512 |
0.441 |
|
10 |
0.639 |
0.597 |
0.477 |
0.409 |
Q21 |
11 |
0.713 |
0.679 |
0.576 |
0.517 |
|
12 |
0.675 |
0.642 |
0.546 |
0.490 |
|
13 |
0.649 |
0.615 |
0.521 |
0.467 |
Q22 |
14 |
0.674 |
0.641 |
0.546 |
0.492 |
|
15 |
0.647 |
0.616 |
0.525 |
0.472 |
|
16 |
0.624 |
0.595 |
0.507 |
0.454 |
|
17 |
0.605 |
0.577 |
0.490 |
0.438 |
|
18 |
0.589 |
0.561 |
0.475 |
0.424 |
|
19 |
0.575 |
0.547 |
0.462 |
0.412 |
|
20 |
0.562 |
0.535 |
0.450 |
0.401 |
[1]from; The Chemists Companion: A Handbook of Practical Data, Techniques and References. A.J. Gordon & R.A. Ford, J. Wiley & Sons Publ., New York, 1972.