CEE 572

1 November 2000

Mid-term Exam

 

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).

 

Answer:

 

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.

 

 

Answer:

 

               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.