[PDF] Appendix

26471_8Appendix.pdf 1071

Appendix

Appendix 1:

Normality

Appendix 2:

Propagation of Uncertainty

Appendix 3:

Single-Sided Normal Distribution

Appendix 4:

Critical Values for the t-Test

Appendix 5:

Critical Values for the F-Test

Appendix 6:

Critical Values for Dixon's Q-Test

Appendix 7:

Critical Values for Grubb's Test

Appendix 8:

Recommended Primary Standards

Appendix 9:

Correcting Mass for the Buoyancy of Air

Appendix 10:

Solubility Products

Appendix 11: Acid-Base Dissociation Constants

Appendix 12: Metal-Ligand Formation Constants

Appendix 13: Standard Reduction Potentials

Appendix 14: Random Number Table

Appendix 15: Polarographic Half-Wave Potentials

Appendix 16: Countercurrent Separations

Appendix 17:

Review of Chemical Kinetics

1072Analytical Chemistry 2.0

Appendix 1: Normality

Normality expresses concentration in terms of the equivalents of one chemical species reacting stoichio-

metrically with another chemical species. Note that this definition makes an equivalent, and thus normality, a

function of the chemical reaction. Although a solution of H 2 SO 4 has a single molarity, its normality depends on its reaction.

We define the number of equivalents, n, using a reaction unit, which is the part of a chemical species par-

ticipating in the chemical reaction. In a precipitation reaction, for example, the reaction unit is the charge of

the cation or anion participating in the reaction; thus, for the reaction Pb 2+ (aq) 2I - (aq) PbI 2 (s) n 2 for Pb 2+ (aq) and n 1 for 2I - (aq). In an acid-base reaction, the reaction unit is the number of H + ions that an acid donates or that a base accepts. For the reaction between sulfuric acid and ammonia H 2 SO 4 (aq) 2NH 3 (aq) 2NH 4 + (aq) SO 4 2- (aq) n 2 for H 2 SO 4 (aq) because sulfuric acid donates two protons, and n 1 for NH 3 (aq) because each ammonia

accepts one proton. For a complexation reaction, the reaction unit is the number of electron pairs that the

metal accepts or that the ligand donates. In the reaction between Ag + and NH 3 Ag + (aq) + 2NH 3 (aq) Ag(NH 3 ) 2 + (aq) n 2 for Ag + (aq) because the silver ion accepts two pairs of electrons, and n 1 for NH 3 because each am-

monia has one pair of electrons to donate. Finally, in an oxidation-reduction reaction the reaction unit is the

number of electrons released by the reducing agent or accepted by the oxidizing agent; thus, for the reaction

2Fe 3+ (aq) Sn 2+ (aq) Sn 4+ (aq) 2Fe 2+ (aq) n 1 for Fe 3+ (aq) and n 2 for Sn 2+ (aq). Clearly, determining the number of equivalents for a chemical species requires an understanding of how it reacts.

Normality is the number of equivalent weights, EW, per unit volume. An equivalent weight is the ratio of

a chemical species' formula weight, FW, to the number of its equivalents, n. EWFW n ?e following simple relationship exists between normality, N, and molarity, M. NnM

1073Appendices

Appendix 2: Propagation of Uncertainty

In Chapter 4 we considered the basic mathematical details of a propagation of uncertainty, limiting our treat-

ment to the propagation of measurement error. ?is treatment is incomplete because it omits other sources of

uncertainty that influence the overall uncertainty in our results. Consider, for example, Practice Exercise 4.2,

in which we determined the uncertainty in a standard solution of Cu 2+ prepared by dissolving a known mass of Cu wire with HNO 3 , diluting to volume in a 500-mL volumetric flask, and then diluting a 1-mL portion

of this stock solution to volume in a 250-mL volumetric flask. To calculate the overall uncertainty we included

the uncertainty in the sample's mass and the uncertainty of the volumetric glassware. We did not consider

other sources of uncertainty, including the purity of the Cu wire, the effect of temperature on the volumetric

glassware, and the repeatability of our measurements. In this appendix we take a more detailed look at the

propagation of uncertainty, using the standardization of NaOH as an example.

Standardizing a Solution of NaOH

1

Because solid NaOH is an impure material, we cannot directly prepare a stock solution by weighing a sample

of NaOH and diluting to volume. Instead, we determine the solution's concentration through a process called

a standardization. 2 A fairly typical procedure is to use the NaOH solution to titrate a carefully weighed sample of previously dried potassium hydrogen phthalate, C 8 H 5 O 4 K, which we will write here, in shorthand notation,

as KHP. For example, after preparing a nominally 0.1 M solution of NaOH, we place an accurately weighed

0.4-g sample of dried KHP in the reaction vessel of an automated titrator and dissolve it in approximately 50

mL of water (the exact amount of water is not important). ?e automated titrator adds the NaOH to the KHP

solution and records the pH as a function of the volume of NaOH. ?e resulting titration curve provides us

with the volume of NaOH needed to reach the titration's endpoint. 3

?e end point of the titration is the volume of NaOH corresponding to a stoichiometric reaction between

NaOH and KHP.

NaOHCHOKCHOKNaHO

854842

4 ()l Knowing the mass of KHP and the volume of NaOH needed to reach the endpoint, we use the following equation to calculate the molarity of the NaOH solution. C

NaOHKHPKHP

KHPNaOH

1000mP

MV where C NaOH is the concentration of NaOH (in mol KHP/L), m KHP is the mass of KHP taken (in g), P KHP is the purity of the KHP (where P KHP 1 means that the KHP is pure and has no impurities), M KHP is the molar mass of KHP (in g KHP/mol KHP), and V NaOH is the volume of NaOH (in mL). ?e factor of 1000 simply converts the volume in mL to L.

Identifying and Analyzing Sources of Uncertainty

Although it seems straightforward, identifying sources of uncertainty requires care as it easy to overlook im-

portant sources of uncertainty. One approach is to use a cause-and-effect diagram, also known as an Ishikawa

1

?is example is adapted from Ellison, S. L. R.; Rosslein, M.; Williams, A. EURACHEM/CITAC Guide: Quantifying Uncertainty in Analytical

Measurement, 2nd Edition, 2000 (available at http://www.measurementuncertainty.org/). 2 See Chapter 5 for further details about standardizations. 3 For further details about titrations, see Chapter 9.

1074Analytical Chemistry 2.0

diagram - named for its inventor, Kaoru Ishikawa - or a fish bone diagram. To construct a cause-and-effect

diagram, we first draw an arrow pointing to the desired result; this is the diagram's trunk. We then add five main

branch lines to the trunk, one for each of the four parameters that determine the concentration of NaOH and

one for the method's repeatability. Next we add additional branches to the main branch for each of these five

factors, continuing until we account for all potential sources of uncertainty. Figure A2.1 shows the complete

cause-and-effect diagram for this analysis.

Before we continue, let's take a closer look at Figure A2.1 to be sure we understand each branch of the

diagram. To determine the mass of KHP we make two measurements: taring the balance and weighing the

gross sample. Each measurement of mass is subject to a calibration uncertainty. When we calibrate a balance,

we are essentially creating a calibration curve of the balance's signal as a function of mass. Any calibration curve

is subject to a systematic uncertainty in the y-intercept (bias) and an uncertainty in the slope (linearity). We

can ignore the calibration bias because it contributes equally to both m

KHP(gross)

and m

KHP(tare)

, and because we determine the mass of KHP by difference. mmm

KHPKHP(gross)KHP(tare)

?e volume of NaOH at the end point has three sources of uncertainty. First, an automated titrator uses

a piston to deliver the NaOH to the reaction vessel, which means the volume of NaOH is subject to an un-

certainty in the piston's calibration. Second, because a solution's volume varies with temperature, there is an

additional source of uncertainty due to any fluctuation in the ambient temperature during the analysis. Finally,

there is a bias in the titration's end point if the NaOH reacts with any species other than the KHP.

Repeatability, R, is a measure of how consistently we can repeat the analysis. Each instrument we use - the

balance and the automatic titrator - contributes to this uncertainty. In addition, our ability to consistently

Figure A2.1 Cause-and-effect diagram for the standardization of NaOH by titration against KHP. ?e trunk, shown in

black, represents the the concentration of NaOH. ?e remaining arrows represent the sources of uncertainty that affect

C NaOH . Light blue arrows, for example, represent the primary sources of uncertainty affecting C NaOH , and green ar-

rows represent secondary sources of uncertainty that affect the primary sources of uncertainty. See the text for additional

details. m m C P m m V V M

1075Appendices

detect the end point also contributes to repeatability. Finally, there are no additional factors that affect the

uncertainty of the KHP's purity or molar mass. Estimating the Standard Deviation for Measurements

To complete a propagation of uncertainty we must express each measurement's uncertainty in the same way,

usually as a standard deviation. Measuring the standard deviation for each measurement requires time and

may not be practical. Fortunately, most manufacture provides a tolerance range for glassware and instruments.

A 100-mL volumetric glassware, for example, has a tolerance of 0.1 mL at a temperature of 20 o

C. We can

convert a tolerance range to a standard deviation using one of the following three approaches. Assume a Uniform Distribution. Figure A2.2a shows a uniform distribution between the limits of , in

which each result between the limits is equally likely. A uniform distribution is the choice when the manufac-

turer provides a tolerance range without specifying a level of confidence and when there is no reason to believe

that results near the center of the range are more likely than results at the ends of the range. For a uniform

distribution the estimated standard deviation, , is 3

?is is the most conservative estimate of uncertainty as it gives the largest estimate for the standard deviation.

Assume a Triangular Distribution. Figure A2.2b shows a triangular distribution between the limits of , in

which the most likely result is at the center of the distribution, decreasing linearly toward each limit. A trian-

gular distribution is the choice when the manufacturer provides a tolerance range without specifying a level of

confidence and when there is a good reason to believe that results near the center of the range are more likely

than results at the ends of the range. For a uniform distribution the estimated standard deviation, , is

6

?is is a less conservative estimate of uncertainty as, for any value of, the standard deviation is smaller than

that for a uniform distribution.

Assume a Normal Distribution. Figure A2.3c shows a normal distribution that extends, as it must, beyond

the limits of , and which is centered at the mid-point between - and . A normal distribution is the choice

when we know the confidence interval for the range. For a normal distribution the estimated standard devia-

tion, , is where is 1.96 for a 95% confidence interval and 3.00 for a 99.7% confidence interval. - xx (a) - xx (b) - xx(c)

Figure A2.2 ?ree possible distributions for estimating the standard deviation from a range: (a) a uniform distribution;

(b) a triangular distribution; and (c) a normal distribution.

1076Analytical Chemistry 2.0

Completing the Propagation of Uncertainty

Now we are ready to return to our example and determine the uncertainty for the standardization of NaOH.

First we establish the uncertainty for each of the five primary sources - the mass of KHP, the volume of NaOH

at the end point, the purity of the KHP, the molar mass for KHP, and the titration's repeatability. Having es-

tablished these, we can combine them to arrive at the final uncertainty.

Uncertainty in the Mass of KHP. After drying the KHP, we store it in a sealed container to prevent it from

readsorbing moisture. To find the mass of KHP we first weigh the container, obtaining a value of 60.5450 g,

and then weigh the container after removing a portion of KHP, obtaining a value of 60.1562 g. ?e mass of

KHP, therefore, is 0.3888 g, or 388.8 mg.

To find the uncertainty in this mass we examine the balance's calibration certificate, which indicates that its

tolerance for linearity is 0.15 mg. We will assume a uniform distribution because there is no reason to believe

that any result within this range is more likely than any other result. Our estimate of the uncertainty for any

single measurement of mass, (), is ()..015

3009mgmg

Because we determine the mass of KHP by subtracting the container's final mass from its initial mass, the un-

certainty of the mass of KHP ( KHP ), is given by the following propagation of uncertainty. ()(.(.. KHP mg)mg)mg009009013 22

Uncertainty in the Volume of NaOH. After placing the sample of KHP in the automatic titrator's reaction ves-

sel and dissolving with water, we complete the titration and find that it takes 18.64 mL of NaOH to reach the

end point. To find the uncertainty in this volume we need to consider, as shown in Figure A2.1, three sources

of uncertainty: the automatic titrator's calibration, the ambient temperature, and any bias in determining the

end point.

To find the uncertainty resulting from the titrator's calibration we examine the instrument's certificate, which

indicates a range of 0.03 mL for a 20-mL piston. Because we expect that an effective manufacturing process

is more likely to produce a piston that operates near the center of this range than at the extremes, we will as-

sume a triangular distribution. Our estimate of the uncertainty due to the calibration, ( cal ) is ().. cal mLmL003 60012

To determine the uncertainty due to the lack of temperature control, we draw on our prior work in the lab,

which has established a temperature variation of 3 o C with a confidence level of 95%. To find the uncertainty, we convert the temperature range to a range of volumes using water's coefficient of expansion

211031864

41
.. oo

CCmL=0.012mL

and then estimate the uncertainty due to temperature, ( temp ) as (). .. temp mLmL0012

1960006

1077Appendices

Titrations using NaOH are subject to a bias due to the adsorption of CO 2 , which can react with OH - , as shown here.

COOHCOHO

2232

2()()()()aqaqaql

If CO 2 is present, the volume of NaOH at the end point includes both the NaOH reacting with the KHP and the NaOH reacting with CO 2 . Rather than trying to estimate this bias, it is easier to bathe the reaction vessel in a stream of argon, which excludes CO 2 from the titrator's reaction vessel.

Adding together the uncertainties for the piston's calibration and the lab's temperature fluctuation gives the

uncertainty in the volume of NaOH, u(V NaOH ) as uV()(.(.. NaOH mL)mL)mL001200060013 22

Uncertainty in the Purity of KHP. According to the manufacturer, the purity of KHP is 100% 0.05%, or

1.0 0.0005. Assuming a rectangular distribution, we report the uncertainty, u(P KHP ) as uP().. KHP 00005

3000029

Uncertainty in the Molar Mass of KHP. ?e molar mass of C 8 H 5 O 4

K is 204.2212 g/mol, based on the fol-

lowing atomic weights: 12.0107 for carbon, 1.00794 for hydrogen, 15.9994 for oxygen, and 39.0983 for po-

tassium. Each of these atomic weights has an quoted uncertainty that we can convert to a standard uncertainty

assuming a rectangular distribution, as shown here (the details of the calculations are left to you).

elementquoted uncertaintystandard uncertainty carbon

0.00080.00046

hydrogen

0.000070.000040

oxygen

0.00030.00017

potassium

0.00010.000058

Adding together the uncertainties gives the uncertainty in the molar mass, u(M KHP ), as uM()(.)(.)(.) KHP

8000046500000404000017

222
(.).000005800038g/mol

Uncertainty in the Titration's Repeatability. To estimate the uncertainty due to repeatability we complete

five titrations, obtaining results for the concentration of NaOH of 0.1021 M, 0.1022 M, 0.1022 M, 0.1021

M, and 0.1021 M. ?e relative standard deviation, s r , for these titrations is s r 5.477

0.1021

1000005

5 .

If we treat the ideal repeatability as 1.0, then the uncertainty due to repeatability, u(R), is equal to the relative

standard deviation, or, in this case, 0.0005.

Combining the Uncertainties. Table A2.1 summarizes the five primary sources of uncertainty. As described

earlier, we calculate the concentration of NaOH we use the following equation, which is slightly modified to

include a term for the titration's repeatability, which, as described above, has a value of 1.0.

1078Analytical Chemistry 2.0

C

NaOHKHPKHP

KHPNaOH

1000mP

MVR Using the values from Table A2.1, we find that the concentration of NaOH is C NaOH

10000388810

204221218641001021..

....MM

Because the calculation of C

NaOH includes only multiplication and division, the uncertainty in the con- centration, u(C NaOH ) is given by the following propagation of uncertainty. uC

CuC()()

.(.) (. NaOH

NaOHNaOH

M01021000013

0388
2 8

8000029

1000038

204221200

22
22
2 )(.) (.)(.) (.)(. 1 13

186400005

10 2 22
2 ) (.)(.) (.)

Solving for u(C

NaOH ) gives its value as 0.00010 M, which is the final uncertainty for the analysis.

Evaluating the Sources of Uncertainty

Figure A2.3 shows the relative uncertainty in the concentration of NaOH and the relative uncertainties

for each of the five contributions to the total uncertainty. Of the contributions, the most important is the

volume of NaOH, and it is here to which we should focus our attention if we wish to improve the overall

uncertainty for the standardization. xux m KHP mass of KHP0.3888 g0.00013 g V NaOH volume of NaOH at end point18.64 mL0.013 mL P KHP purity of KHP1.00.00029 M KHP molar mass of KHP204.2212 g/mol0.0038 g/mol

Rrepeatability1.00.0005

0.00000.00020.00040.00060.00080.0010

m KHP P KHP M KHP V NaOH R C NaOH relative uncertainty Figure A2.3 Bar graph showing the relative uncertainty in C NaOH , and the relative uncertainty in each of the main factors affecting the overall uncertainty.

1079Appendices

Appendix 3: Single-Sided Normal Distribution

The table in this appendix gives the proportion, P, of the area under a normal distribution curve that lies to

the right of a deviation, z zXµ

where X is the value for which the deviation is being defined, is the distribution's mean value and is the

distribution's standard deviation. For example, the proportion of the area under a normal distribution to the

right of a deviation of 0.04 is 0.4840 (see entry in red in the table), or 48.40% of the total area (see the area

shaded blue in the figure to the right). ?e proportion of the area to the left of the deviation is 1 - P. For a

deviation of 0.04, this is 1-0.4840, or 51.60%.

When the deviation is negative - that is, when X is smaller than - the value of z is negative. In this case,

the values in the table give the area to the left of z. For example, if z is -0.04, then 48.40% of the area lies to

the left of the deviation (see area shaded green in the figure shown below on the left).

To use the single-sided normal distribution table, sketch the normal distribution curve for your problem

and shade the area corresponding to your answer (for example, see the figure shown above on the right, which

Deviation (

z )48.40%

230240250260270

Aspirin (mg)

8.08%0.82%91.10%

48.40%

230240250260270

Aspirin (mg)

8.08%0.82%91.10%

is for Example 4.11). ?is divides the normal distribution curve into three regions: the area corresponding to

your answer (shown in blue), the area to the right of this, and the area to the left of this. Calculate the values

of z for the limits of the area corresponding to your answer. Use the table to find the areas to the right and to

the left of these deviations. Subtract these values from 100% and, voilà, you have your answer.

1080Analytical Chemistry 2.0

z0.000.010.020.030.040.050.060.070.080.09

0.00.50000.49600.49200.48800.48400.48010.47610.47210.46810.4641

0.10.46020.45620.45220.44830.44430.44040.43650.43250.42860.4247

0.20.42070.41680.41290.40900.45020.40130.39740.33960.38970.3859

0.30.38210.37830.37450.37070.36690.36320.35940.35570.35200.3483

0.40.34460.34090.33720.33360.33000.32640.32280.31920.31560.3121

0.50.30850.30500.30150.29810.29460.29120.28770.28430.28100.2776

0.60.27430.27090.26760.26430.26110.25780.25460.25140.24830.2451

0.70.24200.23890.23580.23270.22960.22660.22360.22060.21770.2148

0.80.21190.20900.20610.20330.20050.19770.19490.19220.18940.1867

0.90.18410.18140.17880.17620.17360.17110.16850.16600.16350.1611

1.00.15870.15620.15390.15150.14920.14690.14460.14230.14010.1379

1.10.13570.13350.13140.12920.12710.12510.12300.12100.11900.1170

1.20.11510.11310.11120.10930.10750.10560.10380.10200.10030.0985

1.30.09680.09510.09340.09180.09010.08850.08690.08530.08380.0823

1.40.08080.07930.07780.07640.07490.07350.07210.07080.06940.0681

1.50.06680.06550.06430.06300.06180.06060.05940.05820.05710.0559

1.60.05480.05370.05260.05160.05050.04950.04850.04750.04650.0455

1.70.04660.04360.04270.04180.04090.04010.03920.03840.03750.0367

1.80.03590.03510.03440.03360.03290.03220.03140.03070.03010.0294

1.90.02870.02810.02740.02680.02620.02560.02500.02440.02390.0233

2.00.02280.02220.02170.02120.02070.02020.01970.01920.01880.0183

2.10.01790.01740.01700.01660.01620.01580.01540.01500.01460.0143

2.20.01390.01360.01320.01290.01250.01220.01190.01160.01130.0110

2.30.01070.01040.01020.009640.009140.00866

2.40.008200.007760.007340.006950.00657

2.50.006210.005870.005540.005230.00494

2.60.004660.004400.004150.003910.00368

2.70.003470.003260.003070.002890.00272

2.80.002560.002400.002260.002120.00199

2.90.001870.001750.001640.001540.00144

3.00.00135

3.10.000968

3.20.000687

3.30.000483

3.40.000337

3.50.000233

3.60.000159

3.70.000108

3.80.0000723

3.90.0000481

4.00.0000317

1081Appendices

Appendix 4: Critical Values for t-Test

Assuming you have calculated

exp , there are two approaches to interpreting a -test. In the first approach you

choose a value of for rejecting the null hypothesis and read the value of (,) from the table shown below.

If exp (,), you reject the null hypothesis and accept the alternative hypothesis. In the second approach,

you find the row in the table below corresponding to your degrees of freedom and move across the row to find

(or estimate) the corresponding to exp (,); this establishes largest value of for which you can retain

the null hypothesis. Finding, for example, that is 0.10 means that you would retain the null hypothesis at

the 90% confidence level, but reject it at the 89% confidence level. ?e examples in this textbook use the first

approach.

Values of t for...

...a condence interval of:90%95%98%99% ...an value of:0.100.050.020.01

Degrees of Freedom

16.31412.70631.82163.657

22.9204.3036.9659.925

32.3533.1824.5415.841

42.1322.7763.7474.604

52.0152.5713.3654.032

61.9432.4473.1433.707

71.8952.3652.9983.499

81.8602.3062.8963.255

91.8332.2622.8213.250

101.8122.2282.7643.169

121.7822.1792.6813.055

141.7612.1452.6242.977

161.7462.1202.5832.921

181.7342.1012.5522.878

201.7252.0862.5282.845

301.6972.0422.4572.750

501.6762.0092.3112.678

1.6451.9602.3262.576

?e values in this table are for a two-tailed -test. For a one-tail -test, divide the values by 2. For example, the

last column has an value of 0.005 and a confidence interval of 99.5% when conducting a one-tailed -test.

1082Analytical Chemistry 2.0

Appendix 5: Critical Values for the F-Test

The following tables provide values for F(0.05,

num , denom ) for one-tailed and for two-tailed F-tests. To use these tables, decide whether the situation calls for a one-tailed or a t wo-tailed analysis and calculate F exp Fs s exp A B2 2 where s A 2 is greater than s B 2 . Compare F exp to F(0.05, num , denom ) and reject the null hypothesis if F exp >

F(0.05,

num , denom ). You may replace s with if you know the population's standard deviation. (0.05, num , denom ) for a One-Tailed F-Test denomnum oo

123456789101520

1161.4199.5215.7224.6230.2234.0236.8238.9240.5241.9245.9248.0254.3

218.5119.0019.1619.2519.3019.3319.3519.3719.3819.4019.4319.4519.50

310.139.5529.2779.1179.0138.9418.8878.8458.8128.7868.7038.6608.526

47.7096.9946.5916.3886.2566.1636.0946.0415.9995.9645.8585.8035.628

56.6085.7865.4095.1925.0504.9504.8764.8184.7224.7534.6194.5584.365

65.5915.1434.7574.5344.3874.2844.2074.1474.0994.0603.9383.8743.669

75.5914.7374.3474.1203.9723.8663.7873.7263.6773.6373.5113.4453.230

85.3184.4594.0663.8383.6873.5813.5003.4383.3883.3473.2183.1502.928

95.1174.2563.8633.6333.4823.3743.2933.2303.1793.1373.0062.9362.707

104.9654.1033.7083.4783.3263.2173.1353.0723.0202.9782.8452.7742.538

114.8443.9823.5873.2573.2043.0953.0122.9482.8962.8542.7192.6462.404

124.7473.8853.4903.2593.1062.9962.9132.8492.7962.7532.6172.5442.296

134.6673.8063.4113.1793.0252.9152.8322.7672.7142.6712.5332.4592.206

144.6003.7393.3443.1122.9582.8482.7642.6992.6462.6022.4632.3882.131

154.5343.6823.2873.0562.9012.7902.7072.6412.5882.5442.4032.3282.066

164.4943.6343.2393.0072.8522.7412.6572.5912.5382.4942.3522.2762.010

174.4513.5923.1972.9652.8102.6992.6142.5482.4942.4502.3082.2301.960

184.4143.5553.1602.9282.7732.6612.5772.5102.4562.4122.2692.1911.917

194.3813.5523.1272.8952.7402.6282.5442.4772.4232.3782.2342.1551.878

204,3513.4933.0982.8662.7112.5992.5142.4472.3932.3482.2032.1241.843

3.8422.9962.6052.3722.2142.0992.0101.9381.8801.8311.6661.5701.000

1083Appendices

F(0.05,

num , denom ) for a Two-Tailed F-Test denomnum

123456789101520

1647.8799.5864.2899.6921.8937.1948.2956.7963.3968.6984.9993.11018

238.5139.0039.1739.2539.3039.3339.3639.3739.3939.4039.4339.4539.50

317.4416.0415.4415.1014.8814.7314.6214.5414.4714.4214.2514.1713.90

412.2210.659.9799.6059.3649.1979.0748.9808.9058.4448.6578.5608.257

510.018.4347.7647.3887.1466.9786.8536.7576.6816.6196.4286.3296.015

68.8137.2606.5996.2275.9885.8205.6955.6005.5235.4615.2695.1684.894

78.0736.5425.8905.5235.2855.1194.9954.8994.8234.7614.5684.4674.142

87.5716.0595.4165.0534.8174.6524.5294.4334.3574.2594.1013.9993.670

97.2095.7155.0784.7184.4844.3204.1974.1024.0263.9643.7693.6673.333

106.9375.4564.8264.4684.2364.0723.9503.8553.7793.7173.5223.4193.080

116.7245.2564.6304.2754.0443.8813.7593.6443.5883.5263.3303.2262.883

126.5445.0964.4744.1213.8913.7283.6073.5123.4363.3743.1773.0732.725

136.4144.9654.3473.9963.7673.6043.4833.3883.3123.2503.0532.9482.596

146.2984.8574.2423.8923.6633.5013.3803.2853.2093.1472.9492.8442.487

156.2004.7654.1533.8043.5763.4153.2933.1993.1233.0602.8622.7562.395

166.1154.6874.0773.7293.5023.3413.2193.1253.0492.9862.7882.6812.316

176.0424.6194.0113.6653.4383.2773.1563.0612.9852.9222.7232.6162.247

185.9784.5603.9543.6083.3823.2213.1003.0052.9292.8662.6672.5592.187

195.9224.5083.9033.5593.3333.1723.0512.9562.8802.8172.6172.5092.133

205.8714.4613.8593.5153.2893.1283.0072.9132.8372.7742.5732.4642.085

5.0243.6893.1162.7862.5672.4082.2882.1922.1142.0481.8331.7081.000

1084Analytical Chemistry 2.0

Appendix 6: Critical Values for Dixon"s Q-Test

The following table provides critical values for (, ), where is the probability of incorrectly rejecting the

suspected outlier and is the number of samples in the data set. ?ere are several versions of Dixon's Q-Test,

each of which calculates a value for ij where is the number of suspected outliers on one end of the data set

and is the number of suspected outliers on the opposite end of the data set. ?e values given here are for

10 , where exp 10 outliersvaluenearestvalue large s stvaluesmallestvalue ?e suspected outlier is rejected if exp is greater than (, ). For additional information consult Rorabacher,

D. B. "Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon's '' Parameter and Re-

lated Subrange Ratios at the 95% confidence Level," 1991, , 139-146. Critical Values for the Q-Test of a Single Outlier (Q 10 ) a

0.10.050.040.020.01

30.9410.9700.9760.9880.994

40.7650.8290.8460.8890.926

50.6420.7100.7290.7800.821

60.5600.6250.6440.6980.740

70.5070.5680.5860.6370.680

80.4680.5260.5430.5900.634

90.4370.4930.5100.5550.598

100.4120.4660.4830.5270.568

1085Appendices

Appendix 7: Critical Values for Grubb"s Test

The following table provides critical values for G(, n), where is the probability of incorrectly rejecting

the suspected outlier and n is the number of samples in the data set. ?ere are several versions of Grubb's Test,

each of which calculates a value for G ij where i is the number of suspected outliers on one end of the data set

and j is the number of suspected outliers on the opposite end of the data set. ?e values given here are for G

10 , where GGXX s out exp 10 ?e suspected outlier is rejected if G exp is greater than G(, n). (, ) for Grubb"s Test of a Single Outlier a

0.050.01

31.1551.155

41.4811.496

51.7151.764

61.8871.973

72.2022.139

82.1262.274

92.2152.387

102.2902.482

112.3552.564

122.4122.636

132.4622.699

142.5072.755

152.5492.755

1086Analytical Chemistry 2.0

Appendix 8: Recommended Primary Standards

All compounds should be of the highest available purity. Metals should be cleaned with dilute acid to remove

any surface impurities and rinsed with distilled water. Unless otherwise indicated, compounds should be dried

to a constant weight at 110 o C. Most of these compounds are soluble in dilute acid (1:1 HCl or 1:1 HNO 3 ), with gentle heating if necessary; some of the compounds are water soluble.

ElementCompoundFW (g/mol)Comments

aluminumAl metal26.982 antimonySb metal121.760 KSbOC 4 H 4 O 6

324.92prepared by drying KSbC

4 H 4 O 6 ?1/2H 2 O at 110
o

C and storing in a desiccator

arsenicAs metal74.922 As 2 O 3

197.84toxic

bariumBaCO 3

197.84dry at 200

o

C for 4 h

bismuthBi metal208.98 boronH 3 BO 3

61.83do not dry

bromineKBr119.01 cadmiumCd metal112.411

CdO128.40

calciumCaCO 3

100.09

ceriumCe metal140.116 (NH 4 ) 2 Ce(NO 3 ) 4

548.23

cesiumCs 2 CO 3

325.82

Cs 2 SO 4

361.87

chlorineNaCl58.44 chromiumCr metal51.996 K 2 Cr 2 O 7

294.19

cobaltCo metal58.933 copperCu metal63.546

CuO79.54

fluorineNaF41.99do not store solutions in glass containers iodineKI166.00 KIO 3

214.00

ironFe metal55.845 leadPb metal207.2 lithiumLi 2 CO 3 73.89
magnesiumMg metal24.305 manganeseMn metal54.938

1087Appendices

ElementCompoundFW (g/mol)Comments

mercuryHg metal200.59 molybdenumMo metal95.94 nickelNi metal58.693 phosphorousKH 2 PO 4

136.09

P 2 O 5

141.94

potassiumKCl74.56 K 2 CO 3

138.21

K 2 Cr 2 O 7

294.19

KHC 8 H 4 O 2

204.23

siliconSi metal28.085 SiO 2 60.08
silverAg metal107.868 AgNO 3

169.87

sodiumNaCl58.44 Na 2 CO 3

106.00

Na 2 C2O 4

134.00

strontiumSrCO 3

147.63

sulfurelemental S32.066 K 2 SO 4

174.27

Na 2 SO 4

142.04

tinSn metal118.710 titaniumTi metal47.867 tungstenW metal183.84 uraniumU metal238.029 U 3 O 8

842.09

vanadiumV metal50.942 zincZn metal81.37

Sources: (a) Smith, B. W.; Parsons, M. L. J. Chem. Educ. , 50, 679-681; (b) Moody, J. R.; Greenburg, P.

R.; Pratt, K. W.; Rains, T. C. Anal. Chem. , 60, 1203A-1218A.

1088Analytical Chemistry 2.0

Appendix 9: Correcting Mass

for the Buoyancy of Air

Calibrating a balance does not eliminate all sources of determinate error in the signal. Because of the buoy-

ancy of air, an object always weighs less in air than it does in a vacuum. If there is a difference between the

object's density and the density of the weights used to calibrate the balance, then we can make a correction for

buoyancy. 1 An object's true weight in vacuo, W v , is related to its weight in air, W a , by the equation .WWDD11100012 va ow A9.1 where D o is the object's density, D w is the density of the calibration weight, and 0.0012 is the density of air under normal laboratory conditions (all densities are in units of g/cm 3 ). ?e greater the difference between D o and D w the more serious the error in the object's measured weight.

?e buoyancy correction for a solid is small, and frequently ignored. It may be significant, however, for

low density liquids and gases. ?is is particularly important when calibrating glassware. For example, we can

calibrate a volumetric pipet by carefully filling the pipet with water to its calibration mark, dispensing the wa-

ter into a tared beaker, and determining the water's mass. After correcting for the buoyancy of air, we use the

water's density to calculate the volume dispensed by the pipet.

A 10-mL volumetric pipet was calibrated following the procedure just outlined, using a balance calibrated

with brass weights having a density of 8.40 g/cm 3 . At 25 o

C the pipet dispensed 9.9736 g of water. What is

the actual volume dispensed by the pipet and what is the determinate error in this volume if we ignore the

buoyancy correction? At 25 o

C the density of water is 0.997

05 g/cm 3 .

SO L U T I O N

Using equation A9.1 the water's true weight is

W v

9.9736 g10.9970518.4010.00129.9842 g

and the actual volume of water dispensed by the pipet is 99842

0997051001410014.

...g g/cmcmmL 33
If we ignore the buoyancy correction, then we report the pipet's volume as 99736

0997051000310003.

...g g/cmcmmL 33
introducing a negative determinate error of -0.11%. 1 Battino, R.; Williamson, A. G. J. Chem. Educ. 1984, 61, 51-52.

1089Appendices

PR O B L E M S

?e following problems will help you in considering the effect of buoyancy on the measurement of mass.

1.

In calibrating a 10-mL pipet a measured volume of water was transferred to a tared flask and weighed,

yielding a mass of 9.9814 grams. (a) Calculate, with and without correcting for buoyancy, the volume of

water delivered by the pipet. Assume that the density of water is 0.99707 g/cm3 and that the density of

the weights is 8.40 g/cm3. (b) What are the absolute and relative errors introduced by failing to account

for the effect of buoyancy? Is this a significant source of determinate error for the calibration of a pipet?

Explain.

2.

Repeat the questions in problem 1 for the case where a mass of 0.2500 g is measured for a solid that has a

density of 2.50 g/cm3. 3. Is the failure to correct for buoyancy a constant or proportional source of determinate error? 4.

What is the minimum density of a substance necessary to keep the buoyancy correction to less than 0.01%

when using brass calibration weights with a density of 8.40 g/cm3?

1090Analytical Chemistry 2.0

Appendix 10: Solubility Products

The following table provides pK

sp and K sp values for selected compounds, organized by the anion. All values

are from Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. 4. Plenum Press: New York, 1976. Un-

less otherwise stated, values are for 25 o

C and zero ionic strength.

K K

CuBr8.3

5.10 -9

AgBr12.30

5.010 -13 Hg 2 Br 2 22.25
5.610 -13 HgBr 2 (0.5 M) 18.9 1.310 -19 PbBr 2 (4.0 M) 5.68 2.110 -6 K K MgCO 3 7.46 3.510 -8 CaCO 3 (calcite)8.35 4.510 -9 CaCO 3 (aragonite)8.22 6.010 -9 SrCO 3 9.03 9.310 -10 BaCO 3 8.30 5.010 -9 MnCO 3 9.30 5.010 -10 FeCO 3 10.68 2.110 -11 CoCO 3 9.98 1.010 -10 NiCO 3 6.87 1.310 -7 Ag 2 CO 3 11.09 8.110 -12 Hg 2 CO 3 16.05 8.910 -17 ZnCO 3 10.00 1.010 -10 CdCO 3 13.74 1.810 -14 PbCO 3 13.13 7.410 -14 K K

CuCl6.73

1.910 -7

AgCl9.74

1.810 -10 Hg 2 Cl 2 17.91 1.210 -18 PbCl 2 4.78 2.010 -19

1091Appendices

Chromate (CrO

4 2- )pK sp K sp BaCrO 4 9.67 2.110 -10 CuCrO 4 5.44 3.610 -6 Ag 2 CrO 4 11.92 1.210 -12 Hg 2 CrO 4 8.70 2.010 -9

Cyanide (CN

- )pK sp K sp

AgCN15.66

2.210 -16

Zn(CN)

2 (3.0 M) 15.5 3.10 -16 Hg 2 (CN) 2 39.3
5.10 -40

Ferrocyanide [Fe(CN)

6 4- ]pK sp K sp Zn 2 [Fe(CN) 6 ]15.68 2.110 -16 Cd 2 [Fe(CN) 6 ]17.38 4.210 -18 Pb 2 [Fe(CN) 6 ]18.02 9.510 -19

Fluoride (F

- )pK sp K sp MgF 2 8.18 6.610 -9 CaF 2 10.41 3.910 -11 SrF 2 8.54 2.910 -9 BaF 2 5.76 1.710 -6 PbF 2 7.44 3.610 -8

Hydroxide (OH

- )pK sp K sp

Mg(OH)

2 11.15 7.110 -12

Ca(OH)

2 5.19 6.510 -6

Ba(OH)

2 ?8H 2 O3.6 3.10 -4

La(OH)

3 20.7
2.10 -21

Mn(OH)

2 12.8 1.610 -13

Fe(OH)

2 15.1 8.10 -16

Co(OH)

2 14.9 1.310 -15

Ni(OH)

2 15.2 6.10 -16

Cu(OH)

2 19.32 4.810 -20

Fe(OH)

3 38.8
1.610 -39

1092Analytical Chemistry 2.0

Co(OH)

3 (T 19 o C) 44.5
3.10 -45 Ag 2 O (H 2 O 2Ag + 2OH - ) 15.42 3.810 -16 Cu 2 O (H 2 O 2Cu + 2OH - ) 29.4
4.10 -30

Zn(OH)

2 (amorphous)15.52 3.010 -16

Cd(OH)

2 ()14.35 4.510 -15

HgO (red) (H

2 O Hg 2+ 2OH - ) 25.44
3.610 -26

SnO (H

2 O Sn 2+ 2OH - ) 26.2
6.10 -27

PbO (yellow) (H

2 O Pb 2+ 2OH - ) 15.1 8.10 -16

Al(OH)

3 ()33.5 3.10 -34

Iodate (IO

3 - )p sp sp Ca(IO 3 ) 2 6.15 7.110 -7 Ba(IO 3 ) 2 8.81 1.510 -9 AgIO 3 7.51 3.110 -8 Hg 2 (IO 3 ) 2 17.89 1.310 -18 Zn(IO 3 ) 2 5.41 3.910 -6 Cd(IO 3 ) 2 7.64 2.310 -8 Pb(IO 3 ) 2 12.61 2.510 -13

Iodide (I

- )p sp sp

AgI16.08

8.310 -17 Hg 2 I 2 28.33
4.710 -29 HgI 2 (0.5 M) 27.95
1.110 -28 PbI 2 8.10 7.910 -9

Oxalate (C

2 O 4 2- )p sp sp CaC 2 O 4 (0.1 M, T 20 o C) 7.9 1.310 -8 BaC 2 O 4 (0.1 M, T 20 o C) 6.0 1.10 -6 SrC 2 O 4 (0.1 M, T 20 o C) 6.4 4.10 -7

Phosphate (PO

4 3- )p sp sp Fe 3 (PO 4 ) 2 ?8H 2 O36.0 1.10 -36 Zn 3 (PO 4 ) 2 ?4H 2 O35.3 5.10 -36 Ag 3 PO 4 17.55 2.810 -18

1093Appendices

Pb 3 (PO 4 ) 2 (T 38 o C) 43.55
3.010 -44

Sulfate (SO

4 2- )p sp sp CaSO 4 4.62 2.410 -5 SrSO 4 6.50 3.210 -7 BaSO 4 9.96 1.110 -10 Ag 2 SO 4 4.83 1.510 -5 Hg 2 SO 4 6.13 7.410 -7 PbSO 4 7.79 1.610 -8

Sul?de (S

2- )p sp sp

MnS (green)13.5

3.10 -14

FeS18.1

8.10 -19

CoS ()25.6

3.10 -26

NiS ()26.6

3.10 -27

CuS36.1

8.10 -37 Cu 2 S48.5 3.10 -49 Ag 2 S50.1 8.10 -51

ZnS ()24.7

2.10 -25

CdS27.0

1.10 -27 Hg 2

S (red)53.3

5.10 -54

PbS27.5

3.10 -28

Thiocyanate (SCN

- )p sp sp

CuSCN (5.0 M)

13.40 4.010 -14

AgSCN11.97

1.110 -12 Hg 2 (SCN) 2 19.52 3.010 -20

Hg(SCN)

2 (1.0 M) 19.56 2.810 -20

1094Analytical Chemistry 2.0

Appendix 11: Acid Dissociation Constants

The following table provides pK

a and K a values for selected weak acids. All values are from Martell, A. E.;

Smith, R. M. Critical Stability Constants, Vols. 1-4. Plenum Press: New York, 1976. Unless otherwise stated,

values are for 25 o C and zero ionic strength. ?ose values in brackets are considered less reliable.

Weak acids are arranged alphabetically by the names of the neutral compounds from which they are derived. In

some cases - such as acetic acid - the compound is the weak acid. In other cases - such as for the ammonium

ion - the neutral compound is the conjugate base. Chemical formulas or structural formulas are shown for

the fully protonated weak acid. Successive acid dissociation constants are provided for polyprotic weak acids;

where there is ambiguity, the specific acidic proton is identified.

To find the K

b value for a conjugate weak base, recall that K a K b K w for a conjugate weak acid, HA, and its conjugate weak base, A - . K K acetic acidCH 3

COOH4.757

1.7510

-5 adipic acid 4.42 5.42 3.810 -5 3.810 -6 alanine 2.348 (COOH) 9.867 (NH 3 )

4.4910

-3

1.3610

-10 aminobenzene 4.601

2.5110

-5

4-aminobenzene sulfonic acid

3.232

5.8610

-4

2-aminobenozic acid

2.08 (COOH)

4.96 (NH

3 ) 8.310 -3 1.110 -5

2-aminophenol (T 20

o C)

4.78 (NH

3 )

9.97 (OH)

1.710 -5

1.0510

-10 ammoniaNH 4 + 9.244

5.7010

-10

1095Appendices

CompoundConjugate AcidpK

a K a arginine

1.823 (COOH)

8.991 (NH

3 ) [12.48] (NH 2 )

1.5010

-2

1.0210

-9 [3.310 -13 ] arsenic acidH 3 AsO 4 2.24 6.96 11.50 5.810 -3 1.110 -7 3.210 -12 asparagine (0.1 M)

2.14 (COOH)

8.72 (NH

3 ) 7.210 -3 1.910 -9 asparatic acid

1.990 (-COOH)

3.900 (-COOH)

10.002 (NH

3 )

1.0210

-2

1.2610

-4

9.9510

-11 benzoic acid4.202

6.2810

-5 benzylamine 9.35 4.510 -10 boric acid (p a2 , p a3 :20 o C) H 3 BO 3 9.236 [12.74] [13.80]

5.8110

-10 [1.8210 -13 ] [1.5810 -14 ] carbonic acidH 2 CO 3 6.352

10.329

4.4510

-7

4.6910

-11 catechol 9.40 12.8 4.010 -10 1.610 -13 chloroacetic acidClCH 2

COOH2.865

1.3610

-3 chromic acid (p a1 :20 o C) H 2 CrO 4 -0.2 6.51 1.6 3.110 -7

1096Analytical Chemistry 2.0

CompoundConjugate AcidpK

a K a citric acid

3.128 (COOH)

4.761 (COOH)

6.396 (COOH)

7.4510

-4

1.7310

-5

4.0210

-7 cupferrron (0.1 M) 4.16 6.910 -5 cysteine [1.71] (COOH)

8.36 (SH)

10.77 (NH

3 ) [1.910 -2 ] 4.410 -9 1.710 -11 dichloracetic acidCl 2

CHCOOH1.30

5.010 -2 diethylamine(CH 3 CH 2 ) 2 NH 2 +

10.933

1.1710

-11 dimethylamine(CH 3 ) 2 NH 2 +

10.774

1.6810

-11 dimethylglyoxime 10.66 12.0 2.210 -11 1.10 -12 ethylamineCH 3 CH 2 NH 3 +

10.636

2.3110

-11 ethylenediamine + H 3 NCH 2 CH 2 NH 3 + 6.848 9.928

1.4210

-7

1.1810

-10 ethylenediaminetetraacetic acid (EDTA) (0.1 M)

0.0 (COOH)

1.5 (COOH)

2.0 (COOH)

2.66 (COOH)

6.16 (NH)

10.24 (NH)

1.0 3.210 -2 1.010 -2 2.210 -3 6.910 -7 5.810 -11 formic acidHCOOH3.745

1.8010

-4 fumaric acid 3.053 4.494

8.8510

-4

3.2110

-5 glutamic acid

2.33 (-COOH)

4.42 (-COOH)

9.95 (NH

3 ) 5.910 -3 3.810 -5

1.1210

-10

1097Appendices

CompoundConjugate AcidpK

a K a glutamine (0.1 M)

2.17 (COOH)

9.01 (NH

3 ) 6.810 -3 9.810 -10 glycine + H 3 NCH 2 COOH

2.350 (COOH)

9.778 (NH

3 )

4.4710

-3

1.6710

-10 glycolic acidHOOCH 2

COOH3.831 (COOH)

1.4810

-4 histidine (0.1 M)

1.7 (COOH)

6.02 (NH)

9.08 (NH

3 ) 2.10 -2 9.510 -7 8.310 -10 hydrogen cyanideHCN9.21 6.210 -10 hydrogen fluorideHF3.17 6.810 -4 hydrogen peroxideH 2 O 2 11.65 2.210 -12 hydrogen sulfideH 2 S 7.02 13.9 9.510 -8 1.310 -14 hydrogen thiocyanateHSCN0.9 1.310 -1

8-hydroxyquinoline

4.91 (NH)

9.81 (OH)

1.210 -5 1.610 -10 hydroxylamineHONH 3 + 5.96 1.110 -6 hypobromous acidHOBr8.63 2.310 -9 hypochlorous acidHOCl7.53 3.010 -8 hypoiodous acidHOI10.64 2.310 -11 iodic acidHIO 3 0.77 1.710 -1 isoleucine

2.319 (COOH)

9.754 (NH

3 )

4.8010

-3

1.7610

-10

CompoundConjugate AcidpK

a K a leucine

2.329 (COOH)

9.747 (NH

3 )

4.6910

-3

1.7910

-10 lysine (0.1 M)

2.04 (COOH)

9.08 (-NH

3 )

10.69 (-NH

3 ) 9.110 -3 8.310 -10 2.010 -11 maleic acid 1.910 6.332 9.110 -3 9.110 -3 malic acid

3.459 (COOH)

5.097 (COOH)

9.110 -3 9.110 -3 malonic acidHOOCCH 2 COOH 2.847 5.696 9.110 -3 9.110 -3 methionine (0.1 M)

2.20 (COOH)

9.05 (NH

3 ) 9.110 -3 9.110 -3 methylamineCH 3 NH 3 + 10.64 9.110 -3

2-methylanaline

4.447 9.110 -3

4-methylanaline

5.084 9.110 -3

2-methylphenol

10.28 9.110 -3

4-methylphenol10.26

9.110 -3

1099Appendices

CompoundConjugate AcidpK

a K a nitrilotriacetic acid (20 o C) (p a1 : 0.1 m)

1.1 (COOH)

1.650 (COOH)

2.940 (COOH)

10.334 (NH

3 ) 9.110 -3 9.110 -3 9.110 -3 9.110 -3

2-nitrobenzoic acid

2.179 9.110 -3

3-nitrobenzoic acid

3.449 9.110 -3

4-nitrobenzoic acid

3.442

3.6110

-4

2-nitrophenol

7.21 6.210 -8

3-nitrophenol

8.39 4.110 -9

4-nitrophenol

7.15 7.110 -8 nitrous acidHNO 2 3.15 7.110 -4 oxalic acidH 2 C 2 O 4 1.252 4.266

5.6010

-2

5.4210

-5

1,10-phenanthroline

4.86

1.3810

-5 phenol9.98

1.0510

-10

1100Analytical Chemistry 2.0

CompoundConjugate AcidpK

a K a phenylalanine

2.20 (COOH)

9.31 (NH

3 ) 6.310 -3 4.910 -10 phosphoric acidH 3 PO 4 2.148 7.199 12.35

7.1110

-3

6.3210

-8 4.510 -13 phthalic acid 2.950 5.408

1.1210

-3

3.9110

-6 piperdine

11.123

7.5310

-12 proline

1.952 (COOH)

10.640 (NH)

1.1210

-2

2.2910

-11 propanoic acidCH 3 CH 2

COOH4.874

1.3410

-5 propylamineCH 3 CH 2 CH 2 NH 3 +

10.566

2.7210

-11 pryidine 5.229

5.9010

-6 resorcinol 9.30 11.06 5.010 -10 8.710 -12 salicylic acid

2.97 (COOH)

13.74 (OH)

1.110 -3 1.810 -14 serine

2.187 (COOH)

9.209 (NH

3 )

6.5010

-3

6.1810

-10 succinic acid 4.207 5.636

6.2110

-5

2.3110

-6 sulfuric acidH 2 SO 4 strong 1.99 - 1.010 -2

1101Appendices

CompoundConjugate AcidpK

a K a sulfurous acidH 2 SO 3 1.91 7.18 1.210 -2 6.610 -8 ?-tartaric acid

3.036 (COOH)

4.366 (COOH)

9.2010

-4

4.3110

-5 threonine

2.088 (COOH)

9.100 (NH

3 )

8.1710

-3

7.9410

-10 thiosulfuric acidH 2 S 2 O 3 0.6 1.6 3.10 -1 3.10 -2 trichloroacetic acid (0.1 M) Cl 3

CCOOH0.66

2.210 -1 triethanolamine(HOCH 2 CH 2 ) 3 NH + 7.762

1.7310

-8 triethylamine(CH 3 CH 2 ) 3 NH +

10.715

1.9310

-11 trimethylamine(CH 3 ) 3 NH + 9.800

1.5810

-10 tris(hydroxymethyl)amino meth- ane (TRIS or THAM) (HOCH 2 ) 3 CNH 3 + 8.075

8.4110

-9 tryptophan (0.1 M)

2.35 (COOH)

9.33 (NH

3 ) 4.510 -3 4.710 -10 tryosine (p a1 : 0.1 M)

2.17 (COOH)

9.19 (NH

3 )

10.47 (OH)

6.810 -3 6.510 -10 3.410 -11 valine

2.286 (COOH)

9.718 (NH

3 )

5.1810

-3

1.9110

-10

1102Analytical Chemistry 2.0

Appendix 12: Formation Constants

The following table provides K

i and i values for selected metal-ligand complexes, arranged by the ligand.

All values are from Martell, A. E.; Smith, R. M. Critical Stability Constants, Vols. 1-4. Plenum Press: New

York, 1976. Unless otherwise stated, values are for 25 o C and zero ionic strength. ?ose values in brackets are considered less reliable. K K K K K K Mg 2+ 1.27 Ca 2+ 1.18 Ba 2+ 1.07 Mn 2+ 1.40 Fe 2+ 1.40 Co 2+ 1.46 Ni 2+ 1.43 Cu 2+

2.221.41

Ag 2+

0.73-0.09

Zn 2+ 1.57 Cd 2+

1.931.22-0.89

Pb 2+

2.681.40

K K K K K K Ag +

3.313.91

Co 2+ (T 20 o C)

1.991.510.930.640.06-0.73

Ni 2+

2.722.171.661.120.67-0.03

Cu 2+

4.043.432.801.48

Zn 2+

2.212.292.362.03

Cd 2+

2.552.011.340.84

K K K K K K Cu 2+ 0.40 Fe 3+

1.480.65

Ag + ( 5.0 M)

3.701.920.78-0.3

Zn 2+

0.430.18-0.11-0.3

Cd 2+

1.981.62-0.2-0.7

Pb 2+

1.590.21-0.1-0.3

1103Appendices

Cyanide

CN - log K 1 log K 2 log K 3 log K 4 log K 5 log K 6 Fe 2+

35.4 (

6 ) Fe 3+

43.6 (

6 ) Ag +

20.48

2 0.92 Zn 2+

11.07

2

4.983.57

Cd 2+

6.015.114.532.27

Hg 2+

17.0015.753.562.66

Ni 2+ 30.22
( 4 )

Ethylenediamine

log K 1 log K 2 log K 3 log K 4 log K 5 log K 6 Ni 2+

7.386.184.11

Cu 2+

10.489.07

Ag + (20 o

C, 0.1 M)

4.7003.00

Zn 2+

5.664.983.25

Cd 2+

5.414.502.78

EDTA log K 1 log K 2 log K 3 log K 4 log K 5 log K 6 Mg 2+ (20 o

C, 0.1 M)

8.79 Ca 2+ (20 o

C, 0.1 M)

10.69 Ba 2+ (20 o

C, 0.1 M)

7.86 Bi 3+ (20 o

C, 0.1 M)

27.8
Co 2+ + (20 o

C, 0.1 M)

16.31 Ni 2+ (20 o

C, 0.1 M)

18.62 Cu 2+ (20 o

C, 0.1 M)

18.80 Cr 3+ (20 o

C, 0.1 M)

[23.4] Fe 3+ (20 o

C, 0.1 M)

25.1
Ag + (20 o

C, 0.1 M)

7.32 Zn 2+ (20 o

C, 0.1 M)

16.50 Cd 2+ (20 o

C, 0.1 M)

16.46 Hg 2+ (20 o

C, 0.1 M)

21.7
Pb 2+ (20 o

C, 0.1 M)

18.04

1104Analytical Chemistry 2.0

Al 3+ (T 20 o

C, 0.1 M)

16.3

Fluoride

F - log 1 log 2 log 3 log 4 log 5 log 6 Al 3+ ( 0.5 M)

6.115.013.883.01.40.4

Hydroxide

OH - log 1 log 2 log 3 log 4 log 5 log 6 Al 3+

9.01[9.69][8.3]6.0

Co 2+

4.34.11.30.5

Fe 2+

4.5[2.9]2.6-0.4

Fe 3+

11.8110.512.1

Ni 2+

4.13.93.

Pb 2+

6.34.63.0

Zn 2+

5.0[6.1]2.5[1.2]

Iodide

I - log 1 log 2 log 3 log 4 log 5 log 6 Ag + (T 18 o C)

6.58[5.12][1.4]

Cd 2+

2.281.641.081.0

Pb 2+

1.921.280.70.6

Nitriloacetate

log 1 log 2 log 3 log 4 log 5 log 6 Mg 2+ (T 20 o

C, 0.1 M)

5.41 Ca 2+ (T 20 o

C, 0.1 M)

6.41 Ba 2+ (T 20 o

C, 0.1 M)

4.82 Mn 2+ (T 20 o

C, 0.1 M)

7.44 Fe 2+ (T 20 o

C, 0.1 M)

8.33 Co 2+ (T 20 o

C, 0.1 M)

10.38 Ni 2+ (T 20 o

C, 0.1 M)

11.53 Cu 2+ (T 20 o

C, 0.1 M)

12.96 Fe 3+ (T 20 o

C, 0.1 M)

15.9 Zn 2+ (T 20 o

C, 0.1 M)

10.67

1105Appendices

Cd 2+ (T 20 o

C, 0.1 M)

9.83 Pb 2+ (T 20 o

C, 0.1 M)

11.39

Oxalate

C 2 O 4 2- log 1 log 2 log 3 log 4 log 5 log 6 Ca 2+ ( 1 M)

1.661.03

Fe 2+ ( 1 M)

3.052.10

Co 2+

4.722.28

Ni 2+ 5.16 Cu 2+

6.234.04

Fe 3+ ( 0.5 M)

7.536.114.85

Zn 2+

4.872.78

1,10-Phenanthroline

log 1 log 2 log 3 log 4 log 5 log 6 Fe 2+

20.7 (

3 ) Mn 2+ ( 1 M)

4.03.33.0

Co 2+ ( 1 M)

7.086.646.08

Ni 2+

8.68.17.6

Fe 3+

13.8 (

3 ) Ag + ( 1 M)

5.027.04

Zn 2+

6.2[5.9][5.2]

Thiosulfate

S 2 O 3 2- log 1 log 2 log 3 log 4 log 5 log 6 Ag + (T 20 o C)

8.824.850.53

Thiocyanate

SCN - log 1 log 2 log 3 log 4 log 5 log 6 Mn 2+ 1.23 Fe 2+ 1.31 Co 2+ 1.72 Ni 2+ 1.76 Cu 2+ 2.33 Fe 3+ 3.02

1106Analytical Chemistry 2.0

Ag +

4.83.431.270.2

Zn 2+

1.330.580.09-0.4

Cd 2+

1.890.890.02-0.5

Hg 2+ 17.26 ( 2 )2.711.83

1107Appendices

Appendix 13: Standard Reduction Potentials

The following table provides E

o and E o ´ values for selected reduction reactions. Values are from the following

sources: Bard, A. J.; Parsons, B.; Jordon, J., eds. Standard Potentials in Aqueous Solutions, Dekker: New York,

1985; Milazzo, G.; Caroli, S.; Sharma, V. K. Tables of Standard Electrode Potentials, Wiley: London, 1978; Swift,

E. H.; Butler, E. A. Quantitative Measurements and Chemical Equilibria, Freeman: New York, 1972.

Solids, gases, and liquids are identified; all other species are aqueous. Reduction reactions in acidic solution are

written using H + in place of H 3 O + . You may rewrite a reaction by replacing H + with H 3 O + and adding to the opposite side of the reaction one molecule of H 2

O per H

+ ; thus H 3 AsO 4 2H + 2e - HAsO 2 2H 2 O becomes H 3 AsO 4 2H 3 O + + 2e - HAsO 2 4H 2 O

Conditions for formal potentials (E

o ´ ) are listed next to the potential. EE AlAl 3 3 es()-1.676

Al(OH)AlOH

4 34
es()-2.310

AlFAlF

63
36
es()-2.07 EE

SbHSbH

33
3 eg()-0.510

SbOHSbOHO

522

6423()()sle

0.605

SbOHSbHO

2

23esl()()0.212

EE

AsHAsH

33
3 eg()-0.225

HAsOHHAsOHO

3242
222
el()0.560

HAsOHAsHO

22
332
esl()()0.240 EE BaBa 2 2 es()-2.92

BaOHBaHO

2 ()()()ssle

222.365

1108Analytical Chemistry 2.0

BerylliumE° (V)E°"(V)

BeBe 2 2 ()-1.99

BismuthE° (V)E°"(V)

BiBi 3 3 ()0.317

BiClBiCl

4 34
()0.199

BoronE° (V)E°"(V)

B(OHHBHO

2 )()() 3 333
-0.890

B(OHBOH)()

4 34
-1.811

BromineE° (V)E°"(V)

BrBr 2

221.087

HOBrHBrHO

2

2()1.341

HOBrHBrHO

2 12 ()1.604

BrOHOBrOH

2 ()220.76 in NaOH

BrOHBrHO

23122
653
()1.5

BrOHBrHO

23
663
1.478

CadmiumE° (V)E°"(V)

CdCd 2 2 ()-0.4030

Cd(CN)CdCN

42
24
()-0.943

Cd(NH)CdNH

342
3 24
()-0.622

CalciumE° (V)E°"(V)

CaCa 2 2 ()-2.84

1109Appendices

CarbonE° (V)E°"(V)

COHCOHO

22

22()()()

-0.106

COHHCOH

22
22()
-0.20 222
2224

COHHCO()

-0.481

HCHOHCHOH

22
3

0.2323

CeriumE° (V)E°"(V)

CeCe 3 3 ()-2.336 CeCe 43
1.72

1.70 in HClO

4

1.44 in H

2 SO 4

1.61 in HNO

3

1.28 in HCl

ChlorineE° (V)E°"(V)

ClCl 2 22()
1.396

ClOHOClOH

2 ()() 122

20.421 in NaOH

ClOHOClOH

2 ()220.890 in NaOH

HClOHHOClHO

22
22
1.64

ClOHClOHO

232
2 ()1.175

ClOHHClOHO

232
32
1.181

ClOHClOHO

243
22
1.201

ChromiumE° (V)E°"(V)

CrCr 32
-0.424 CrCr 2 2 ()-0.90

CrOHCrHO

22723
14627
()1.36

CrOHOCrOHOH

242
4 4324
()()-0.13 in NaOH

1110Analytical Chemistry 2.0

CobaltE° (V)E°"(V)

CoCo 2 2 ()-0.277 CoCo 32
1.92

Co(NHCo(NH

363
362
)) 0.1

Co(OHCo(OHOH))()()

32
0.17

Co(OHCoOH)()()

2 22
-0.746

CopperE° (V)E°"(V)

CuCu ()0.520 CuCu 2 0.159 CuCu 2 2 ()0.3419

CuICuI

2 ()0.86

CuClCuCl

2 ()0.559

FluorineE° (V)E°"(V)

FHHF 2 222()
3.053 FF 2 22()
2.87

GalliumE° (V)E°"(V)

GaGa 3 3 ()

GoldE° (V)E°"(V)

AuAu ()1.83 AuAu 3 2 1.36 AuAu 3 3 ()1.52

AuClAuCl

4 34
()1.002

1111Appendices

HydrogenE° (V)E°"(V)

22
2 HH ()0.00000 HOHOH 2 122
()-0.828

IodineE° (V)E°"(V)

II 2 22()

0.5355

II 3 23
0.536

HIOHIHO

2

2()0.985

IOHIHO

23122
653
()()1.195

IOHOIOH

23
366
()0.257

IronE° (V)E°"(V)

FeFe 2 2 ()-0.44 FeFe 3 3 ()-0.037 FeFe 32
0.771

0.70 in HCl

0.767 in HClO

4

0.746 in HNO

3

0.68 in H

2 SO 4

0.44 in H

3 PO 4

Fe(CN)Fe(CN)

63
64
0.356

Fe(phen)Fe(phen)

63
62
1.147

LanthanumE° (V)E°"(V)

LaLa 3 3 ()-2.38

LeadE° (V)E°"(V)

PbPb 2 2 ()-0.126

PbOOHPbHO

222

422()()

1.46

PbOOHPbSOHO

2242
4

4422()()()

1.690

PbSOPbSO

442
2()() -0.356

1112Analytical Chemistry 2.0

LithiumE° (V)E°"(V)

LiLi ()-3.040

MagnesiumE° (V)E°"(V)

MgMg 2 2 ()-2.356

Mg(OH)MgOH

2

22()()

-2.687

ManganeseE° (V)E°"(V)

MnMn 2 2 ()-1.17 MnMn 32
1.5

MnOHMnHO

222

422()()

1.23

MnOHMnOHO

242
432
()()1.70

MnOHMnHO

242
854
()1.51

MnOHOMnOOH

242
234
()()0.60

MercuryE° (V)E°"(V)

HgHg 2 2 ()0.8535 22
2 22
HgHg 0.911 HgHg 22
22
()0.7960

HgClHgCl

22

222()()

0.2682

HgOHHgHO

2 ()()()

220.926

HgBrHgBr

22

222()()

1.392

HgIHgI

22

222()()

-0.0405

1113Appendices

MolybdenumE° (V)E°"(V)

MoMo 3 3 ()-0.2

MoOHMoHO

22

442()()()

-0.152

MoOHOMoOH

242
468
()()-0.913

NickelE° (V)E°"(V)

NiNi 2 2 ()-0.257

NiOHNiOH()()

2 22
-0.72

NiNHNiNH()()

362
3 26
-0.49

NitrogenE° (V)E°"(V)

NHNH 225
54()
-0.23

NOHNHO

222

22()()()

1.77 222
2

NOHNOHO

2 ()()() 1.59

HNOHNOHO

22
()()0.996 2443
22

HNOHNOHO

2 ()()1.297

NOHNOHO

223
32
()0.94

OxygenE° (V)E°"(V)

OHHO 222
22()
0.695 OHHO 22

442()()

1.229 HOHHO 222
222
()1.763 OHOOH 22

244()()

0.401 OHOHO 232

22()()()

2.07

1114Analytical Chemistry 2.0

PhosphorousE° (V)E°"(V)

PHPHwhite(,)()

33
3

HPOHHPOHO

33322
22()

HPOHHPOHO

33243
22
()

PlatinumE° (V)E°"(V)

PtPt 2 2 ()

PtClPtCl

42
24
()

PotassiumE° (V)E°"(V)

KK ()

RutheniumE° (V)E°"(V)

RuRu 32
0.249

RuOHRuHO

22

442()()()

0.68

RuNHRuRuNH()()()

363
362
0.10

RuCNRuRuCN()()()

63
64
0.86

SeleniumE° (V)E°"(V)

SeSe()

2 2 -0.67 in NaOH

SeHHSe()()

22
2 -0.115

HSeOHSeHO

223
443
()()0.74

SeOHHSeOHO

243
23
4 ()1.151

SiliconE° (V)E°"(V)

SiFSiF

62
46
()-1.37

SiOHSiHO

22

442()()()

-0.909

SiOHSiHHO

224

882()()()

-0.516

1115Appendices

SilverE° (V)E°"(V)

AgAg ()0.7996

AgBrAgBr()()

0.071

AgCOAgCO

224242

22()()

0.47

AgClAgCl()()

0.2223

AgIAgI()()

-0.152

AgSAgS

22

22()()

-0.71

AgNHAgNH()()

323
2 -0.373

SodiumE° (V)E°"(V)

NaNa ()-2.713

StrontiumE° (V)E°"(V)

SrSr 2 2 ()-2.89

SulfurE° (V)E°"(V)

SS() 2 2 -0.407

SHHS()

22
2 0.144

SOHHSO

262
23
422
0.569 SOSO 282
42
22
1.96 SOSO 462
232
22
0.080 2224
32
242

SOHOSOOH

2 ()-1.13 2346
32
232

SOHOSOOH

2 ()-0.576 in NaOH 2422
42
262

SOHSOHO

2 ()-0.25

SOHOSOOH

242
32
22
()-0.936

SOHHSOHO

242
232
42
()0.172

1116Analytical Chemistry 2.0

ThalliumE° (V)E°"(V)

TlTl 3 2

1.25 in HClO

4

0.77 in HCl

TlTl 3 3 ()0.742

TinE° (V)E°"(V)

SnSn 2 2 ()-0.19 in HCl SnSn 42
2

0.1540.139 in HCl

TitaniumE° (V)E°"(V)

TiTi 2 2 ()-0.163 TiTi 32
-0.37

TungstenE° (V)E°"(V)

WOHWHO

22

442()()()

-0.119

WOHWHO

23

663()()()

-0.090

UraniumE° (V)E°"(V)

UU 3 3 ()-1.66 UU 43
-0.52

UOHUHO

224
42
()0.27 UOUO 22
2 0.16

UOHUHO

2224
422
()0.327

VanadiumE° (V)E°"(V)

VV 2 2 ()-1.13 VV 32
-0.255

VOHVHO

223
2 ()0.337

VOHVOHO

2222
2 ()1.000

1117Appendices

ZincE° (V)E°"(V)

ZnZn 2 2 ()-0.7618

Zn(OH)ZnOH

42
24
()-1.285

Zn(NH)ZnNH

342
3 24
()-1.04

Zn(CN)ZnCN

42
24
()-1.34

1118Analytical Chemistry 2.0

Appendix 14: Random Number Table

The following table provides a list of random numbers in which the digits 0 through 9 appear with approxi-

mately equal frequency. Numbers are arranged in groups of five to make the table easier to view. ?is arrange-

ment is arbitrary, and you can treat the table as a sequence of random individual digits (1, 2, 1, 3, 7, 4...going

down the first column of digits on the left side of the table), as a sequence of three digit numbers (111, 212,

104, 367, 739... using the first three columns of digits on the left side of the table), or in any other similar

manner.

Let's use the table to pick 10 random numbers between 1 and 50. To do so, we choose a random starting point,

perhaps by dropping a pencil onto the table. For this exercise, we will assume that the starting point is the fifth

row of the third column, or 12032. Because the numbers must be between 1 and 50, we will use the last two

digits, ignoring all two-digit numbers less than 01 or greater than 50, and rejecting any duplicates. Proceeding

down the third column, and moving to the top of the fourth column when necessary, gives the following 10

random numbers: 32, 01, 05, 16, 15, 38, 24, 10, 26, 14.

?ese random numbers (1000 total digits) are a small subset of values from the publication Million Random

Digits (Rand Corporation, 2001) and used with permission. Information about the publication, and a link to

a text file containing the million random digits is available at http://www.rand.org/pubs/monograph_reports/

MR1418/.

11164363187506137674263207510010431204181922891792

21215917917683158678870543168793205436851973208468

10438444826655837649088829087012462418100180602977

36792262363326666583608819739520461367420285250564

73944047731203251414823843837000249807097260567497

49563128721406393104784837271768714180482500504151

64208482374170173117332424231483049219339281304763

51486728753860529341807498015133835526027914708868

99756263606451617971484780961004638171410922710606

71325552171301572907004314511733827928730295385474

65285971981213853010956011583816805610044351617020

17264573273822429301313813810934976656929856629550

95639997543119992558683680498551092377804026114479

61555764048621011808128414514797438600221264562000

78137987680468987130792250815384967645397949374917

624909921584987287

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