Common Mathematical Operations in Chemistry - … Appendix A • Common Mathematical Operations in...

3.2 Section • Determining the Formula of an Unknown Compound A-1

Common Mathematical Operations in Chemistry

In addition to basic arithmetic and algebra, four mathematical operations are used frequently in general chemistry: manipulating logarithms, using exponential nota-

tion, solving quadratic equations, and graphing data. Each is discussed briefly below.

ManIpUlatIng logarIthMsMeaning and Properties of LogarithmsA logarithm is an exponent. Specifically, if xn A, we can say that the logarithm to the base x of the number A is n, and we can denote it as

logx A n

Because logarithms are exponents, they have the following properties:

logx 1 0

logx (A 3 B) logx A 1 logx B

logx A

B5 logx A 2 logx B

logx Ay y logx A

Types of LogarithmsCommon and natural logarithms are used in chemistry and the other sciences.

1. For common logarithms, the base (x in the examples above) is 10, but they are written without specifying the base; that is, log10 A is written more simply as log A; thus, the notation log means base 10. The common logarithm of 1000 is 3; in other words, you must raise 10 to the 3rd power to obtain 1000:

log 1000 3 or 103 1000

Similarly, we have

log 10 1 or 101 10 log 1,000,000 6 or 106 1,000,000 log 0.001 23 or 1023 0.001 log 853 2.931 or 102.931 853

The last example illustrates an important point about significant figures with all loga-rithms: the number of significant figures in the number equals the number of digits to the right of the decimal point in the logarithm. That is, the number 853 has three significant figures, and the logarithm 2.931 has three digits to the right of the decimal point. To find a common logarithm with an electronic calculator, enter the number and press the log button.

2. For natural logarithms, the base is the number e, which is 2.71828 . . . , and loge A is written ln A; thus, the notation ln means base e. The relationship between the common and natural logarithms is easily obtained:

log 10 1 and ln 10 2.303

Appendix A

A-1

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A-2 Appendix A • Common Mathematical Operations in Chemistry

Therefore, we have

ln A 5 2.303 log A

To find a natural logarithm with an electronic calculator, enter the number and press the ln button. If your calculator does not have an ln button, enter the number, press the log button, and multiply by 2.303.

AntilogarithmsThe antilogarithm is the base raised to the logarithm:

antilogarithm (antilog) of n is 10n

Using two of the earlier examples, the antilog of 3 is 1000, and the antilog of 2.931 is 853. To obtain the antilog with a calculator, enter the number and press the 10x button. Similarly, to obtain the natural antilogarithm, enter the number and press the ex button. [On some calculators, enter the number and first press inv and then the log (or ln) button.]

Using ExponEntiAl (sciEntific) notAtionMany quantities in chemistry are very large or very small. For example, in the conven-tional way of writing numbers, the number of gold atoms in 1 gram of gold is

59,060,000,000,000,000,000,000 atoms (to four significant figures)

As another example, the mass in grams of one gold atom is

0.0000000000000000000003272 g (to four significant figures)

Exponential (scientific) notation provides a much more practical way of writing such numbers. In exponential notation, we express numbers in the form

A10n

where A (the coefficient) is greater than or equal to 1 and less than 10 (that is, 1 A 10), and n (the exponent) is an integer. If the number we want to express in exponential notation is larger than 1, the exponent is positive (n 0); if the number is smaller than 1, the exponent is negative (n 0). The size of n tells the number of places the decimal point (in conventional notation) must be moved to obtain a coefficient A greater than or equal to 1 and less than 10 (in exponential notation). In exponential notation, 1 gram of gold contains 5.9061022 atoms, and each gold atom has a mass of 3.2721022 g.

Changing Between Conventional and Exponential NotationIn order to use exponential notation, you must be able to convert to it from conven-tional notation, and vice versa.

1. To change a number from conventional to exponential notation, move the decimal point to the left for numbers equal to or greater than 10 and to the right for num-bers between 0 and 1:

75,000,000 changes to 7.5107 (decimal point 7 places to the left)0.006042 changes to 6.042103 (decimal point 3 places to the right)

2. To change a number from exponential to conventional notation, move the deci-mal point the number of places indicated by the exponent to the right for num-bers with positive exponents and to the left for numbers with negative exponents:

1.38105 changes to 138,000 (decimal point 5 places to the right)8.41106 changes to 0.00000841 (decimal point 6 places to the left)

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Appendix A • Common Mathematical Operations in Chemistry A-3

3. An exponential number with a coefficient greater than 10 or less than 1 can be changed to the standard exponential form by converting the coefficient to the stan-dard form and adding the exponents:

582.3106 changes to 5.823 102 106 5 5.82310(26) 5 5.823108

0.0043104 changes to 4.3 103 104 5 4.310[(3)(4)] 5 4.3107

Using Exponential Notation in CalculationsIn calculations, you can treat the coefficient and exponents separately and apply the properties of exponents (see earlier section on logarithms).

1. To multiply exponential numbers, multiply the coefficients, add the exponents, and reconstruct the number in standard exponential notation:

(5.5103)(3.1105) 5 (5.5 3.1)10(35) 5 17108 5 1.7109

(9.71014)(4.31020) 5 (9.7 4.3)10[14(20)] 5 42106 5 4.2105

2. To divide exponential numbers, divide the coefficients, subtract the exponents, and reconstruct the number in standard exponential notation:

2.63106

5.83102 52.6

5.8 10(62) 5 0.45104 5 4.5103

1.731025

8.231028 51.7

8.2 10[(5)(8)] 5 0.21103 5 2.1102

3. To add or subtract exponential numbers, change all numbers so that they have the same exponent, then add or subtract the coefficients:

(1.45104) (3.2103) 5 (1.45104) (0.32104) 5 1.77104

(3.22105) (9.02104) 5 (3.22105) (0.902105) 5 2.32105

solving QUAdrAtic EQUAtionsA quadratic equation is one in which the highest power of x is 2. The general form of a quadratic equation is

ax2 bx c 5 0

where a, b, and c are numbers. For given values of a, b, and c, the values of x that satisfy the equation are called solutions of the equation. We calculate x with the qua-dratic formula:

x 52b 6"b2 2 4ac

2a

We commonly require the quadratic formula when solving for some concentration in an equilibrium problem. For example, we might have an expression that is rearranged into the quadratic equation

4.3x2 0.65x 8.7 5 0 a b c

Applying the quadratic formula, with a 5 4.3, b 5 0.65, and c 5 8.7, gives

x 520.65 6"10.65 22 2 4 14.3 2 128.7 2

2 14.3 2The “plus or minus” sign () indicates that there are always two possible values for x. In this case, they are

x 5 1.3 and x 5 1.5

In any real physical system, however, only one of the values will have any meaning. For example, if x were [H3O], the negative value would give a negative concentra-tion, which has no physical meaning.

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A-4 appendix a • Common Mathematical Operations in Chemistry

graphIng Data In thE ForM oF a straIght lInEVisualizing changes in variables by means of a graph is used throughout science. In many cases, it is most useful if the data can be graphed in the form of a straight line. Any equation will appear as a straight line if it has, or can be rearranged to have, the following general form:

y mx 1 b

where y is the dependent variable (typically plotted along the vertical axis), x is the independent variable (typically plotted along the horizontal axis), m is the slope of the line, and b is the intercept of the line on the y axis. The intercept is the value of y when x 0:

y m(0) 1 b b

The slope of the line is the change in y for a given change in x:

Slope (m) 5y2 2 y1

x2 2 x15Dy

Dx

The sign of the slope tells the direction of the line. If y increases as x increases, m is positive, and the line slopes upward with higher values of x; if y decreases as x increases, m is negative, and the line slopes downward with higher values of x. The magnitude of the slope indicates the steepness of the line. A line with m 3 is three times as steep (y changes three times as much for a given change in x) as a line with m 1. Consider the linear equation y 2x 1 1. A graph of this equation is shown in Figure A.1. In practice, you can find the slope by drawing a right triangle to the line, using the line as the hypotenuse. Then, one leg gives y, and the other gives x. In the figure, y 8 and x 4. At several places in the text, an equation is rearranged into the form of a straight line in order to determine information from the slope and/or the intercept. For exam-ple, in Chapter 16, we obtained the following expression:

ln 3A 403A 4t

5 kt

Based on the properties of logarithms, we have

ln [A]0 2 ln [A]t kt

Rearranging into the form of an equation for a straight line gives

ln [A]t 2kt 1 ln [A]0

y mx 1 b

Thus, a plot of ln [A]t vs. t is a straight line, from which you can see that the slope is 2k (the negative of the rate constant) and the intercept is ln [A]0 (the natural logarithm of the initial concentration of A). At many other places in the text, linear relationships occur that were not shown in graphical terms. For example, the conversion of temperature scales in Chapter 1 can also be expressed in the form of a straight line:

°F 95 °C 1 32

y mx 1 b

Figure A.1

14

12

10

8

6

4

2

y 2x 1 1

Slope 8⁄4 2

Intercept

20

2

2 4 6

x

y


3.2 Section • Determining the Formula of an Unknown Compound 5

Standard Thermodynamic Values for Selected Substances*

CaCO3(s)CaO(s)Ca(OH)2(s)Ca3(PO4)2(s)CaSO4(s)

CarbonC(graphite)C(diamond)C(g)CO(g)CO2(g)CO2(aq)CO3

22(aq)HCO3

2(aq)H2CO3(aq)CH4(g)C2H2(g)C2H4(g)C2H6(g)C3H8(g)C4H10(g)C6H6(l)CH3OH(g)CH3OH(l)HCHO(g)HCOO2(aq)HCOOH(l)HCOOH(aq)C2H5OH(g)C2H5OH(l)CH3CHO(g)CH3COOH(l)C6H12O6(s)C12H22O11(s)CN2(aq)HCN(g)HCN(l)HCN(aq)CS2(g)CS2(l)CH3Cl(g)CH2Cl2(l)

e2(g)Aluminum

Al(s)Al31(aq)AlCl3(s)Al2O3(s)

BariumBa(s)Ba(g)Ba21(g)Ba21(aq)BaCl2(s)BaCO3(s)BaO(s)BaSO4(s)

BoronB(-rhombo-

hedral)BF3(g)BCl3(g)B2H6(g)B2O3(s)H3BO3(s)

BromineBr2(l)Br2(g)Br(g)Br2(g)Br2(aq)HBr(g)

CadmiumCd(s)Cd(g)Cd21(aq)CdS(s)

CalciumCa(s)Ca(g)Ca21(g)Ca21(aq)CaF2(s)CaCl2(s)

0

0 2524.7 2704.2 21676

0 175.6 1649.9 2538.36 2806.06 21219 2548.1 21465

0

21137.0 2403.8 35 21272 21094.3

0 30.91 111.9 2218.9 2120.9 236.3

0 112.8 272.38 2144

0 192.6 1934.1 2542.96 21215 2795.0

21206.9 2635.1 2986.09 24138 21432.7

0 1.896 715.0 2110.5 2393.5 2412.9 2676.26 2691.11 2698.7 274.87 227 52.47 284.667 2105 2126 49.0 2201.2 2238.6 2116 2410 2409 2410 2235.1 2277.63 2166 2487.0 21273.322221.7 151 135 105 105 117 87.9 283.7 2117

0

0 2481.2 2628.9 21582

0 144.8 — 2560.7 2810.9 21139 2520.4 21353

0

21120.3 2388.7 86.6 21193 2969.01

0 3.13 82.40 — 2102.82 253.5

0 78.20 277.74 2141

0 158.9

— 2553.04 21162 2750.2

21128.8 2603.5 2898.56 23899 21320.3

0 2.866 669.6 2137.2 2394.4 2386.2 2528.10 587.06 2623.42 250.81 209 68.36 232.89 224.5 216.7 124.5 2161.9 2166.2 2110 2335 2346 2356 2168.6 2174.8 2133.7 2392 2910.5621544.3 166 125 121 112 66.9 63.6 260.2 263.2

20.87

28.3 2313 110.7 50.94

62.5 170.28 — 13 126 112 72.07 132

5.87

254.0 290.0 232.0 53.8 88.83

152.23 245.38 174.90 — 80.71 198.59

51.5 167.64 261.1 71

41.6 154.78

— 255.2 68.87 114

92.9 38.2 83.39 263 107

5.686 2.439 158.0 197.5 213.7 121 253.1 95.0 191 186.1 200.85 219.22 229.5 269.9 310 172.8 238 127 219 91.6 129.0 164 282.6 161 266 160 212.1 360.24 118 201.7 112.8 129 237.79 151.0 234 179

(continued)*All values at 298 K.

Substance or Ion

DH 8f (kJ/mol)

DG 8f (kJ/mol)

S 8 (J/molK)

Substance or Ion

DH 8f (kJ/mol)

DG 8f (kJ/mol)

S 8 (J/molK)

Appendix B

A-5


A-6 appendix B • Standard Thermodynamic Values for Selected Substances

Fe21(aq)FeCl2(s)FeCl3(s)FeO(s)Fe2O3(s)Fe3O4(s)

LeadPb(s)Pb21(aq)PbCl2(s)PbO(s)PbO2(s)PbS(s)PbSO4(s)

LithiumLi(s)Li(g)Li1(g)Li1(aq)LiF(s)LiCl(s)LiBr(s)LiI(s)

MagnesiumMg(s)Mg(g)Mg21(g)Mg21(aq)MgCl2(s)MgCO3(s)MgO(s)Mg3N2(s)

ManganeseMn(s, )Mn21(aq)MnO2(s)MnO4

2(aq)Mercury

Hg(l)Hg(g)Hg21(aq)Hg2

21(aq)HgCl2(s)Hg2Cl2(s)HgO(s)

NitrogenN2(g)N(g)N2O(g)NO(g)NO2(g)N2O4(g)N2O5(g)N2O5(s)NH3(g)NH3(aq)N2H4(l)

CHCl3(l)CCl4(g)CCl4(l)COCl2(g)

CesiumCs(s)Cs(g)Cs1(g)Cs1(aq)CsF(s)CsCl(s)CsBr(s)CsI(s)

ChlorineCl2(g)Cl(g)Cl2(g)Cl2(aq)HCl(g)HCl(aq)ClO2(g)Cl2O(g)

ChromiumCr(s)Cr31(aq)CrO4

22(aq)Cr2O7

22(aq)Copper

Cu(s)Cu(g)Cu1(aq)Cu21(aq)Cu2O(s)CuO(s)Cu2S(s)CuS(s)

FluorineF2(g)F(g)F2(g)F2(aq)HF(g)

HydrogenH2(g)H(g)H1(aq)H1(g)

IodineI2(s)I2(g)I(g)I2(g)I2(aq)HI(g)

IronFe(s)Fe31(aq)

2132 296.0 2139 2220

0 76.7 458.5 2248 2554.7 2442.8 2395 2337

0 121.0 2234 2167.46 292.31 2167.46 102 80.3

0 21971 2863.2 21461

0 341.1 51.9 64.39 2168.6 2157.3 279.5 253.1

0 78.9 2255.6 2329.1 2273

0 218.0 0 1536.3

0 62.442 106.8 2194.7 255.94 25.9

0 247.7

287.9 2341.8 2399.5 2272.0 2825.5 21121

0 1.6 2359 2218 2276.6 298.3 2918.39

0 161 687.163 2278.46 2616.9 2408 2351 2270

0 150 2351 2461.96 2641.6 21112 2601.2 2461

0 2219 2520.9 2518.4

0 61.30 171 172 2230 2264.9 290.79

0 473 82.05 90.29 33.2 9.16 11 243.1 245.9 280.83 50.63

271.5 253.7 268.6 2206

0 49.7 427.1 2282.0 2525.4 2414 2383 2333

0 105.0 2240 2131.17 295.30 2131.17 120 97.9

0—

2706.3 21257

0 301.4 50.2 64.98 2146.0 2130 286.2 253.6

0 61.8 2262.5 2276.5 2275

0 203.30 0 1517.1

0 19.38 70.21

— 251.67 1.3

0 210.5

284.94 2302.3 2334.1 2251.4 2743.6 21018

0 224.3 2314 2198 2219.0 296.7 2811.24

0 128 649.989 2293.8 2588.7 2384 2342 2270

0 115

— 2456.01 2592.1 21028 2569.0 2401

0 2223 2466.1 2425.1

0 31.8 164.4 153.6 2184 2210.66 258.50

0 456 104.2 86.60 51 97.7 118 114 216 26.7 149.2

203 309.7 214.4 283.74

85.15 175.5 169.72 133 88 101.18 121 130

223.0 165.1 153.25 55.10 186.79 55.06 256.7 266.1

23.8—

38 214

33.1 166.29 226 298.7 93.1 42.63 120.9 66.5

202.7 158.64 145.47 29.6 173.67

130.6 114.60 0 108.83

116.14 260.58 180.67

— 109.4 206.33

27.3 2293

113 117.9 142 60.75 87.400 145.3

64.785 21 136 68.70 76.6 91.3 147

29.10 138.67 132.91 14 35.66 59.30 74.1 85.8

32.69 148.55

— 118 89.630 65.86 26.9 88

31.8 284 53.1 190

76.027 174.87 232 84.5 144 196 70.27

191.5 153.2 219.7 210.65 239.9 304.3 346 178 193 110 121.2

(continued )

Substance or Ion

DH 8f (kJ/mol)

DG 8f (kJ/mol)

S 8 (J/molK)

Substance or Ion

DH 8f (kJ/mol)

DG 8f (kJ/mol)

S 8 (J/molK)


appendix B • Standard Thermodynamic Values for Selected Substances A-7

AgF(s)AgCl(s)AgBr(s)AgI(s)AgNO3(s)Ag2S(s)

SodiumNa(s)Na(g)Na1(g)Na1(aq)NaF(s)NaCl(s)NaBr(s)NaOH(s)Na2CO3(s)NaHCO3(s)NaI(s)

StrontiumSr(s)Sr(g)Sr21(g)Sr21(aq)SrCl2(s)SrCO3(s)SrO(s)SrSO4(s)

SulfurS(rhombic)S(monoclinic)S(g)S2(g)S8(g)S22(aq)HS2(aq)H2S(g) H2S(aq)SO2(g)SO3(g)SO4

22(aq)HSO4

2(aq)H2SO4(l)H2SO4(aq)

TinSn(white)Sn(gray)SnCl4(l)SnO2(s)

TitaniumTi(s)TiCl4(l)TiO2(s)

ZincZn(s)Zn(g)Zn21(aq)ZnO(s)ZnS(s, zinc

blende)

NO32(aq)

HNO3(l)HNO3(aq)NF3(g)NOCl(g)NH4Cl(s)

OxygenO2(g)O(g)O3(g)OH2(aq)H2O(g)H2O(l)H2O2(l)H2O2(aq)

PhosphorusP4(s, white)P(g)P(s, red)P2(g)P4(g)PCl3(g)PCl3(l)PCl5(g)PCl5(s)P4O10(s)PO4

32(aq)HPO4

22(aq)H2PO4

2(aq)H3PO4(aq)

PotassiumK(s)K(g)K1(g)K1(aq)KF(s)KCl(s)KBr(s)KI(s)KOH(s)KClO3(s)KClO4(s)

RubidiumRb(s)Rb(g)Rb1(g)Rb1(aq)RbF(s)RbCl(s)RbBr(s)RbI(s)

SiliconSi(s)SiF4(g)SiO2(s)

SilverAg(s)Ag(g)Ag1(aq)

2206.57 2173.23 2206.57 2125 51.71 2314.4

0 249.2 143 2229.94 2241.826 2285.840 2187.8 2191.2

0 314.6 217.6 144 58.9 2287 2320 2402 2443.5 22984 21266 21281 21285 21277

0 89.2 514.197 2251.2 2568.6 2436.7 2394 2328 2424.8 2397.7 2432.75

0 85.81 495.04 2246 2549.28 2435.35 2389.2 2328

0 21614.9 2910.9

0 289.2 105.9

2203 2127.03 299.51 262.38 245.06 231.8

0 107.76 609.839 2239.66 2575.4 2411.1 2361 2425.609 21130.8 2947.7 2288

0 164 1784 2545.51 2828.4 21218 2592.0 21445

0 0.3 279 129 101 41.8 217.7 220.2 239 2296.8 2396 2907.51 2885.75 2813.989 2907.51

0 3 2545.2 2580.7

0 2804.2 2944.0

0 130.5 2152.4 2348.0 2203

2110.5 279.914 2110.5 283.3 66.07 2203.0

0 231.7 163 2157.30 2228.60 2237.192 2120.4 2134.1

0 278.3 212.1 104 24.5 2268 2272 2323

— 22698 21013 21082 21135 21019

0 60.7 481.202 2282.28 2538.9 2409.2 2380 2323 2379.1 2296.3 2303.2

0 55.86

— 2282.2

— 2407.8 2378.1 2326

0 21572.7 2856.5

0 250.4 77.111

2185 2109.72 295.939 266.32 19.1 240.3

0 77.299 574.877 2261.87 2545.1 2384.0 2349 2379.53 21048.1 2851.9 2285

0 110

— 2557.3 2781.2 21138 2562.4 21334

0 0.096 239 80.1 49.1 83.7 12.6 233 227.4 2300.2 2371 2741.99 2752.87 2690.059 2741.99

0 4.6 2474.0 2519.7

0 2737.2 2888.8

0 94.93 2147.21 2318.2 2198

146 155.6 146 260.6 261.6 94.6

205.0 160.95 238.82 210.54 188.72 69.940 110 144

41.1 163.1 22.8 218 280 312 217 353

— 229 2218 236 89.1 228

64.672 160.23 154.47 103 66.55 82.59 95.94 106.39 78.87 143.1 151.0

69.5 169.99

— 124

— 95.90 108.3 118.0

18.0 282.4 41.5

42.702 172.892 73.93

84 96.11 107.1 114 128.2 146

51.446 153.61 147.85 60.2 51.21 72.12 86.82 64.454 139 102 98.5

54.4 164.54

— 239 117 97.1 55.5 122

31.9 32.6 168 228.1 430.211 22 61.1 205.6 122 248.1 256.66 17 126.9 156.90 17

51.5 44.8 259 52.3

30.7 252.3 50.6

41.6 160.9 2106.5 43.9 57.7

Substance or Ion

DH 8f (kJ/mol)

DG 8f (kJ/mol)

S 8 (J/molK)

Substance or Ion

DH 8f (kJ/mol)

DG 8f (kJ/mol)

S 8 (J/molK)


8 Chapter 1 • Keys to the Study of Chemistry

H C

H

H

HOC

O

H

C C

CC

C C

H

HH

C

C C

H

H

H

H

O

O

O

O

CH O

O

C

O

C

H

H

C

H

H

C

H

H

C

H

H

HO

As H

H

H OO

O

O

H O

O

HO

C

C

C H

H

H

HH

O

O

CH

C

C

C O

H

C C

C

CC

C C

H

H

H

H

C HO

O

CH HO O

O

C

O

C

H

H

HOCl

H O OCl

Acetic acid CH3COOH

1.831025

Acetylsalicylic acidCH3COOC6H4COOH

3.631024

Adipic acidHOOC(CH2)4COOH

3.831025 3.831026

Arsenic acid H3AsO4

631023 1.131027 3310212

Ascorbic acid H2C6H6O6

1.031025 5310212

Benzoic acid C6H5COOH

6.331025

Carbonic acid H2CO3

4.531027 4.7310211

Chloroacetic acid ClCH2COOH

1.431023

Chlorous acid HClO2

1.131022

(continued)*All values at 298 K, except for acetylsalicylic acid, which is at 37ºC (310 K) in 0.15 M NaCl.†Acidic (ionizable) proton(s) shown in red. Structures have lowest formal charges. Benzene rings show one resonance form.

Equilibrium Constants for Selected Substances*

Name and Formula Lewis Structure† Ka1 Ka2 Ka3

Dissociation (Ionization) Constants (Ka) of Selected Acids

Appendix C

A-8


Appendix C • Equilibrium Constants for selected substances A-9

Equilibrium Constants for Selected Substances*

H C HO

O

H O C HO

O

C C

HH

H

O

H

C

H

H

H O C HO

O

C

H

O C HO

O

H C N

H F

HSH

ClOH

IOH

C O

H

CO

OO H

H HC C

O

C HOC

H O

H

H

H

C

H

O

OIOH

OH Br

CH O

O O

C

O

C

C

H

O

C

H

C

H

H H

HO

H

O

(continued )

Citric acid HOOCCH2C(OH)(COOH)CH2COOH

7.431024 1.731025 4.031027

Formic acid HCOOH

1.831024

Glyceric acid HOCH2CH(OH)COOH

2.931024

Glycolic acid HOCH2COOH

1.531024

Glyoxylic acid HC(O)COOH

3.5 31024

Hydrocyanic acidHCN

6.2310210

Hydrofluoric acidHF

6.831024

Hydrosulfuric acidH2S

931028 1310217

Hypobromous acidHBrO

2.331029

Hypochlorous acidHClO

2.931028

Hypoiodous acidHIO

2.3310211

Iodic acidHIO3

1.631021

Lactic acidCH3CH(OH)COOH

1.431024

Maleic acidHOOCCH CHCOOH

1.231022 4.731027


Dissociation (Ionization) Constants (Ka) of Selected Acids


A-10 Appendix C • Equilibrium Constants for selected substances

HOCC C

OO

OH

H

C C

C

CC

C C

H

H

H

H

HO

C C

H

H

C

O

H H

C C

C

C

C C

H

HH

HO

O H

O

PH HO

OH

O H

O

P HO

C

H

H

C

H

H

C

O

HOH

C HOC

H

H

CH

OO

C C

H

H

C

H

H

C HO

OO

OH

O

O

SH HOO

O

SH HOO

HOCC C

H

H

OO

OH

N OOH

Malonic acidHOOCCH2COOH

1.431023 2.031026

Nitrous acidHNO2

7.131024

Oxalic acidHOOCCOOH

5.631022 5.431025

PhenolC6H5OH

1.0310210

Phenylacetic acidC6H5CH2COOH

4.931025

Phosphoric acidH3PO4

7.231023 6.331028 4.2310213

Phosphorous acidHPO(OH)2

331022 1.731027

Propanoic acidCH3CH2COOH

1.331025

Pyruvic acidCH3C(O)COOH

2.831023

Succinic acidHOOCCH2CH2COOH

6.231025 2.331026

Sulfuric acidH2SO4

Very large 1.031022

Sulfurous acidH2SO3

1.431022 6.531028

(continued )


Dissociation (Ionization) Constants (Ka) of Selected Acids (continued )



NH

H

H

H

C C

C

C

C C

H

H

H

H

NC

H

H

NC

H

H

C

H

H

C

H

HH

C

H

H

H H

NC

H

H

C

H

HH

HH

N

H

H

H

C

H

H

HCOH

HN

H

C

H

H

C

H

H

H

N C

H

HH

NC

H

H H

HH

HNC

H

H H

H

HN

C C C

H

H

H

HC

H

H

H H

H

H

HN

H

C

H

H

C

H

H

C

H

H

H

C C

C

C

C

N HH

H

H

HH H

H H

H

H

(continued )†Blue type indicates the basic nitrogen and its lone pair.

Ammonia NH3

1.7631025

Aniline C6H5NH2

4.0310210

Diethylamine(CH3CH2)2NH

8.631024

Dimethylamine(CH3)2NH

5.931024

EthanolamineHOCH2CH2NH2

3.231025

EthylamineCH3CH2NH2

4.331024

EthylenediamineH2NCH2CH2NH2

8.531025 7.131028

Methylamine CH3NH2

4.431024

tert-Butylamine(CH3)3CNH2

4.831024

Piperidine C5H10NH

1.331023

n-PropylamineCH3CH2CH2NH2

3.531024

Name and Formula Lewis Structure† Kb1 Kb2

Dissociation (Ionization) Constants (Kb) of Selected Amine Bases


A-12 Appendix C • Equilibrium Constants for selected substances

H

C C C

H

H H H

H

H H

H

HN

HHHH

N

N

H

C

H

C

H

C

H

H

H

C C

C

C

C C

H

H

H

H

N

NC

H

H

C C

H

H

C

H

H

C

H

H

CH H

H H

H

H

H

NC C

H

H

H

H

H

H

CH H

H

Isopropylamine(CH3)2CHNH2

4.731024

1,3-PropylenediamineH2NCH2CH2CH2NH2

3.131024 3.031026

Pyridine C5H5N

1.731029

Triethylamine(CH3CH2)3N

5.231024

Trimethylamine(CH3)3N

6.331025

Fe31

Sn21

Cr31

Al31

Cu21

Pb21

Zn21

Co21

Ni21

Fe(H2O)631(aq)

Sn(H2O)621(aq)

Cr(H2O)631(aq)

Al(H2O)631(aq)

Cu(H2O)621(aq)

Pb(H2O)621(aq)

Zn(H2O)621(aq)

Co(H2O)621(aq)

Ni(H2O)621(aq)

631023

431024

131024

131025

331028

331028

131029

2310210

1310210

Ag(CN)22

Ag(NH3)21

Ag(S2O3)232

AlF632

Al(OH)42

Be(OH)422

CdI422

Co(OH)422

Cr(OH)42

Cu(NH3)421

Fe(CN)642

Fe(CN)632

Hg(CN)422

Ni(NH3)621

Pb(OH)32

Sn(OH)32

Zn(CN)422

Zn(NH3)421

Zn(OH)422

3.031020

1.73107

4.731013

4 31019

3 31033

4 31018

1 3106

5 3109

8.031029

5.631011

3 31035

4.031043

9.331038

2.03108

8 31013

3 31025

4.231019

7.83108

3 31015

Name and Formula Lewis Structure† Kb1 Kb2

Dissociation (Ionization) Constants (Kb) of Selected Amine Bases (continued )

Free Ion Hydrated Ion Ka

Dissociation (Ionization) Constants (Ka) of Some Hydrated Metal Ions

Complex Ion Kf

Formation Constants (Kf) of Some Complex Ions



CarbonatesBarium carbonate, BaCO3Cadmium carbonate, CdCO3Calcium carbonate, CaCO3Cobalt(II) carbonate, CoCO3Copper(II) carbonate, CuCO3Lead(II) carbonate, PbCO3Magnesium carbonate, MgCO3Mercury(I) carbonate, Hg2CO3Nickel(II) carbonate, NiCO3Strontium carbonate, SrCO3Zinc carbonate, ZnCO3

ChromatesBarium chromate, BaCrO4Calcium chromate, CaCrO4Lead(II) chromate, PbCrO4Silver chromate, Ag2CrO4

CyanidesMercury(I) cyanide, Hg2(CN)2Silver cyanide, AgCN

HalidesFluoridesBarium fluoride, BaF2Calcium fluoride, CaF2Lead(II) fluoride, PbF2Magnesium fluoride, MgF2Strontium fluoride, SrF2ChloridesCopper(I) chloride, CuClLead(II) chloride, PbCl2Silver chloride, AgClBromidesCopper(I) bromide, CuBrSilver bromide, AgBrIodidesCopper(I) iodide, CuILead(II) iodide, PbI2Mercury(I) iodide, Hg2I2Silver iodide, AgI

HydroxidesAluminum hydroxide, Al(OH)3Cadmium hydroxide, Cd(OH)2Calcium hydroxide, Ca(OH)2

Cobalt(II) hydroxide, Co(OH)2Copper(II) hydroxide, Cu(OH)2Iron(II) hydroxide, Fe(OH)2Iron(III) hydroxide, Fe(OH)3Magnesium hydroxide, Mg(OH)2Manganese(II) hydroxide, Mn(OH)2Nickel(II) hydroxide, Ni(OH)2Zinc hydroxide, Zn(OH)2

Iodates Barium iodate, Ba(IO3)2Calcium iodate, Ca(IO3)2Lead(II) iodate, Pb(IO3)2Silver iodate, AgIO3Strontium iodate, Sr(IO3)2Zinc iodate, Zn(IO3)2

OxalatesBarium oxalate dihydrate, BaC2O42H2OCalcium oxalate monohydrate, CaC2O4H2OStrontium oxalate monohydrate,

SrC2O4H2OPhosphates

Calcium phosphate, Ca3(PO4)2Magnesium phosphate, Mg3(PO4)2Silver phosphate, Ag3PO4

SulfatesBarium sulfate, BaSO4Calcium sulfate, CaSO4Lead(II) sulfate, PbSO4Radium sulfate, RaSO4Silver sulfate, Ag2SO4Strontium sulfate, SrSO4

SulfidesCadmium sulfide, CdSCopper(II) sulfide, CuSIron(II) sulfide, FeSLead(II) sulfide, PbSManganese(II) sulfide, MnSMercury(II) sulfide, HgSNickel(II) sulfide, NiSSilver sulfide, Ag2STin(II) sulfide, SnSZinc sulfide, ZnS

2.031029

1.8310214

3.331029

1.0310210

3.0310212

7.4310214

3.531028

8.9310217

1.331027

5.4310210

1.0310210

2.1310210

1.031028

2.3310213

2.6310212

5.0310240

2.2310216

1.531026

3.2310211

3.631028

7.431029

2.631029

1.931027

1.731025

1.8310210

5 31029

5.0310213

1 310212

7.931029

4.7310229

8.3310217

3 310234

7.2310215

6.531026

1.3310215

2.2310220

4.1310215

1.6310239

6.3310210

1.6310213

6.0310216

3.0310216

1.531029

7.131027

2.5310213

3.131028

3.331027

3.931026

1.131027

2.331029

5.631028

1.2310229

5.2310224

2.6310218

1.1310210

2.431025

1.631028

2.0310211

1.531025

3.231027

1.0310224

8.0310234

8.0310216

3.0310225

3.0310211

2.0310250

3.0310216

8.0310248

1.3310223

2.0310222

Name, Formula Ksp Name, Formula Ksp

Solubility-Product Constants (Ksp) of Slightly Soluble Ionic Compounds


14 Chapter 1 • Keys to the Study of Chemistry

F2(g) 1 2e2 2F2(aq)O3(g) 1 2H1(aq) 1 2e2 O2(g) 1 H2O(l)Co31(aq) 1 e2 Co21(aq)H2O2(aq) 1 2H1(aq) 1 2e2 2H2O(l)PbO2(s) 1 3H1(aq) 1 HSO4

2(aq) 1 2e2 PbSO4(s) 1 2H2O(l)Ce41(aq) 1 e2 Ce31(aq)MnO4

2(aq) 1 8H1(aq) 1 5e2 Mn21(aq) 1 4H2O(l)Au31(aq) 1 3e2 Au(s)Cl2(g) 1 2e2 2Cl2(aq)Cr2O7

22(aq) 1 14H1(aq) 1 6e2 2Cr31(aq) 1 7H2O(l)MnO2(s) 1 4H1(aq) 1 2e2 Mn21(aq) 1 2H2O(l)O2(g) 1 4H1(aq) 1 4e2 2H2O(l)Br2(l) 1 2e2 2Br2(aq)NO3

2(aq) 1 4H1(aq) 1 3e2 NO(g) 1 2H2O(l)2Hg21(aq) 1 2e2 Hg2

21(aq)Hg2

21(aq) 1 2e2 2Hg(l)Ag1(aq) 1 e2 Ag(s)Fe31(aq) 1 e2 Fe21(aq)O2(g) 1 2H1(aq) 1 2e2 H2O2(aq)MnO4

2(aq) 1 2H2O(l) 1 3e2 MnO2(s) 1 4OH2(aq)I2(s) 1 2e2 2I2(aq)O2(g) 1 2H2O(l) 1 4e2 4OH2(aq)Cu21(aq) 1 2e2 Cu(s)AgCl(s) 1 e2 Ag(s) 1 Cl2(aq)SO4

22(aq) 1 4H1(aq) 1 2e2 SO2(g) 1 2H2O(l)Cu21(aq) 1 e2 Cu1(aq)Sn41(aq) 1 2e2 Sn21(aq)2H1(aq) 1 2e2 H2(g)Pb21(aq) 1 2e2 Pb(s)Sn21(aq) 1 2e2 Sn(s)N2(g) 1 5H1(aq) 1 4e2 N2H5

1(aq)Ni21(aq) 1 2e2 Ni(s)Co21(aq) 1 2e2 Co(s)PbSO4(s) 1 H1(aq) 1 2e2 Pb(s) 1 HSO4

2(aq)Cd21(aq) 1 2e2 Cd(s)Fe21(aq) 1 2e2 Fe(s)Cr31(aq) 1 3e2 Cr(s)Zn21(aq) 1 2e2 Zn(s)2H2O(l) 1 2e2 H2(g) 1 2OH2(aq)Mn21(aq) 1 2e2 Mn(s)Al31(aq) 1 3e2 Al(s)Mg21(aq) 1 2e2 Mg(s)Na1(aq) 1 e2 Na(s)Ca21(aq) 1 2e2 Ca(s)Sr21(aq) 1 2e2 Sr(s)Ba21(aq) 1 2e2 Ba(s)K1(aq) 1 e2 K(s)Li1(aq) 1 e2 Li(s)

12.8712.0711.8211.7711.7011.6111.5111.5011.3611.3311.2311.2311.0710.96 10.9210.8510.8010.7710.6810.5910.5310.4010.3410.2210.2010.1510.13

0.0020.1320.1420.2320.2520.2820.3120.4020.4420.7420.7620.8321.1821.6622.3722.7122.8722.8922.9022.9323.05

*All values at 298 K. Written as reductions; E value refers to all components in their standard states: 1 M for dissolved species; 1 atm pressure for the gas behaving ideally; the pure substance for solids and liquids.

BA

BABA

BA

BA

BABA

BABA

BA

BA

BABA

BABA

BA

BABABABA

BABA

BABABABABABABA

BA

BABABABA

BA

BABA

BABA

BABA

BABABA

BABA

BABA

Standard Electrode (Half-Cell) Potentials*Half-Reaction E 8 (V)

Appendix D

A-14


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