Appendix A
3.2 Section • Determining the Formula of an Unknown Compound A-1
Common Mathematical
Operations in Chemistry
I
n addition to basic arithmetic and algebra, four mathematical operations are used
frequently in general chemistry: manipulating logarithms, using exponential notation, solving quadratic equations, and graphing data. Each is discussed briefly
below.
Manipulating Logarithms
Meaning and Properties of Logarithms
A 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 5 n
Because logarithms are exponents, they have the following properties:
logx 1
logx (A 3 B)
A
logx
B
logx Ay
50
5 logx A 1 logx B
5 logx A 2 logx B
5 y logx A
Types of Logarithms
Common 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 5 3
or
103 5 1000
Similarly, we have
log 10
log 1,000,000
log 0.001
log 853
5
5
5
5
1
6
23
2.931
or
or
or
or
101
106
1023
102.931
5
5
5
5
10
1,000,000
0.001
853
The last example illustrates an important point about significant figures with all logarithms: 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 5 1
and
ln 10 5 2.303
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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.
Antilogarithms
The 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) Notation
Many quantities in chemistry are very large or very small. For example, in the conventional 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
A10n
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
5.9061022 atoms, and each gold atom has a mass of 3.2721022 g.
Changing Between Conventional and Exponential Notation
In order to use exponential notation, you must be able to convert to it from conventional 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 numbers between 0 and 1:
75,000,000 changes to 7.53107 (decimal point 7 places to the left)
0.006042 changes to 6.04231023 (decimal point 3 places to the right)
2. To change a number from exponential to conventional notation, move the decimal point the number of places indicated by the exponent to the right for numbers with positive exponents and to the left for numbers with negative
exponents:
1.383105 changes to 138,000 (decimal point 5 places to the right)
8.4131026 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 standard form and adding the exponents:
582.3106 changes to 5.823  102  106  5.82310(26)  5.823108
0.0043104 changes to 4.3  103  104  4.310[(3)(4)]  4.3107
Using Exponential Notation in Calculations
In 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:
(5.5103)(3.1105)  (5.5  3.1)10(35)  17108  1.7109
(9.71014)(4.31020)  (9.7  4.3)10[14(20)]  42106  4.2105
2. To divide exponential numbers, divide the coefficients, subtract the exponents, and
reconstruct the number in standard exponential notation:
2.63106
2.6
5
 10(62)  0.45104  4.5103
2
5.8
5.8310
1.7
1.7310 25
 10[(5)(8)]  0.21103  2.1102
5
28
8.2
8.2310
3. To add or subtract exponential numbers, change all numbers so that they have the
same exponent, then add or subtract the coefficients:
(1.45104)  (3.2103)  (1.45104)  (0.32104)  1.77104
(3.22105)  (9.02104)  (3.22105)  (0.902105)  2.32105
Solving Quadratic Equations
A quadratic equation is one in which the highest power of x is 2. The general form
of a quadratic equation is
ax2 1 bx 1 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 quadratic formula:
x5
2b 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 1 0.65x 2 8.7 5 0
a
b
c
Applying the quadratic formula, with a  4.3, b  0.65, and c  8.7, gives
x5
2 0.65 6 " 1 0.65 2 2 2 4 1 4.3 2 128.7 2
2 1 4.3 2
The “plus or minus” sign () indicates that there are always two possible values for
x. In this case, they are
x  1.3 and x  21.5
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 concentration, 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 Line
Visualizing 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 5 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 5 m(0) 1 b 5 b
The slope of the line is the change in y for a given change in x:
Slope (m) 5
14
y  2x 1 1
12
10
8
Slope
 8⁄4  2
y
6
2
2
0
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. 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 example, in Chapter 16, we obtained the following expression:
x
4
ln
4
2
Figure A.1
3 A 40
5 kt
3 A 4t
Based on the properties of logarithms, we have
Intercept
2
y2 2 y1
Dy
5
x 2 2 x1
Dx
ln [A]0  ln [A]t 5 kt
6
Rearranging into the form of an equation for a straight line gives
ln [A]t  kt  ln [A]0
y  mx  b
Thus, a plot of ln [A]t vs. t is a straight line, from which you can see that the slope
is k (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  59 °C  32
y  mx  b
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Appendix B
3.2 Section • Determining the Formula of an Unknown Compound 5
Standard Thermodynamic Values
for Selected Substances*
Substance
or Ion
e2(g)
Aluminum
Al(s)
Al31(aq)
AlCl3(s)
Al2O3(s)
Barium
Ba(s)
Ba(g)
Ba21(g)
Ba21(aq)
BaCl2(s)
BaCO3(s)
BaO(s)
BaSO4(s)
Boron
B(-rhombohedral)
BF3(g)
BCl3(g)
B2H6(g)
B2O3(s)
H3BO3(s)
Bromine
Br2(l)
Br2(g)
Br(g)
Br2(g)
Br2(aq)
HBr(g)
Cadmium
Cd(s)
Cd(g)
Cd21(aq)
CdS(s)
Calcium
Ca(s)
Ca(g)
Ca21(g)
Ca21(aq)
CaF2(s)
CaCl2(s)
DH 8f
(kJ/mol)
0
DG 8f
(kJ/mol)
0
S 8
(J/molK)
20.87
0
2524.7
2704.2
21676
0
2481.2
2628.9
21582
28.3
2313
110.7
50.94
0
175.6
1649.9
2538.36
2806.06
21219
2548.1
21465
0
144.8
—
2560.7
2810.9
21139
2520.4
21353
62.5
170.28
—
13
126
112
72.07
132
0
0
5.87
21120.3
2388.7
86.6
21193
2969.01
254.0
290.0
232.0
53.8
88.83
0
30.91
111.9
2218.9
2120.9
236.3
0
3.13
82.40
—
2102.82
253.5
152.23
245.38
174.90
—
80.71
198.59
0
112.8
272.38
2144
0
78.20
277.74
2141
51.5
167.64
261.1
71
0
192.6
1934.1
2542.96
21215
2795.0
0
158.9
—
2553.04
21162
2750.2
41.6
154.78
—
255.2
68.87
114
21137.0
2403.8
35
21272
21094.3
Substance
or Ion
CaCO3(s)
CaO(s)
Ca(OH)2(s)
Ca3(PO4)2(s)
CaSO4(s)
Carbon
C(graphite)
C(diamond)
C(g)
CO(g)
CO2(g)
CO2(aq)
CO322(aq)
HCO32(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)
DH 8f
(kJ/mol)
21206.9
2635.1
2986.09
24138
21432.7
21128.8
2603.5
2898.56
23899
21320.3
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
21273.3
22221.7
151
135
105
105
117
87.9
283.7
2117
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
2910.56
21544.3
166
125
121
112
66.9
63.6
260.2
263.2
*All values at 298 K.
siL02656_apA-D_A-1_A-14.indd 5
DG 8f
(kJ/mol)
S 8
(J/molK)
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)
A-5
12/9/10 8:28:16 AM
A-6 Appendix B • Standard Thermodynamic Values for Selected Substances
Substance
or Ion
CHCl3(l)
CCl4(g)
CCl4(l)
COCl2(g)
Cesium
Cs(s)
Cs(g)
Cs1(g)
Cs1(aq)
CsF(s)
CsCl(s)
CsBr(s)
CsI(s)
Chlorine
Cl2(g)
Cl(g)
Cl2(g)
Cl2(aq)
HCl(g)
HCl(aq)
ClO2(g)
Cl2O(g)
Chromium
Cr(s)
Cr31(aq)
CrO422(aq)
Cr2O722(aq)
Copper
Cu(s)
Cu(g)
Cu1(aq)
Cu21(aq)
Cu2O(s)
CuO(s)
Cu2S(s)
CuS(s)
Fluorine
F2(g)
F(g)
F2(g)
F2(aq)
HF(g)
Hydrogen
H2(g)
H(g)
H1(aq)
H1(g)
Iodine
I2(s)
I2(g)
I(g)
I2(g)
I2(aq)
HI(g)
Iron
Fe(s)
Fe31(aq)
DG 8f
(kJ/mol)
S 8
(J/molK)
2132
296.0
2139
2220
271.5
253.7
268.6
2206
203
309.7
214.4
283.74
0
76.7
458.5
2248
2554.7
2442.8
2395
2337
0
49.7
427.1
2282.0
2525.4
2414
2383
2333
85.15
175.5
169.72
133
88
101.18
121
130
0
121.0
2234
2167.46
292.31
2167.46
102
80.3
0
105.0
2240
2131.17
295.30
2131.17
120
97.9
223.0
165.1
153.25
55.10
186.79
55.06
256.7
266.1
DH 8f
(kJ/mol)
0
21971
2863.2
21461
0
—
2706.3
21257
23.8
—
38
214
0
341.1
51.9
64.39
2168.6
2157.3
279.5
253.1
0
301.4
50.2
64.98
2146.0
2130
286.2
253.6
33.1
166.29
226
298.7
93.1
42.63
120.9
66.5
0
78.9
2255.6
2329.1
2273
0
61.8
2262.5
2276.5
2275
202.7
158.64
145.47
29.6
173.67
0
218.0
0
1536.3
0
203.30
0
1517.1
130.6
114.60
0
108.83
0
62.442
106.8
2194.7
255.94
25.9
0
19.38
70.21
—
251.67
1.3
116.14
260.58
180.67
—
109.4
206.33
0
247.7
0
210.5
27.3
2293
Substance
or Ion
Fe21(aq)
FeCl2(s)
FeCl3(s)
FeO(s)
Fe2O3(s)
Fe3O4(s)
Lead
Pb(s)
Pb21(aq)
PbCl2(s)
PbO(s)
PbO2(s)
PbS(s)
PbSO4(s)
Lithium
Li(s)
Li(g)
Li1(g)
Li1(aq)
LiF(s)
LiCl(s)
LiBr(s)
LiI(s)
Magnesium
Mg(s)
Mg(g)
Mg21(g)
Mg21(aq)
MgCl2(s)
MgCO3(s)
MgO(s)
Mg3N2(s)
Manganese
Mn(s, )
Mn21(aq)
MnO2(s)
MnO42(aq)
Mercury
Hg(l)
Hg(g)
Hg21(aq)
Hg221(aq)
HgCl2(s)
Hg2Cl2(s)
HgO(s)
Nitrogen
N2(g)
N(g)
N2O(g)
NO(g)
NO2(g)
N2O4(g)
N2O5(g)
N2O5(s)
NH3(g)
NH3(aq)
N2H4(l)
DH 8f
(kJ/mol)
DG 8f
(kJ/mol)
S 8
(J/molK)
284.94
2302.3
2334.1
2251.4
2743.6
21018
113
117.9
142
60.75
87.400
145.3
0
1.6
2359
2218
2276.6
298.3
2918.39
0
224.3
2314
2198
2219.0
296.7
2811.24
64.785
21
136
68.70
76.6
91.3
147
0
161
687.163
2278.46
2616.9
2408
2351
2270
0
128
649.989
2293.8
2588.7
2384
2342
2270
29.10
138.67
132.91
14
35.66
59.30
74.1
85.8
287.9
2341.8
2399.5
2272.0
2825.5
21121
0
150
2351
2461.96
2641.6
21112
2601.2
2461
0
115
—
2456.01
2592.1
21028
2569.0
2401
0
2219
2520.9
2518.4
0
2223
2466.1
2425.1
31.8
284
53.1
190
0
61.30
171
172
2230
2264.9
290.79
0
31.8
164.4
153.6
2184
2210.66
258.50
76.027
174.87
232
84.5
144
196
70.27
0
473
82.05
90.29
33.2
9.16
11
243.1
245.9
280.83
50.63
0
456
104.2
86.60
51
97.7
118
114
216
26.7
149.2
191.5
153.2
219.7
210.65
239.9
304.3
346
178
193
110
121.2
32.69
148.55
—
118
89.630
65.86
26.9
88
(continued )
siL02656_apA-D_A-1_A-14.indd 6
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Appendix B • Standard Thermodynamic Values for Selected Substances A-7
Substance
or Ion
NO32(aq)
HNO3(l)
HNO3(aq)
NF3(g)
NOCl(g)
NH4Cl(s)
Oxygen
O2(g)
O(g)
O3(g)
OH2(aq)
H2O(g)
H2O(l)
H2O2(l)
H2O2(aq)
Phosphorus
P4(s, white)
P(g)
P(s, red)
P2(g)
P4(g)
PCl3(g)
PCl3(l)
PCl5(g)
PCl5(s)
P4O10(s)
PO432(aq)
HPO422(aq)
H2PO42(aq)
H3PO4(aq)
Potassium
K(s)
K(g)
K1(g)
K1(aq)
KF(s)
KCl(s)
KBr(s)
KI(s)
KOH(s)
KClO3(s)
KClO4(s)
Rubidium
Rb(s)
Rb(g)
Rb1(g)
Rb1(aq)
RbF(s)
RbCl(s)
RbBr(s)
RbI(s)
Silicon
Si(s)
SiF4(g)
SiO2(s)
Silver
Ag(s)
Ag(g)
Ag1(aq)
siL02656_apA-D_A-1_A-14.indd 7
DH 8f
(kJ/mol)
DG 8f
(kJ/mol)
2206.57
2173.23
2206.57
2125
51.71
2314.4
2110.5
279.914
2110.5
283.3
66.07
2203.0
0
249.2
143
2229.94
2241.826
2285.840
2187.8
2191.2
0
231.7
163
2157.30
2228.60
2237.192
2120.4
2134.1
0
314.6
217.6
144
58.9
2287
2320
2402
2443.5
22984
21266
21281
21285
21277
0
278.3
212.1
104
24.5
2268
2272
2323
—
22698
21013
21082
21135
21019
S 8
(J/molK)
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
0
89.2
514.197
2251.2
2568.6
2436.7
2394
2328
2424.8
2397.7
2432.75
0
60.7
481.202
2282.28
2538.9
2409.2
2380
2323
2379.1
2296.3
2303.2
64.672
160.23
154.47
103
66.55
82.59
95.94
106.39
78.87
143.1
151.0
0
85.81
495.04
2246
2549.28
2435.35
2389.2
2328
0
55.86
—
2282.2
—
2407.8
2378.1
2326
69.5
169.99
—
124
—
95.90
108.3
118.0
0
21614.9
2910.9
0
289.2
105.9
0
21572.7
2856.5
0
250.4
77.111
18.0
282.4
41.5
42.702
172.892
73.93
Substance
or Ion
DH 8f
(kJ/mol)
AgF(s)
2203
AgCl(s)
2127.03
AgBr(s)
299.51
AgI(s)
262.38
AgNO3(s)
245.06
Ag2S(s)
231.8
Sodium
Na(s)
0
Na(g)
107.76
Na1(g)
609.839
Na1(aq)
2239.66
NaF(s)
2575.4
NaCl(s)
2411.1
NaBr(s)
2361
NaOH(s)
2425.609
Na2CO3(s)
21130.8
NaHCO3(s)
2947.7
NaI(s)
2288
Strontium
Sr(s)
0
Sr(g)
164
Sr21(g)
1784
Sr21(aq)
2545.51
SrCl2(s)
2828.4
SrCO3(s)
21218
SrO(s)
2592.0
SrSO4(s)
21445
Sulfur
S(rhombic)
0
S(monoclinic)
0.3
S(g)
279
S2(g)
129
S8(g)
101
S22(aq)
41.8
HS2(aq)
217.7
H2S(g)
220.2
H2S(aq)
239
SO2(g)
2296.8
SO3(g)
2396
SO422(aq)
2907.51
HSO42(aq)
2885.75
H2SO4(l)
2813.989
H2SO4(aq)
2907.51
Tin
Sn(white)
0
Sn(gray)
3
SnCl4(l)
2545.2
SnO2(s)
2580.7
Titanium
Ti(s)
0
TiCl4(l)
2804.2
TiO2(s)
2944.0
Zinc
Zn(s)
0
Zn(g)
130.5
Zn21(aq)
2152.4
ZnO(s)
2348.0
ZnS(s, zinc
2203
blende)
DG 8f
(kJ/mol)
S 8
(J/molK)
2185
2109.72
295.939
266.32
19.1
240.3
84
96.11
107.1
114
128.2
146
0
77.299
574.877
2261.87
2545.1
2384.0
2349
2379.53
21048.1
2851.9
2285
51.446
153.61
147.85
60.2
51.21
72.12
86.82
64.454
139
102
98.5
0
110
—
2557.3
2781.2
21138
2562.4
21334
54.4
164.54
—
239
117
97.1
55.5
122
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
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
0
4.6
2474.0
2519.7
51.5
44.8
259
52.3
0
2737.2
2888.8
30.7
252.3
50.6
0
94.93
2147.21
2318.2
2198
41.6
160.9
2106.5
43.9
57.7
12/9/10 8:28:17 AM
Appendix C
8 Chapter 1 • Keys to the Study of Chemistry
Equilibrium Constants for Selected Substances*
Dissociation (Ionization) Constants (Ka) of Selected Acids
Name and Formula
Acetic acid
CH3COOH
Lewis Structure†
H
H
O
C
C
Ka2
Ka3
1.831025
H
O
H
H
Acetylsalicylic acid
CH3COOC6H4COOH
Ka1
H
H
O
C
C
C
C
C
C
O
H
C
O
O
H
C
C
3.631024
H
H
H
Adipic acid
HOOC(CH2)4COOH
H
O
O
H
H
H
H
O
C
C
C
C
C
C
H
H
H
H
O
H
3.831025
3.831026
631023
1.131027
1.031025
5310212
O
Arsenic acid
H3AsO4
H
O
As
O
O
H
H
H
O
C
H
H
O
H
C
C
H
H
H
Benzoic acid
C6H5COOH
3310212
H
C
C
O
O
H
O
C
C
H
O
C
O
Ascorbic acid
H2C6H6O6
H
C
C
C
C
O
H
6.331025
C
H
H
O
Carbonic acid
H2CO3
Chloroacetic acid
ClCH2COOH
Chlorous acid
HClO2
H
Cl
O
C
O
H
O
C
C
O
Cl
O
H
H
4.531027
4.7310211
1.431023
H
H
O
1.131022
*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.
(continued)
A-8
siL02656_apA-D_A-1_A-14.indd 8
12/9/10 8:28:17 AM
Appendix C • Equilibrium Constants for Selected Substances A-9
Dissociation (Ionization) Constants (Ka) of Selected Acids
Name and Formula
Lewis Structure†
Ka1
Ka2
7.431024
1.731025
Ka3
H
Citric acid
HOOCCH2C(OH)(COOH)CH2COOH
H
O
O
H
O
H
O
C
C
C
C
C
C
H
O
O
H
H
O
H
4.031027
O
Formic acid
HCOOH
Glyceric acid
HOCH2CH(OH)COOH
Glycolic acid
HOCH2COOH
Glyoxylic acid
HC(O)COOH
Hydrocyanic acid
HCN
Hydrofluoric acid
HF
Hydrosulfuric acid
H 2S
Hypobromous acid
HBrO
Hypochlorous acid
HClO
Hypoiodous acid
HIO
H
H
H
C
O
O
1.831024
O
H
H
H
O
C
C
C
H
O
H
H
O
C
C
O
O
H
O
H
H
2.931024
1.531024
H
H
O
O
C
C
H
C
N
H
F
H
S
H
931028
H
O
Br
2.331029
H
O
Cl
2.931028
H
O
I
2.3310211
3.5 31024
6.2310210
6.831024
1310217
O
Iodic acid
HIO3
Lactic acid
CH3CH(OH)COOH
H
H
O
I
O
H
H
O
C
C
C
H
O
H
O
H
1.431024
H
H
Maleic acid
HOOCCH CHCOOH
1.631021
C
C
O
C
C
O
H
O
O
H
1.231022
4.731027
(continued )
siL02656_apA-D_A-1_A-14.indd 9
12/9/10 8:28:18 AM
A-10 Appendix C • Equilibrium Constants for Selected Substances
Dissociation (Ionization) Constants (Ka) of Selected Acids (continued )
Name and Formula
Malonic acid
HOOCCH2COOH
Nitrous acid
HNO2
Oxalic acid
HOOCCOOH
Lewis Structure†
H
O
O
H
O
C
C
C
H
H
O
O
N
O
O
O
C
C
1.431023
2.031026
Ka3
H
O
H
5.631022
O
H
1.0310210
H
O
C
C
5.431025
H
C
C
C
C
H
H
H
C
C
H
7.131024
C
C
H
Phenylacetic acid
C6H5CH2COOH
H
Ka2
H
H
Phenol
C6H5OH
O
Ka1
C
C
C
C
H
O
H
4.931025
H
H
O
Phosphoric acid
H3PO4
H
P
O
O
H
P
O
H
O
H
H
H
O
C
C
C
H
H
H
O
O
C
C
O
H
7.231023
6.331028
331022
1.731027
4.2310213
O
Phosphorous acid
HPO(OH)2
Propanoic acid
CH3CH2COOH
Pyruvic acid
CH3C(O)COOH
Succinic acid
HOOCCH2CH2COOH
H
H
H
O
H
1.331025
C
O
H
2.831023
O
H
H
O
C
C
C
C
H
H
O
O
H
H
O
6.231025
2.331026
H
Very large
1.031022
H
1.431022
6.531028
O
H
O
Sulfuric acid
H2SO4
H
O
S
O
O
Sulfurous acid
H2SO3
H
O
S
(continued)
siL02656_apA-D_A-1_A-14.indd 10
12/9/10 8:28:18 AM
Appendix C • Equilibrium Constants for Selected Substances A-11
Dissociation (Ionization) Constants (Kb) of Selected Amine Bases
Lewis Structure†
Name and Formula
Ammonia
NH3
N
H
H
H
C
C
H
C
C
C
C
H
Ethanolamine
HOCH2CH2NH2
Ethylamine
CH3CH2NH2
Ethylenediamine
H2NCH2CH2NH2
H
H
H
H
4.0310210
H
H
H
H
C
C
H
H
H
Dimethylamine
(CH3)2NH
N
H
H
Diethylamine
(CH3CH2)2NH
Kb2
1.7631025
H
H
Aniline
C6H5NH2
Kb1
H
H
N
C
C
H
H
H
H
8.631024
H
C
N
C
H
H
H
H
H
O
C
C
N
H
H
H
H
5.931024
H
H
H
C
C
N
H
H
H
H
H
N
C
C
N
H
H
H
H
C
N
H
H
H
H
3.231025
4.331024
H
8.531025
7.131028
H
Methylamine
CH3NH2
tert-Butylamine
(CH3)3CNH2
H
H
4.431024
H H
N
H H
C
C
C
H H
C
H H
H
4.831024
H
H H
H
Piperidine
C5H10NH
C
H
N
C
H
C
H
n-Propylamine
CH3CH2CH2NH2
†
H
H
C
1.331023
H
C
H H
H
H
H
H
C
C
C
N
H
H
H
H
H
Blue type indicates the basic nitrogen and its lone pair.
siL02656_apA-D_A-1_A-14.indd 11
3.531024
(continued )
12/9/10 8:28:19 AM
A-12 Appendix C • Equilibrium Constants for Selected Substances
Dissociation (Ionization) Constants (Kb) of Selected Amine Bases
(continued )
Lewis Structure†
Name and Formula
Isopropylamine
(CH3)2CHNH2
1,3-Propylenediamine
H2NCH2CH2CH2NH2
H
H
H H
N
H H
C
C
C
H
H
H
H
H
N
C
C
C
N
H
H
H
H
H
H
C
C
C
H
3.031026
1.731029
N
C
H
Triethylamine
(CH3CH2)3N
3.131024
H
H
C
Pyridine
C5H5N
Kb2
4.731024
H
H
H
Kb1
H
H
H
H
H
C
C
N
C
C
H
H H
C
HH
H
H
C
H
5.231024
H
H
H
Trimethylamine
(CH3)3N
H
H
C
N
C
H H
C
HH
6.331025
H
H
Dissociation (Ionization) Constants
(Ka) of Some Hydrated Metal Ions
Formation Constants (Kf)
of Some Complex Ions
Free
Ion
Complex Ion
Kf
Ag(CN)2
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
31
Fe
Sn21
Cr31
Al31
Cu21
Pb21
Zn21
Co21
Ni21
siL02656_apA-D_A-1_A-14.indd 12
Hydrated Ion
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)
Ka
2
6310
431024
131024
131025
331028
331028
131029
2310210
1310210
23
12/9/10 8:28:20 AM
Appendix C • Equilibrium Constants for Selected Substances A-13
Solubility-Product Constants (Ksp) of Slightly Soluble Ionic Compounds
Name, Formula
Carbonates
Barium carbonate, BaCO3
Cadmium carbonate, CdCO3
Calcium carbonate, CaCO3
Cobalt(II) carbonate, CoCO3
Copper(II) carbonate, CuCO3
Lead(II) carbonate, PbCO3
Magnesium carbonate, MgCO3
Mercury(I) carbonate, Hg2CO3
Nickel(II) carbonate, NiCO3
Strontium carbonate, SrCO3
Zinc carbonate, ZnCO3
Chromates
Barium chromate, BaCrO4
Calcium chromate, CaCrO4
Lead(II) chromate, PbCrO4
Silver chromate, Ag2CrO4
Cyanides
Mercury(I) cyanide, Hg2(CN)2
Silver cyanide, AgCN
Halides
Fluorides
Barium fluoride, BaF2
Calcium fluoride, CaF2
Lead(II) fluoride, PbF2
Magnesium fluoride, MgF2
Strontium fluoride, SrF2
Chlorides
Copper(I) chloride, CuCl
Lead(II) chloride, PbCl2
Silver chloride, AgCl
Bromides
Copper(I) bromide, CuBr
Silver bromide, AgBr
Iodides
Copper(I) iodide, CuI
Lead(II) iodide, PbI2
Mercury(I) iodide, Hg2I2
Silver iodide, AgI
Hydroxides
Aluminum hydroxide, Al(OH)3
Cadmium hydroxide, Cd(OH)2
Calcium hydroxide, Ca(OH)2
siL02656_apA-D_A-1_A-14.indd 13
Ksp
Name, Formula
2.0310
1.8310214
3.331029
1.0310210
3.0310212
7.4310214
3.531028
8.9310217
1.331027
5.4310210
1.0310210
29
2.1310210
1.031028
2.3310213
2.6310212
5.0310240
2.2310216
1.5310
3.2310211
3.631028
7.431029
2.631029
26
1.931027
1.731025
1.8310210
5 31029
5.0310213
1 310212
7.931029
4.7310229
8.3310217
3 310234
7.2310215
6.531026
Cobalt(II) hydroxide, Co(OH)2
Copper(II) hydroxide, Cu(OH)2
Iron(II) hydroxide, Fe(OH)2
Iron(III) hydroxide, Fe(OH)3
Magnesium hydroxide, Mg(OH)2
Manganese(II) hydroxide, Mn(OH)2
Nickel(II) hydroxide, Ni(OH)2
Zinc hydroxide, Zn(OH)2
Iodates
Barium iodate, Ba(IO3)2
Calcium iodate, Ca(IO3)2
Lead(II) iodate, Pb(IO3)2
Silver iodate, AgIO3
Strontium iodate, Sr(IO3)2
Zinc iodate, Zn(IO3)2
Oxalates
Barium oxalate dihydrate, BaC2O42H2O
Calcium oxalate monohydrate, CaC2O4H2O
Strontium oxalate monohydrate,
SrC2O4H2O
Phosphates
Calcium phosphate, Ca3(PO4)2
Magnesium phosphate, Mg3(PO4)2
Silver phosphate, Ag3PO4
Sulfates
Barium sulfate, BaSO4
Calcium sulfate, CaSO4
Lead(II) sulfate, PbSO4
Radium sulfate, RaSO4
Silver sulfate, Ag2SO4
Strontium sulfate, SrSO4
Sulfides
Cadmium sulfide, CdS
Copper(II) sulfide, CuS
Iron(II) sulfide, FeS
Lead(II) sulfide, PbS
Manganese(II) sulfide, MnS
Mercury(II) sulfide, HgS
Nickel(II) sulfide, NiS
Silver sulfide, Ag2S
Tin(II) sulfide, SnS
Zinc sulfide, ZnS
Ksp
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
12/9/10 8:28:20 AM
Appendix D
14 Chapter 1 • Keys to the Study of Chemistry
Standard Electrode
(Half-Cell) Potentials*
Half-Reaction
E 8 (V)
A 2F2(aq)
F2(g) 1 2e2B
A O2(g) 1 H2O(l)
O3(g) 1 2H1(aq) 1 2e2 B
A Co21(aq)
Co31(aq) 1 e2 B
A 2H2O(l)
H2O2(aq) 1 2H1(aq) 1 2e2 B
A PbSO4(s) 1 2H2O(l)
PbO2(s) 1 3H1(aq) 1 HSO42(aq) 1 2e2B
A Ce31(aq)
Ce41(aq) 1 e2B
A Mn21(aq) 1 4H2O(l)
MnO42(aq) 1 8H1(aq) 1 5e2B
A Au(s)
Au31(aq) 1 3e2B
A 2Cl2(aq)
Cl2(g) 1 2e2B
22
A 2Cr31(aq) 1 7H2O(l)
Cr2O7 (aq) 1 14H1(aq) 1 6e2B
A Mn21(aq) 1 2H2O(l)
MnO2(s) 1 4H1(aq) 1 2e2B
A 2H2O(l)
O2(g) 1 4H1(aq) 1 4e2B
A 2Br2(aq)
Br2(l) 1 2e2B
A NO(g) 1 2H2O(l)
NO32(aq) 1 4H1(aq) 1 3e2B
A Hg221(aq)
2Hg21(aq) 1 2e2B
A 2Hg(l)
Hg221(aq) 1 2e2B
A Ag(s)
Ag1(aq) 1 e2B
A Fe21(aq)
Fe31(aq) 1 e2B
A H2O2(aq)
O2(g) 1 2H1(aq) 1 2e2B
A MnO2(s) 1 4OH2(aq)
MnO42(aq) 1 2H2O(l) 1 3e2B
2
2
B
A
2I (aq)
I2(s) 1 2e
A 4OH2(aq)
O2(g) 1 2H2O(l) 1 4e2B
21
2
Cu (aq) 1 2e B
A Cu(s)
AgCl(s) 1 e2 B
A Ag(s) 1 Cl2(aq)
SO422(aq) 1 4H1(aq) 1 2e2 B
A SO2(g) 1 2H2O(l)
Cu1(aq)
Cu21(aq) 1 e2 B
A
Sn41(aq) 1 2e2 B
A Sn21(aq)
H2(g)
2H1(aq) 1 2e2 B
A
Pb(s)
Pb21(aq) 1 2e2 B
A
Sn(s)
Sn21(aq) 1 2e2 B
A
A N2H51(aq)
N2(g) 1 5H1(aq) 1 4e2 B
21
2
A Ni(s)
Ni (aq) 1 2e B
A Co(s)
Co21(aq) 1 2e2B
A Pb(s) 1 HSO42(aq)
PbSO4(s) 1 H1(aq) 1 2e2B
21
2
A Cd(s)
Cd (aq) 1 2e B
A
Fe(s)
Fe21(aq) 1 2e2B
A Cr(s)
Cr31(aq) 1 3e2B
A Zn(s)
Zn21(aq) 1 2e2 B
2H2O(l) 1 2e2B
A H2(g) 1 2OH2(aq)
21
2
A Mn(s)
Mn (aq) 1 2e B
A
Al(s)
Al31(aq) 1 3e2B
A
Mg(s)
Mg21(aq) 1 2e2B
A Na(s)
Na1(aq) 1 e2B
A Ca(s)
Ca21(aq) 1 2e2B
A
Sr(s)
Sr21(aq) 1 2e2B
A
Ba(s)
Ba21(aq) 1 2e2B
K(s)
K1(aq) 1 e2B
A
A Li(s)
Li1(aq) 1 e2B
12.87
12.07
11.82
11.77
11.70
11.61
11.51
11.50
11.36
11.33
11.23
11.23
11.07
10.96
10.92
10.85
10.80
10.77
10.68
10.59
10.53
10.40
10.34
10.22
10.20
10.15
10.13
0.00
20.13
20.14
20.23
20.25
20.28
20.31
20.40
20.44
20.74
20.76
20.83
21.18
21.66
22.37
22.71
22.87
22.89
22.90
22.93
23.05
*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.
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