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Mathematical Operations
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A.l EXPONENTIAL NOTATION
The numbers used in chemistry are often either extremely large or extremely
small. Such numbers are conveniently expressed in the form
N
10n
X
where N is a number between 1 and 10, and n is the exponent. Some examples
of this exponential notation, which is also called scientific notation, follow.
. 1,200,000 is 1.2 X 106
(read "one point two times ten to the sixth power")
0.000604 is 6.04 X 10- 4 (read "six point zero four times ten to the negative
fourth power")
A positive exponent, as in the first example, tells us how many times a
number must be multiplied by 10 to give the long form of the number:
1.2
X
106 = 1.2
X
10
X
10
X
10
10
X
X
10
X
10 (six tens)
= 1,200,000
It is also convenient to think of the positive exponent as the number of places the
decimal point must be moved to the left to obtain a number greater than 1 and
less than 10: If we begin with 3450 and move the decimal point three places to
the left, we end up with 3.45 X 103 .
In a related fashion, a negative exponent tells us how many times we must
divide a num~er by 10 to give the long form of the number.
6.04
X
-4 -
10
-
10
X
6.04
X
10 10
X
10
- 0.000604
It is convenient to think of the negative exponent as the number of places the
decimal point must be moved to the right to obtain a number greater than 1 but
less than 10: If we begin with 0.0048 and move the decimal point three places to
the right, we end up with 4.8 X 10- 3 .
In the system of exponential notation, with each shift of the decimal point
one place to the right, the exponent decreases by 1:
4.8
X
10:::-3
=
48
X
10- 4
Similarly, with each shift of the decimal point one place to the left, the exponent
increases by 1:
4.8 X 10- 3 = 0.48 X 10- 2
Many scientific calculators have a key labeled EXP or EE, which is used to
enter numbers in exponential notation. To enter the number 5.8 X 103 on such
a calculator, the key sequence is
~
D [Ill EXP I(or [ill) [II
On some calculators the display will show 5.8, then a space, followed by 03,
the exponent. On other calculators, a small10 is shown with an exponent 3.
1104
A.1
To enter a negative exponent, use the key labeled +/-. For example, to enter
the number 8.6 X 10- 5, the key sequence is
[II D 01 EXP II +/-I~
When entering a number in exponential notation, do not key in the 10
the EXP or EE button.
if you use
In working with exponents, it is important to recall that 10° = 1. The following rules are useful for carrying exponents through calculations.
1.
Addition and Subtraction In order to add or subtract numbers expressed in
exponential notation, the powers of 10 must be the same.
(5.22
X
104) + (3.21
102) = (522
X
X
102) + (3.21
X
102)
= 525 X 102 (3 significant figures)
= 5.25
(6.25
X
10- 2)
-
(5.77
X
104
X
10-3) = (6.25
X
10- 2)
-
(0.577
X
10- 2)
= 5.67 X 10- 2 (3 significant figures)
When you use a calculator to add or subtract, you need not be concerned
with having numbers with the same exponents, because the calculator automatically takes care of this matter.
2.
Multiplication and Division When numbers expressed in exponential notation are multiplied, the exponents are added; when numbers expressed in
exponential notation are divided, the exponent of the denominator is subtracted from the e~ponent of the numerator.
(5.4
X
102)(2.1
X
103) = (5.4)(2.1)
=
11 X 105
= 1.1
(1.2
X
105)(3.22
X
X
106
10- 3) = (1.2)(3.22)
3.2 X 105
3.2
--- = 6.5 X 102
6.5
X
5 2
X
10 -
X
10 - -
7
5.7
5.7 X 10
---- = 8.5
8.5 X 10- 2
3.
102 + 3
X
105 +( - 3) = 3.9
= 0.49
7 ( 2)
X
= 0.67
3
X
102
10 = 4.9
X
9
X
10 = 6.7
10
X
2
8
10
Powers and Roots When numbers expressed in exponential notation are
raised to a power, the exponents are multiplied by the power. When the
roots of numbers expressed in exponential notation are taken, the exponents are divided by the root.
(1.2
X
105 ) 3 = (1.2) 3
= 1.7
X
X
105 X 3
1015
V'2.5 X 106 = \o/2.5 X 106/ 3
=
1.3
X
102
Scientific calculators usually have keys labeled x2 and Vx for sq{J.aring and
taking the square root of a number, respectively. To take higher powers or
roots, many calculators have yx and ~ (or INV yx) keys. For example, to
perform the operation \o/'7.5 X 10- 4 on such a calculator, you would key in
7.5 X 10-4, press the ~key (or the INV and then the~ keys), enter the
root, 3, and finally press =.The result is 9.1 X 10-2 .
Exponential Notation
1105
1106
APPENDIX A
Mathematical Operations
SAMPLE EXERCISE 1 I Using Exponential Notation
Perform each of the following operations, using your calculator where possible:
(a) Write the number 0.0054 in standard exponential notation
(b) (5.0 X 10- 2) + (4.7 X 10- 3)
(c) (5.98 X 1012)(2.77 X 10- 5)
(d) 'V'L75 X 10- 12
SOLUTION
(a) Because we move the decimal point three places to the right to convert 0.0054 to
5.4, the exponent is -3:
5.4 X 10- 3
Scientific calculators are generally able to convert numbers to exponential notation
using one or two keystrokes. Consult your instruction manual to see how this operation is accomplished on your calculator.
(b) To add these numbers longhand, we must convert them to the same exponent.
(5.0
X
10- 2) + (0.47
X
10- 2) = (5.0 + 0.47)
X
10- 2 = 5.5
X
10- 2
(Note that the result has only two significant figures.) To perform this operation on a
calculator, we enter the first number, strike the + key, then enter the second number
and strike the = key.
(c) Performing this operation longhand, we have
(5.98
X
2.77)
X
1012 - 5 = 16.6
X
10 7 = 1.66
X
108
On a scientific calculator, we enter 5.98 X 1012, press the X key, enter 2.77 X 10- 5,
and press the = key.
(d) To perform this operation on a calculator, we enter the number, press the Vy key
(or the INV and y"r keys), enter 4, and press the = key. The result is 1.15 X 10- 3 .
PRACTICE EXERCISE
Perform the following operations:
(a) Write 67,000 in exponential notation, showing two significant figures
(b) (3.378 X 10- 3) - (4.97 X 10- 5 )
(c) (1.84 X 1015 )(7.45 X 10- 2)
(d) (6.67 X 10- 8) 3
Answers:
(a) 6.7 X 104, (b) 3.328 X 10- 3, (c) 2.47 X 1016, (d) 2.97 X 10- 22
A.2 LOGARITHMS
Common Logarithms
The common, or base-10, logarithm (abbreviated log) of any number is the
power to which 10 must be raised to equal the number. For example, the common logarithm of 1000 (written log 1000) is 3 because raising 10 to the third
power gives 1000.
103 = 1000, therefore, log 1000 = 3
Further examples are
log 105
=
5
log 1
=
0
log
10- 2 =
(Remember that 10° = 1)
-2
In these examples the common logarithm can be obtained by inspection. However, it is not possible to obtain the logarithm of a number such as 31.25 by inspection. The logarithm of 31.25 is the number x that satisfies the following
relationship:
lOx = 31.25
A.2
Most electronic calculators have a key labeled LOG that can be used to obtain
logarithms. For example, on many calculators we obtain the value of log 31.25
by entering 31.25 and pressing the LOG key. We obtain the following result:
log 31.25 = 1.4949
Notice that 31.25 is greater than 10 (10 1) and less than 100 (10 2). The value for
log 31.25 is accordingly between log 10 and log 100, that is, between 1 and 2.
Significant Figures and Common Logarithms
For the common logarithm of a measured quantity, the number of digits after
the decimal point equals the number of significant figures in the original number. For example, if 23.5 is a measured quantity (three significant figures), then
log 23.5 = 1.371 (three significant figures after the decimal point).
Antilogarithms
The process of determining the number that corresponds to a certain logarithm
is known as obtaining an antilogarithm. It is the reverse of taking a logarithm.
For example, we saw above that log 23.5 = 1.371. This means that the antilogarithm of 1.371 equals 23.5.
log 23.5 = 1.371
antilog 1.371 = 23.5
The process of taking the antilog of a number is the same as raising 10 to a
power equal to that number.
antilog 1.371 = 101.371 = 23.5
Many calculators have a key labeled lOx that allows you to obtain antilogs directly. On others, it will be necessary to press a key labeled INV (for inverse), followed by the LOG key.
Natural Logarithms
Logarithms based on the number e are called natural, or base e,logarithms (abbreviated ln). The natural log of a number is the power to which e (which has
the value 2.71828 ... ) must be raised to equal the number. For example, the naturallog of 10 equals 2.303.
e2·303 = 10, therefore ln 10 = 2.303
Your calculator probably has a key labeled LN that allows you to obtain natural logarithms. For example, to obtain the natural log of 46.8, you enter 46.8 and
press the LN key.
ln 46.8 = 3.846
The natural antilog of a number is e raised to a power equal to that number.
If your calculator can calculate natural logs, it will also be able to calculate natural antilogs. On some calculators there is a key labeled ~ that allows you to
calculate natural antilogs directly; on others, it will be necessary to first press
the INV key followed by the LN key. For example, the natural antilog of 1.679 is
given by
Natural antilog 1.679 = el. 679 = 5.36
The relation between common and natural logarithms is as follows:
ln a = 2.303 log a
~
Notice that the factor relating the two, 2.303, is the natural log of 10, which we
calculated above.
Logarithms
1107
1108
APPENDIX A
Mathematical Operations
Mathematical Operations Using Logarithms
Because logarithms are exponents, mathematical operations involving logarithms follow the rules for the use of exponents. For example, the product of za
and zb (where z is any number) is given by
2 a. 2 b = 2 (a+b)
Similarly, the logarithm (either common or natural) of a product equals the sum
of the logs of the individual numbers.
log ab = log a + log b
ln ab = ln a + ln b
For the log of a quotient,
log(a/ b)
=
ln(a/ b) = ln a - ln b
log a - log b
Using the properties of exponents, we can also derive the rules for the logarithm of a number raised to a certain power.
lnan = n lna
log an = n log a
1
log a 1n = (1/n) log a
ln alin = (1/ n) ln a
pH Problems
One of the most frequent uses for common logarithms in general chemistry is in
working pH problems. The pH is defined as -log[H+], where [H+] is the
hydrogen ion concentration of a solution (Section 16.4). The following sample
exercise illustrates this application.
-
SAMPLE EXERCISE 2 I Using Logarithms
(a) What is the pH of a solution whose hydrogen ion concentration is 0.015 M?
(b) If the pH of a solution is 3.80, what is its hydrogen ion concentration?
SOLUTION
1. We are given the value of [H+]. We use the LOG key of our calculator to calculate
the value of log[H+]. The pH is obtained by changing the sign of the value obtained. (Be sure to change the sign after taking the logarithm.)
[H+] = 0.015
= - 1.82
(2 significant figures)
pH = - (- 1.82) = 1.82
log[H+]
2. To obtain the hydrogen ion concentration when given the pH, we must take the
antilog of -pH.
pH = - log[H+] = 3.80
log[H+] = -3.80
[H+] = antilog( - 3.80) = 10- 3·80 = 1.6
-
X
10- 4 M
PRACTICE EXERCISE
Perform the following operations: (a) log(2.5
X
10- 5), (b) ln 32.7, (c) antilog - 3.47,
(d) e- 1.89.
Answers: (a) -4.60, (b) 3.487, (c) 3.4
X
10- 4, (d) 1.5
X
10- 1
A.3 QUADRATIC EQUATIONS
An algebraic equation of the form ax 2 + bx + c = 0 is called a quadratic equation. The two solutions to such an equation are given by the quadratic formula:
x=
-b ±
Vb 2 2a
4ac
A.4
Graphs
1109
SAMPLE EXERCISE 3 I Using the Quadratic Formula
Find the values of x that satisfy the equation 2x 2 + 4x = 1.
-
SOLUTION
To solve the given equation for x, we must first put it in the form
ax 2 + bx + c = 0
and then use the quadratic formula. If
2x 2 + 4x = 1
then
2x 2 + 4x - 1 = 0
Using the quadratic formula, where a = 2, b = 4, and c = -1, we have
X
-4 ± v(4)(4) - 4(2)( -1)
2(2)
=
-4 :±:
V16+8
----- =
4
- 4 :±: V24
-4 :±: 4.899
= ---4
4
The two solutions are
x =
0
·~ 9
= 0.225 and x =
- 8~899
= -2.225
Often in chemical problems the negative solution has no physical meaning, and only
the positive answer is used.
A.4 GRAPHS
TABLE A-1 • Interrelation between
Often the clearest way to represent the interrelationship between two variables
Pressure and Temperature
is to graph them. Usually, the variable that is being experimentally varied,
Temperature
Pressure
called the independent variable, is shown along the horizontal axis (x-axis).
(oC)
(atm)
The variable that responds to the change in the independent variable, called the
dependent variable, is then shown along the vertical axis (y-axis). For example,
20.0
0.120
consider an experiment in which we vary the temperature of an enclosed gas
30.0
0.124
and measure its pressure. The independent variable is temperature, and the
40.0
0.128
0.132
dependent variable is pressure. The data shown in Table A-1 .,.. can be obtained
50.0
by means of this experiment. These data are shown graphically in Figure A.1 ... . The relationship between temperature
0.140 r - - - - - - : - - - - . , . . - - - - - - - , - - - - - - - ,
and pressure is linear. The equation for any straight-line
graph has the form
y = mx + b
where m is the slope of the line and b is the intercept with
they-axis. In the case of Figure 1, we could say that therelationship between temperature and pressure takes the
form
P = mT + b
0.130
i
~
Q)
gs~ 0.120
Q)
&::
/
/
where P is pressure in atm and T is temperature in °C. As
shown in Figure 1, the slope is 4.10 x 10- 4 atm;oc, and the
intercept-the point where the line crosses they-axis-is
0.112 atm. Therefore, the equation for the line is
P
=
4 atm)
( 4.10 X 10- oc T + 0.112 atm
/
/
/
0.110
0
20.0
40.0
60.0
Temperature (°C)
.A Figure A.l
80.0
1110
APPENDIX A
Mathematical Operations
A.5 STANDARD DEVIATION
The standard deviation from the mean, s, is a common method from describing
precision. We define the standard deviation as follows:
N
L(Xi- :X )2
s
i= l
=
N -1
where N is the number of measurements, :X is the average (also called the mean),
and Xi represents the individual measurements. Electronic calculators with
built-in statistical functions can calculate s directly by inputting the individual
measurements.
A smaller value of s indicates a higher precision, meaning that the data is
more closely clustered around the average. The standard deviation has a statistical significance. Thus, if a large number of measurements is made, 68% of the
measured values is expected to be within one standard deviation of the average, assuming only random errors are associated with the measurements.
•
SAMPLE EXERCISE 4 I Calculating an Average and Standard Deviation
The percent carbon in a sugar is measured four times: 42.01 %, 42.28%, 41.79%, and
42.25%. Calculate (a) the average and (b) the standard deviation for these measurements.
SOLUTION
(a) The average is found by adding the quantities and dividing by the number of
measurements:
x=
42.01
+ 42.28 + 41.79 + 42.25
4
168.33
4
= -
=
42.08
(b) The standard deviation is found using the equation above:
N
~(xi- x )2
i= l
s=
N - 1
N
Let's tabulate the data so the calculation of ~(xi -
x? can be seen clearly.
i= l
Percent C
Difference between Measurement
and Average, (xi - :X)
42.01
42.28
41.79
42.25
42.01
42.28
41.79
42.25
-
Square of Difference,
(xi - :X) 2
(-0.07) 2 = 0.005
(0.20) 2 = 0.040
( - 0.29) 2 = 0.084
(0.17) 2 = 0.029
42.08 = - 0.07
42.08 = 0.20
42.08 = -0.29
42.08 = 0.17
The sum of the quantities in the last column is
N
~(xi - x )2
= 0.005 +
0.040
+ 0.084 + 0.029 = 0.16
i= l
Thus, the standard deviation is
s=
N
2
~(xi:X) = ~.16 =
z= l
N- 1
4- 1
N
0.16
3
=
VQ.053
=
0.23
Based on these measurements, it would be appropriate to represent the measured
percent carbon as 42.08 ± 0.23.
><
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Properties ofWater
~
P-.
P-.
~
0.99987 g/ mL at 0 oc
Density:
1.00000 g/mL at 4 oc
0.99707 g/ mL at 25
oc
0.95838 g/ mL at 100 °C
Heat of fusion:
6.008 kJ/mol at 0 oc
Heat of vaporization:
44.94 kJ/mol at 0 oc
44.02 kJ/ mol at 25
oc
40.67 kJ/mol at 100 oc
Ion-product constant, Kw:
Specific heat:
1.14
X
10- 15 at 0 oc
1.01
X
10- 14 at 25 °C
5.47
X
10- 14 at 50 °C
Ice (at - 3 °C) 2.092 J/ g-K
Water (at 14.5 °C) 4.184 J/ g-K
Steam (at 100 °C) 1.841 J/ g-K
Vapor Pressure (torr)
T(°C)
p
T(°C)
p
T(°C)
p
T(°C)
p
0
5
10
12
14
16
17
18
19
20
4.58
6.54
9.21
10.52
11.99
13.63
14.53
15.48
16.48
17.54
21
22
23
24
25
26
27
28
29
30
18.65
19.83
21.07
22.38
23.76
25.21
26.74
28.35
30.04
31.82
35
40
45
50
55
60
65
70
80
90
42.2
55.3
71.9
92.5
118.0
149.4
187.5
233.7
355.1
525.8
92
94
96
98
100
102
104
106
108
110
567.0
610.9
657.6
707.3
760.0
815.9
875.1
937.9
1004.4
1074.6
1111
Thermodynamic Quantities
for Selected Substances at
298.15 K (25 °C)
><
a
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t:.I.l
~
~
~
so
11HJ
(kJ/mol)
11GJ
(kJ/mol)
0
-705.6
-1669.8
0
-630.0
-1576.5
28.32
109.3
51.00
BaC03(s)
BaO(s)
0
-1216.3
-553.5
0
-1137.6
-525.1
63.2
112.1
70.42
Beryllium
Be(s)
BeO(s)
Be(OHh(s)
0
-608.4
-905.8
0
-579.1
-817.9
9.44
13.77
50.21
111.8
-120.9
30.71
0
-36.23
82.38
-102.8
3.14
0
-53.22
174.9
80.71
245.3
152.3
198.49
145.5
0
-1128.76
-748.1
-1167.3
-604.17
-898.5
-1321.8
154.8
41.4
92.88
104.6
68.87
39.75
83.4
106.7
Substance
Aluminum
Al(s)
A1Cl3(s)
Al203(s)
Barium
Ba(s)
Bromine
Br(g)
Br-(aq)
Br2(g)
Br2(Z)
HBr(g)
Calcium
Ca(g)
Ca(s)
CaC03(s, calcite)
CaCl2(s)
CaF2(s)
CaO(s)
Ca(OHh(s)
CaS04(s)
Carbon
C(g)
C(s, diamond)
C(s, graphite)
CCl4(g)
CCl4(l)
CF4(g)
CH4(g)
C2H2(g)
1112
179.3
0
-1207.1
-795.8
-1219.6
-635.5
-986.2
-1434.0
718.4
1.88
0
-106.7
-139.3
-679.9
-74.8
226.77
672.9
2.84
0
-64.0
-68.6
-635.1
-50.8
209.2
(Jjmol-K)
158.0
2.43
5.69
309.4
214.4
262.3
186.3
200.8
Substance
C2H4(g)
C2H6(g)
C3Hs(g)
C4H10(g)
C4H10(Z)
C6H6(g)
C6H6(1)
CH30H(g)
CH30H(l)
C 2H 50H(g)
C2H50H(Z)
C6H1206(s)
CO(g)
C02 (g)
CH3COOH(Z)
Cesium
Cs(g)
Cs(l)
Cs(s)
CsCl(s)
Chlorine
Cl(g)
Cl- (aq)
Cl2(g)
HCl(aq)
HCl(g)
Chromium
Cr(g)
Cr(s)
11HJ
(kJ/mol)
11GJ
(kJ/mol)
so
(J/mol-K)
52.30
-84.68
-103.85
-124.73
-147.6
82.9
49.0
-201.2
-238.6
-235.1
-277.7
-1273.02
-110.5
-393.5
-487.0
68.11
-32.89
-23.47
-15.71
-15.0
129.7
124.5
- 161.9
-166.23
-168.5
-174.76
-910.4
-137.2
-394.4
-392.4
219.4
229.5
269.9
310.0
231.0
269.2
172.8
237.6
126.8
282.7
160.7
212.1
197.9
213.6
159.8
76.50
2.09
0
-442.8
49.53
0.03
0
-414.4
175.6
92.07
85.15
101.2
121.7
-167.2
0
-167.2
-92.30
105.7
-131.2
0
-131.2
-95.27
165.2
56.5
222.96
56.5
186.69
397.5
0
-1139.7
352.6
0
-1058.1
174.2
23.6
81.2
Cobalt
Co (g)
Co(s)
439
0
393
0
179
28.4
Copper
Cu(g)
Cu(s)
338.4
0
298.6
0
166.3
33.30
Cr203(s)
i
APPENDIX C
Thermodynamic Quantities for Selected Substances at 298.15 K (25 °C)
so
1113
so
!1HJ
(kJ/mol)
!1GJ
(kJ/mol)
(J/mol-K)
-601.8
-924.7
-569.6
-833.7
26.8
63.24
158.7
-13.8
202.7
173.51
Manganese
Mn(g)
Mn(s)
MnO(s)
Mn02(s)
Mn04- (aq)
280.7
0
-385.2
-519.6
-541.4
238.5
0
-362.9
-464.8
-447.2
173.6
32.0
59.7
53.14
191.2
203.26
0
1517.0
0
114.60
0
108.9
130.58
Mercury
Hg(g)
Hg(Z)
HgC12(s)
Hg2Cl2(s)
60.83
0
-230.1
-264.9
31.76
0
-184.0
-210.5
174.89
77.40
144.5
192.5
106.60
-55.19
62.25
0
25.94
70.16
-51.57
19.37
0
1.30
180.66
111.3
260.57
116.73
206.3
Nickel
Ni(g)
Ni(s)
NiC12(s)
NiO(s)
429.7
0
-305.3
-239.7
384.5
0
-259.0
-211.7
182.1
29.9
97.65
37.99
415.5
0
-87.86
-47.69
-341.8
-400
-271.9
-822.16
-1117.1
-171.5
369.8
0
-84.93
-10.54
-302.3
-334
-255.2
-740.98
-1014.2
-160.1
180.5
27.15
113.4
293.3
117.9
142.3
60.75
89.96
146.4
52.92
0
-277.4
-699.1
-421.3
-451.9
-217.3
0
-260.7
-625.5
-246.9
-187.9
68.85
161
131.0
303.3
68.70
LiCl(s)
159.3
0
-278.5
685.7
-408.3
126.6
0
-273.4
648.5
-384.0
138.8
29.09
12.2
133.0
59.30
Magnesium
Mg(g)
Mg(s)
MgC12(s)
147.1
0
-641.6
112.5
0
-592.1
148.6
32.51
89.6
Substance
11HJ
(kJ/mol)
!1GJ
(kJ/mol)
CuCl2(s)
CuO(s)
Cu20(s)
-205.9
-156.1
-170.7
-161.7
-128.3
-147.9
108.1
42.59
92.36
80.0
-332.6
0
-268.61
61.9
-278.8
0
-270.70
217.94
0
1536.2
0
Fluorine
F(g)
F-(aq)
F2(g)
HF(g)
Hydrogen
H(g)
H+(aq)
H+(g)
H2(g)
Iodine
I (g)
1- (aq)
12(g)
l2(s)
HI(g)
Iron
Fe(g)
Fe(s)
Fe 2+(aq)
Fe 3+(aq)
FeC12(s)
FeCl3(s)
FeO(s)
Fe203(s)
Fe304(s)
FeS2(s)
Lead
Pb(s)
PbBr2(s)
PbC03(s)
Pb(N03h(aq)
Pb(N03h(s)
PbO(s)
Lithium
Li(g)
Li(s)
u+(aq)
Li+(g)
(J/mol-K)
Substance
MgO(s)
Mg(OHh(s)
Nitrogen
N(g)
N2(g)
NH3(aq)
NH3(g)
NH 4+(aq)
N2H4(g)
NH4CN(s)
NH4Cl(s)
NH4N03(s)
NO(g)
N02(g)
N20(g)
N204(g)
NOCl(g)
HN03(aq)
HN03(g)
Oxygen
O(g)
02(g)
03(g)
OH-(aq)
H20(g)
H20(l)
H202(g)
H202(g)
Phosphorus
P(g)
P2(g)
472.7
0
-80.29
-46.19
-132.5
95.40
0.0
-314.4
-365.6
90.37
33.84
81.6
9.66
52.6
-206.6
-134.3
455.5
0
-26.50
-16.66
-79.31
159.4
153.3
191.50
111.3
192.5
113.4
238.5
-203.0
-184.0
86.71
51.84
103.59
98.28
66.3
-110.5
-73.94
94.6
151
210.62
240.45
220.0
304.3
264
146
266.4
247.5
0
142.3
-230.0
-241.82
-285.83
-136.10
-187.8
230.1
0
163.4
-157.3
-228.57
-237.13
-105.48
-120.4
161.0
205.0
237.6
-10.7
188.83
69.91
232.9
109.6
316.4
144.3
280.0
103.7
163.2
218.1
1114
Thermodynamic Quantities for Selected Substances at 298.15 K (25 oc)
APPENDIX C
Substance
1:1HJ
(kJ/mol)
Phosphorus (cont.)
P4(g)
P4(s, red)
P 4(s, white)
PCl3(g)
PCl3(l)
PF5 (g)
PH3(g)
P406(s)
P 4010(s)
POCl3(g)
POCl3(l)
H3P04(aq)
58.9
-17.46
0
-288.07
-319.6
-1594.4
,5.4
-1640.1
-2940.1
-542.2
-597.0
-1288.3
Potassium
K(g)
K(s)
KCl(s)
KC103(s)
KCl03(aq)
KzC03(s)
KN0 3(s)
K20(s)
K0 2 (s)
KzOz(s)
KOH(s)
KOH(aq)
Rubidium
Rb(g)
Rb(s)
RbCl(s)
RbCl03(s)
1:1GJ
(kJ/mol)
so
(Jfmol-K)
24.4
-12.03
0
-269.6
- 272.4
-1520.7
13.4
-2675.2
- 502.5
-520.9
-1142.6
280
22.85
41.08
311.7
217
300.8
210.2
228.9
325
222
158.2
89.99
0
-435.9
-391.2
-349.5
-1150.18
-492.70
-363.2
-284.5
-495.8
-424.7
-482.4
61.17
0
-408.3
-289.9
-284.9
- 1064.58
-393.13
-322.1
-240.6
- 429.8
- 378.9
-440.5
160.2
64.67
82.7
143.0
265.7
155.44
132.9
94.14
122.5
113.0
78.91
91.6
85.8
0
-430.5
-392.4
55.8
0
-412.0
-292.0
170.0
76.78
92
152
Scandium
Sc(g)
Sc(s)
377.8
0
336.1
0
174.7
34.6
Selenium
HzSe(g)
29.7
15.9
219.0
Silicon
Si(g)
Si(s)
SiC(s)
SiCl4(l)
Si02 (s, quartz)
Silver
Ag(s)
Ag+(aq)
368.2
0
-73.22
-640.1
-910.9
~
323.9
0
-70.85
-572.8
-856.5
167.8
18.7
16.61
239.3
41.84
'
0
105.90
0
77.11
42.55
73.93
Substance
AgCl(s)
Ag 20(s)
AgN03(s)
Sodium
Na(g)
Na(s)
Na+(aq)
Na+(g)
NaBr(aq)
NaBr(s)
NazC03(s) ·
NaCl(aq)
NaCl(g)
NaCl(s)
NaHC03(s)
NaN0 3 (aq)
NaN03(s)
NaOH(aq)
NaOH(s)
Strontium
SrO(s)
Sr(g)
Sulfur
S(s, rhombic)
1:1HJ
(kJ/mol)
1:1GJ
(kJ/mol)
-127.0
-31.05
-124.4
-109.70
-11.20
-33.41
107.7
0
-240.1
609.3
-360.6
-361.4
-1130.9
-407.1
-181.4
-410.9
-947.7
-446.2
-467.9
-469.6
-425.6
77.3
0
-261.9
574.3
-364.7
-349.3
-1047.7
-393.0
-201.3
-384.0
-851.8
-372.4
-367.0
-419.2
-379.5
-592.0
164.4
561.9
110.0
so
(J/mol-K)
96.11
121.3
140.9
153.7
51.45
59.0
148.0
141.00
86.82
136.0
115.5
229.8
72.33
102.1
207
116.5
49.8
64.46
54.9
164.6
0
102.3
-296.9
-395.2
-909.3
- 245.6
-20.17
-909.3
-814.0
0
49.7
-300.4
-370.4
-744.5
31.88
430.9
248.5
256.2
20.1
-33.01
-744.5
- 689.9
205.6
20.1
156.1
Titanium
Ti(g)
Ti(s)
TiCl4(g)
TiCl4(l)
Ti02 (s)
468
0
-763.2
-804.2
-944.7
422
0
-726.8
-728.1
-889.4
180.3
30.76
354.9
221.9
50.29
Vanadium
V(g)
V(s)
514.2
0
453.1
0
Zinc
Zn(g)
Zn(s)
ZnC12 (s)
ZnO(s)
130.7
0
- 415.1
-348.0
95.2
0
-369.4
-318.2
Ss(g)
SOz(g)
S03(g)
S04 2- (aq)
SOC12 (l)
HzS(g)
HzS04(aq)
HzS04(l)
182.2
28.9
160.9
41.63
111.5
43.9
><
a
z
Aqueous Equilibrium Constants
~
~
~
~
TABLE D-1 • Dissociation Constants for Acids at 25
oc
Name
Formula
Ka1
Acetic
CH3COOH (or HC 2H302)
H 3As04
H 3As03
1.8
X
5.6
X
5.1
X
H2C6H606
C6H 5COOH (or HC7H50 2)
8.0
X
6.3
X
H3B03
C3H7COOH (or HC4H702)
5.8
X
1.5
X
4.3
X
Chloroacetic
H2C03
CH2ClCOOH (or HC 2H 20 2Cl)
Chlorous
HC102
Citric
HOOCC(OH)(CH2COOH)z (or H3C6H507)
HCNO
7.4
X
3.5
X
HCOOH (or HCH02)
1.8
X
HN3
HCN
1.9
X
4.9
X
6.8
X
3.0
X
2.4
X
Hydrogen selenate ion
H202
HSe0 4-
10- 7
10- 12
2.2
X
10- 2
Hydrosulfuric
H 2S
9.5
X
Hypobromous
HBrO
2.5
X
10- 8
10- 9
Hypochlorous
HClO
3.0
X
10- 8
Hypoiodous
Iodic
HIO
2.3
X
HI03
CH3CH(OH)COOH (or HC 3H 50 3)
1.7
X
10- 11
10- 1
1.4
X
10- 4
CH2(COOH)z (or H2C3H204)
HN02
1.5
X
Arsenic
Arsenous
Ascorbic
Benzoic
Boric
Butanoic
Carbonic
Cyanic
Formic
Hydroazoic
Hydrocyanic
Hydrofluoric
Hydrogen chromate ion
Hydrogen peroxide
Lactic
Malonic
Nitrous
Oxalic
Par aperiodic
HF
HCr04-
(COOH)z (or H2C204)
H 5I06
Ka2
Ka3
10- 5
10- 3
1.0
X
10-7
10- 10
10- 5
1.6
X
10-12
5.6
X
10- 11
1.7
X
10- 5
10- 5
10- 7
4.5
X
5.9
X
2.8
X
10- 4
10- 4
4.0
X
10- 7
10- 4
10- 5
10- 10
10- 4
1
X
10- 19
10- 6
10- 3
10- 4
2.0
X
10- 2
10- 2
6.4
X
5.3
X
10-5
10- 9
10- 3
10- 5
6.2
X
10- 8
4.2
X
10- 13
2.1
X
10- 7
C6H50H (or HC6H50)
1.3
Phosphoric
H3P04
C2H5COOH (or HC3H502)
7.5
X
1.3
X
H4P207
H 2Se03
3.0
X
4.4
X
2.3
X
10- 2
10- 3
5.3
X
10- 3
10- 9
Sulfuric
H2S04
1.2
X
10- 2
Sulfurous
H2S03
HOOC(CJ-lOH)zCOOH (or H2C 4H 40 6)
Strong acid
1.7 X 10- 2
1.0 X 10- 3
6.4
X
4.6
X
Tartaric
10- 12
1.4 X 10- 3
1.1 X 10- 2
Phenol
Pyrophosphoric
Selenous
X
10- 5
10- 10
X 10- 10
Propionic
3.0
10- 8
10- 5
1115
1116
APPENDIX D
Aqueous Equilibrium Constants
TABlE D-2 • Dissociation Constants for Bases at 25
Name
Formula
Kb
Ammonia
NH3
C6H 5NH2
1.8
X
4.3
X
(CH3hNH
C 2H 5NH2
5.4
X
6.4
X
H2NNH2
HONH2
1.3
X
1.1
X
10-6
10- 8
4.4
X
10-4
Pyridine
CH3NH2
C5H 5N
1.7
X
Trimethylamine
(CH3)3N
6.4
X
Aniline
Dimethylamine
Ethylamine
Hydrazine
Hydroxylamine
Methylamine
oc
10-5
10-10
10-4
10- 4
10-9
10-5
.......,.
TABlE D-3 • Solubility-Product Constants for Compounds at 25
Name
Formula
Ksp
5.0
Barium chromate
BaC03
BaCr04
X 10- 9
2.1
X
Barium fluoride
BaF2
1.7
X
10- 10
10- 6
Barium oxalate
BaC204
1.6
X
10- 6
BaS04
1.1
X 10- 10
Cadmium carbonate
CdC03
Cadmium hydroxide
Cd(OHh
Cadmium sulfide*
CdS
1.8 x 10- 14
2.s x 10- 14
8 X 10- 28
Barium carbonate
Barium sulfate
Calcium carbonate (calcite)
Calcium chromate
Calcium fluoride
CaC03
CaCr04
CaF2
4.5
X 10- 9 ·
10- 4
oc
Name
Formula
Ksp
Lead(II) fluoride
PbF2
3.6
X
Lead(II) sulfate
PbS04
PbS
6.3
X
Lead(II) sulfide*
Magnesium hydroxide
Mg(OHh
1.8
X
Magnesium carbonate
MgC03
3.5
X
Magnesium oxalate
MgC204
8.6
X
Manganese(II) carbonate
MnC03
5.0
X
Manganese(II) hydroxide
1.6
X
Manganese(II) sulfide*
Mn(OHh
MnS
Mercury(!) chloride
Hg2Cl2
Mercury(!) iodide
1.3
X
Nickel(II) hydroxide
Ni(OHh
NiS
6.0
X
3
10- 29
10- 5
2.0
X
Calcium sulfate
CaS04
2.4
X
Chromium(III) hydroxide
Cr(OHh
1.6 x 1o- 30
Cobalt(II) carbonate
CoC03
1.0
X 10- 10
Cobalt(II) hydroxide
Co(OHh
1.3
X
Cobalt(II) sulfide*
CoS
5
Copper(!) bromide
CuBr
5.3
X
X
Nickel(II) sulfide*
Silver bromate
X
AgBr03
AgBr
5.5
X
5.0
X
8.1
X
1.8
X
Silver bromide
10- 9
Silver chloride
Ag2C03
AgCl
Silver chromate
Ag 2Cr04
1.2
X
Silver iodide
Agl
8.3
X
Silver sulfate
Ag2S04
1.5
X
Silver sulfide*
6
Strontium carbonate
Ag2S
SrC03
Tin(II) sulfide*
SnS
1
Zinc carbonate
ZnC03
1.0
X
Copper(II) carbonate
CuC03
2.3
Copper(II) hydroxide
Cu(OHh
4.8
X
Copper(II) sulfide*
CuS
6
Iron(II) carbonate
FeC03
Iron(II) hydroxide .
Fe(OHh
2.1
7.9
Lanthanum fluoride
Lanthanum iodate
LaF3
La(I03h
10- 11
X 10- 16 .
2 X 10- 19
6.1 X 10- 12
Lead(II) carbonate
PbC03
7.4
X
Lead(II) chloride
PbCl2
1.7
Lead(II) chromate
PbCr04
2.8
10- 20
10- 37
X
Silver carbonate
X
9.3
X
10- 12
10- 17
10- 10
10-26
Zinc hydroxide
Zn(OHh
3.0
X
Zinc oxalate
2.7
X
X
10- 13
Zinc sulfide*
ZnC204
ZnS
*For a solubility equilibrium of the type MS(s) + H 20(/) ~ M 2+(aq) + HS- (aq) + OH- (aq)
10- 12
10- 10
X
X
X
10- 5
10- 13
10- 5
10-51
10- 14
10- 5
2
10- 7
10- 16
10- 20
10- 15
10-22
X 10- 10
X
10- 13
10-53
NiC03
Mercury(II) sulfide*
Ca3(P04h
10- 5
10- 10
Nickel(II) carbonate
10- 6
Calcium phosphate
10- 11
10- 8
Hg2I2
HgS
3.9
X
X
10-28
10- 18
1.1 x 1o- 28
2 X 10- 53
X 10- 11
6.5
2
X
X
X
Ca(OHh
3
1.2
7.1
Calcium hydroxide
'
10- 8
10- 7
10- 10
10-16
10- 8
10-25
Standard Reduction
Potentials at 25 °C
><:
a
z
~
A..
A..
~
Half-Reaction
E 0 (V)
Half-Reaction
E 0 (V)
A g+(aq) + e- ~ Ag(s)
+0.799
+0.095
+0.222
-0.31
+0.446
-0.151
+0.01
-1.66
2 H 20(Z) + 2 e- ~ H 2_(g) + 2 OH- (aq)
H02- (aq) + H 20(l) + 2 e- ~ 3 OH- (aq)
H 20 2(aq) + 2 H +(aq) + 2 e- ~ 2 H 20(l)
Hg22+(aq) + 2 e- ~ 2 Hg(l)
2 Hg 2+(aq) + 2 e- ~ Hgl+(aq)
Hg 2+(aq) + 2 e- ~ Hg(l)
12(-s) + 2 e- ~ 2 1- (aq)
210 3- (aq) + 12 H +(aq) + 10 e- ~
l2(s) + 6 H 20(Z)
K +(aq) + e- ~ K(s)
Li+(aq) + e- ~ Li(s)
Mg 2+(aq) + 2 e- ~ Mg(s)
Mn2+(aq) + 2 e- ~ Mn(s)
Mn0 2(s) + 4 H +(aq) + 2 e- ~
Mn2+(aq) + 2 H 20(l)
Mn04- (aq) + 8 H +(aq) + 5 e- ~
Mn2+(aq) + 4 H20(l)
Mn04- (aq) + 2 H20(Z) + 3 e- ~
Mn0 2(s) + 4 OH- (aq)
HN02(aq) + H +(aq) + e- ~ NO(g) + H 20(l)
N2(g) + 4 H20(l) + 4 e- ~ 4 OH- (aq) + N 2H 4(aq)
N2(g) + 5 H +(aq) + 4 e- ~ N2Hs+(aq)
N03- (aq) + 4 H +(aq) + 3 e- ~ NO(g) + 2 H20(l)
N-a+(aq) + e- ~ Na(s)
Ni2+(aq) + 2 e- ~ Ni(s)
0 2(g) + 4 H +(aq) + 4 e- ~ 2 H2 0(~)
02(g) + 2 H20(Z) + -4 e- ~ 4 OH- (aq)
02(g) + 2 H +(aq) + 2 e- ~ H 20 2(aq)
0 3(g) + 2 H +(aq) + 2 e- ~ 0 2(g) + H 20(Z)
Pb 2+(aq) + 2 e- ~ Pb(s)
Pb0 2(s) + HS0 4- (aq) + 3 H +(aq) + 2 e- ~
PbS0 4(s) + 2 H20(l)
PbS0 4(s) + H +(aq) + 2 e- ~ Pb(s) + HS0 4- (aq)
PtC142- (aq) + 2 e- ~ Pt(s) + 4 Cl- (aq)
S(s) + 2 H +(aq) + 2 e- ~ H2S(g) ·
H 2S03(aq) + 4 H +(aq) + 4 e- ~ S(s) + 3 H 20(l)
HS0 4- (aq) + 3 H +(aq) + 2 e- ~
H2S03(aq) + H 20(Z)
Sn2+(aq) + 2 e- ~ Sn(s)
Sn4+(aq) + 2 e- ~ Sn2+(aq)
V02+(aq) + 2 H +(aq) + e- ~ V0 2+(aq) + H 20(Z)
Zn2+(aq) + 2 e- ~ Zn(s)
-0.83
+0.88
+ 1.776
+0.789
+0.920
+0.854
+0.536
AgBr(s) + e- ~ Ag(s) + Br- (aq)
AgCl(s) + e- ~ Ag(s) + Cl- (aq)
Ag(CNh - (aq) + e- ~ Ag(s) + 2 CN- (aq)
Ag2Cr04(s) + 2 e- ~ 2 Ag(s) + Cr042- (aq)
Agl(s) + e- ~ Ag(s) + 1- (aq)
Ag(S203h 3- (aq) + e- ~ Ag(s) + 2 S2032- (aq)
Al3+(aq) + 3 e- ~ Al(s)
H 3As0 4(aq) + 2 H +(aq) + 2 e- ~
H 3As03(aq) + H20(Z)
Ba 2+(aq) + 2 e~ ~ Ba(s)
BiO+(aq) + 2 H+(aq) + 3 e- ~ Bi(s) + H 20(Z)
Br2 (Z) + 2 e~ ~ 2 Br- (aq)
2 Br03- (aq) + 12 H +(aq) + 10 e- ~
Br2(l) + 6 H20(l)
2 C02(g) + 2 H +(aq) + 2 e- ~ H2C204(aq)
ea2+(aq) + 2 e- ~ Ca(s)
""'·
Cd 2+(alJ) + 2 e- ~ Cd(s)
Ce4 ~(aq) + e- ~ Ce3+(aq)
Cl2(g) + 2 e- ~ 2 Cl- (aq)
2 HClO(aq) + 2 H +(aq) + 2 e- ~
Cl2(g) + 2 H20(l)
ClO- (aq) + H 20(l) + 2 e- ~ Cl- (aq) + 2 OH- (aq)
2 Cl0 3- (aq) + 12 H +(aq) + 10 e- ~
Cl2(g) + 6 H20(l)
Co 2+(aq) + 2 e- ~ Co(s)
Co 3+(aq) + e- ~ Co 2+(aq)
Cr 3+(aq) + 3 e- ~ Cr(s)
Cr 3+(aq) + e- ~ Cr2+(aq)
Cr0 7 2- (aq) + 1'21: H +(aq) + 6 e- ~
2 cr-?7 (aq) + 7 B 20(l)
Cr0 42- (aq) + 4 H20(l) + 3 e- ~
Cr(OH)3(s) + 5 OH- (aq)
Cu2+(aq) + 2 e- ~ Cu(s)
Cu 2+(aq) + e- ~ Cu+(aq)
Cu+(aq) + e- ~ Cu(s)
Cul(s) + e- ~ Cu(s) + 1- (aq)
F2(g) + 2 e- ~ 2 F- (aq)
Fe2+(aq) + 2 e- ~ Fe(s)
Fe3+(aq) + e- ~ Fe 2+(aq)
Fe(CN)63- (aq) + e- ~ Fe(CN) 64- (aq)
2 H +-(aq) + 2 e- ~ H 2(g)
,...;.
+0.559
-2.90
+0.32
+1.065
+1.52
-0.49
' -2.87
-0.403
+1.61
+1.359
+1.63
+0.89
+1.47
-0.277
+1.842
-0.74
-0.41
+1.33
-0.13
+0.337
+0.153
+0.521
-0.185
+2.87
-0.440
+0.771
+0.36
0.000
+ 1.195
- 2.925
-3.05
-2.37
-1.18
+1.23
+1.51
+0.59
+1.00
-1.16
-0.23
+0.96
-2.7
-0.28
+1.23]
+0.40
+0.68
+2.07
-0.126
+1.685
-0.356
+0.73
+0.141
+0.45
+0.17
- 0.136
+0.154
+1.00
-0.763
1117
·. ,,.
><
a
z
AP Exam Practice Problems
~
~
~
-<
UNIT I. ATOMS, MOLECULES,
IONS, AND
STOICHIOMETRY
Multiple-Choice Questions
1.1 What volume will contain 5.0 mol of aluminum? The density of aluminum is 2.7 g mL- l.
(a) 10. mL
(b) 20.mL
(c) 40. mL
(d) 50. mL
(e) 100. mL
1.2 Which metal reacts most vigorously with water?
(a) K
(b) Na
(c) Ca
(d) Li
(e) Zn
1.3 Which of these compounds is the least soluble in water?
(a) sodium sulfate
(b) potassium hydrogen carbonate
(c) lead(II) nitrate
(d) magnesium chloride
(e) calcium phosphate
1.4 Under the conditions of excess oxygen, the reaction of one
mole of glucose, C6H1206, with atmospheric oxygen can
theoretically produce:
(a) 6 mol of C02 and 6 mol of H 20
(b) 6 mol of C02 and 3 mol of H 20
(c) 3 mol of C02 and 6 mol of H 20
(d) 3 mol of C02 and 6 mol of H 20
(e) 6 mol of CO and 6 mol of H 20
1.5 Carbon monoxide reduces iron(III) oxide to metallic iron:
Fe203
+CO~
Fe+ C0 2 (unbalanced)
How many moles of CO are required to form one mole of
Fe from Fe203?
(a) 0.5
(b) 1
(c) 1.5
(d) 2
(e) 3
1.6 Which of the following species will not react with acid to
produce a gas?
(a) NazS
(b) NaHC03
(c) NazS03
(d) Zn
(e) (NH4)zS04
1.7 Which of the following 0.1 M solutions will form a precipitate with 0.1 M copper(II) sulfate?
(a) NazS04
(b) KCl
(c) LiCzH302
(d ) NH4N03
(e) Pb(N03)z
1.8 When added to water, which substance produces a basic
solution?
(a) HN3
(b) NaCl
(c) Ca
(d) H2S
(e) NH4Cl
1.9 Of the metals that do react with water, which reacts least
readily?
(a) Zn
(b) Mg
(c)
K
(d) Li
(e) Cu
1.10 Strong heating of 7.534 g of a hydrate yields 5.957 g of
anhydrous calcium sulfate. What is the ratio of water molecules to calcium sulfate units in the hydrate?
(a) [(7.534 - 5.957)/ 18] -:-- (5.957/ 136)
(b) (5.957/ 136) -;- [(7.534 - 1.577)/ 18]
(c) (7.534/ 18) -:-- (5.957/ 136)
(d ) [(7.534 - 5.957)/ 18] -;- (7.534/ 136)
(e) (5.957/ 136) -:-- (7.534/ 18)
1.11 If 56 g of lithium reacts with 56 grams of nitrogen and the
reaction proceeds with a 50% yield of product, how many
grams of lithium nitride are obtained?
(a) 21 g
(b) 28 g
(c) 47 g
(d) 56 g
(e) 84 g
1.12 Which is a strong acid?
I. HBr
II. HC103
(a) I only .
(b) I and II only
(c) I and III only
(d) II and III only
(e) I, II, and III
III. HN02
1119
1120
APPENDIX F
AP Exam Practice Problems
1.13 Which set of reactants produces a gaseous product?
I. 6 M HCl(aq) + Zn(s)
II. 6 M HN0 3 (aq) + MgC0 3(s)
Ill. CH4(g) + 0 2(g)
(a) I only
(b) I and II only
(c) I and III only
(d) II and III only
(e) I, II, and III
1.14 What products result when aqueous solutions of Co(N03h
and K2C03 are mixed?
(a) CoC03(aq) and KN03(s)
(b) CoC03(s) and KN03(aq)
(c) CoC03(aq) and KN03(aq)
(d) CoC03(s) and KN03(s)
(e) CoC03(s) and K2N03(aq)
1.15 Which aqueous solution contains the largest number of
ions dissolved in solution?
(a) 0.5 M NaOH
(b) 0.2 M FeCl3
(c) 0.3 M Ca(N03h
(d) 0.4 M K2S04
(e) 0.2 M Al2(S04)3
Free-Response Questions
1.1 Decomposition of 36.54 g of a pure solid compound produces 4.06 g of nitrogen gas, 10.44 g of water, and a solid
metal oxide. The metal oxide is found to contain 68.42%
chromium.
(a) What is the simplest formula for the metal oxide?
(b) What is the oxidation number of chromium in the
oxide?
(c) How many moles of each element are present in the
unknown compound?
(d) What is the simplest formula for the unknown compound?
(e) Express the formula of the compound in terms of a
common cation-anion pair and name the compound.
(f) Write and balance a chemical equation for the decomposition reaction.
1.2 Muriatic acid is a solution of hydrochloric acid used by masons to clean brick work and etch concrete. An experiment
was carried out to determine the percent of hydrochloric
acid in a bottle of muriatic acid by titration.
(a) First, the concentration of a standard sodium hydroxide solution was determined by titration of potassium
acid phthalate, KHC 8H 80 4, a solid monoprotic acid. It
was found that 1.789 g of KHP required 24.25 mL of
NaOH solution to reach a suitable end point. Calculate
the concentration of NaOH.
(b) A 50.00 mL sample of muriatic acid was diluted to a
total volume of 1000.0 mL. Then 20.00 mL of the diluted acid required 27.40 mL of standard NaOH solution
to reach the end point. Calculate the concentration of
the diluted muriatic acid solution.
(c) Calculate the concentration of the original muriatic
acid solution.
(d) The density of the original muriatic acid solution was
found to be 1.15 g/ mL. What is the percent by mass of
HCl in the original muriatic acid solution?
Laboratory grade hydrochloric acid is 37.0% HCl and
has a density of 1.185 g/ mL. Calculate the molarity of
laboratory hydrochloric acid.
(f) Tell why it would not be practical to use laboratory
hydrochloric acid to prepare a solution of the same
concentration as the original muriatic acid in this
experiment.
(e)
1.3 Two experiments are carried out to determine the molecular formula of a monoprotic organic acid containing only
carbon, hydrogen, and oxygen.
First, combustion of 3.332 grams of the acid produces
8.624 grams of carbon dioxide and 1'.764 g of water.
In a second experiment, titration of 0.4326 g of acid requires 18.15 mL of 0.1752 M NaOH solution to reach a suitable end point.
(a) How many moles of oxygen gas are needed for the
combustion reaction?
(b) What is the simplest formula of the acid?
(c) Calculate the molar mass of the acid.
(d) What is the molecular formula of the acid?
(e) Write and balance an equation for the complete combustion of the acid.
1.4 Write balanced net ionic equations for each of the following
laboratory situations. Then answer the questions. Assume
a reaction occurs in each case.
(a) Aqueous nickel(II) sulfate is added to a solution of
sodium hydroxide.
i. Would you expect any of the reactants and/ or
products to be colored? If so, which? Explain.
ii. What would you observe if excess hydrochloric
acid is added to the resulting reaction mixture?
Write a net ionic equation to explain your predicted
observation.
iii. Which (if any) of these reactions can be classified as
redox? Explain.
(b) Nitric acid solution is added to solid sodium sulfide.
i. Classify this reaction as acid-base, redox, combustion, or complex ion.
ii. Would you expect this procedure to be dangerous?
Why or why not?
(c) Silver nitrate solution is added to a piece of aluminum
foil.
i. How many electrons transfer in the balanced
equation?
ii. Would a potassium nitrate solution cause a similar
reaction with aluminum? Explain.
(d) Zinc metal is placed in a solution of acetic acid.
i. What would you observe happening?
ii. Is this an acid-base reaction or a redox reaction?
Explain.
(e) Stomach acid (hydrochloric acid) reacts with a solid
antacid tablet (active ingredient: calcium carbonate).
i. What other substances contain calcium carbonate?
ii. Solid calcium sulfite undergoes a similar reaction
with hydrochloric acid. Write a net ionic equation.
1.5 A mixture contains NaCl, NaC103, NaHC03, and Na2C03.
The mixture is heated and the following reactions occur:
+ 2 C02(g) + H 20(g)
Na20(s) + C02(g)
2 NaCl(s) + 3 0 2(g)
2 NaHC03 ~ Na20(s)
Na2C03
~
2 NaC10 3 ~
NaCl
~no
reaction
APPENDIX F
When 200.0 g of the mixture is heated, 5.50 g of water,
38.70 g of carbon dioxide, and 16.57 g of oxygen are produced. Assume complete decomposition of the mixture.
(a) How many grams of NaHC03 are in the mixture?
(b) How many grams of C02(g) are formed from the decomposition of sodium carbonate?
(c) How many mvles of NaC103 are in the mixture?
(d) Calculate the % composition of the original mixture.
(e) Upon heating another 200.0 g sample of the mixture, it
was found that all the sodium hydrogen carbonate decomposed but some of the sodium carbonate remained.
If 9.20 g of sodium carbonate remained, how many
grams of C02 would have formed in this experiment?
AP Exam Practice Problems
1121
2.7 When placed in the highest to lowest order for ionization
energy, what is the correct order for the species, Cl- , Ar, K+?
(a) Cl- > Ar > K+
(b) Ar > K+ > Cl(c) K+ > Cl- > Ar
(d) K+ > Ar > Cl(e) Cl- = Ar = K+
2.8 Which set contains all trigonal pyramidal species?
(a) NH3, S03, N03<b> NF3, C032- , so/<c> BF3, H 30 +, NH3
(d) so3, N03- , co3 2<e> NF3, S032-, H 30 +
2.9 What is the correct order of increasing bond energy?
UNIT II. ATOMIC STRUCTURE,
PERIODICITY,
AND BONDING
Multiple-Choice Questions
2.1 Which of these molecules contains two pi bonds?
C2H6
C2H4
CH20
co
CH3COOH
2.2 Which electronic transition in the hydrogen atom results in
the emission of visible light?
(a)
(b)
(c)
(d)
(e)
(a)
n = 3 ton =
=
=
=
=
(b) n = 3 to n
(c) n = 4 ton
(d) n = 2 to n
(e) n = 2 to n
2
1
3
4
6
2.3 The maximum number of electrons in an atom that can
have quantum numbers n = 5, l = 3 is
(a) 2
(b) 6
(c) 8
(d) 10
(e) 14
(a)
(b)
(c)
(d)
(e)
Br- Br < Br - Cl < Br- F
Br - F < Br-Cl < Br- Br
Br-Cl < Br - Br < Br- F
Br - F < Br- Br < Br-Cl
Br- Br < Br- F < Br - Cl
2.10 What geometrical arrangement is associated with orbitals
that are sp 2 hybridized?
(a) linear
(b) octahedral
(c) trigonal bipyramidal
(d) trigonal planar
(e) tetrahedral
2.11 Which compounds contain both ionic and covalent bonds?
I. NH4N03
II. KAl(S04h
Ill. CH3COOH
(a) II only
(b) II and III only
(c) I and II only
(d) I and III only
(e) I, II, and III
2.12 When the following species are arranged according to in-
creasing 0-S - 0 bond angle, what is the correct order?
(a) S02 < S03 < S0 42- < so/(b) so3 < S04 2- < so3- < S032(c) so/-< S04 2- < so2 < so3
(d) so3 < so2 < S04 2- < S032(e) S0 42- < so/- < so2 < S03
2.4 Which compound is expected to have the highest melting
point?
(a) NaF
(b) KF
(c) RbF
(d) KCl
(e) NaCl
2.5 What is the electron configuration of the Ti 3+ ion?
(a) 1s 22s 22p 63s 23p63d24s 2
(b) 1s 22s 22p 63s23p63d2
(c) 1s22s 22p63s 23p63d 1
(d) 1s 22s 22p63s 23p64s 1
(e) 1s 22s 22p63s 23p6
2.13 Which compound is expected to have the largest lattice
energy?
(a) KF
(b) CaO
(c) CaCl2
(d) NaF
(e) KCl
2.6 What is the total number of completely or partially filled
" p" orbitals in a gaseous arsenic atom in the ground state?
(a) 3
2.15 Which energy transition in the hydrogen atom will be the
greatest?
(a) n = 2 ton = 1
(b) n = 3 to n = 2
(c) n = 4 to n = 3
(d) n = 5 to n = 4
(e) n = 6 to n = 5
(b) 6
(c) 8
(d) 9
(e) 10
2.14 Which element has the largest first ionization energy?
(a) Be
(b) B
(c) C
(d) N
(e)
0
1122
APPENDIX F
AP Exam Practice Problems
Unit II. Free-Response Questions
2.1 Fluorine combines with sulfur to form SF2, SF4, and SF 6.
(a) Draw a Lewis structure for SF2.
(b) Identify the hybridization of the sulfur in SF4.
(c) State the geometry of SF6.
(d) Predict the F-S- F bond angles for each of the three
compounds: SF2, SF4, and SF 6. State your reasons.
(e) Predict which, if any, of the three sulfur compounds is
(are) polar. Explain your reasoning.
(f) Explain why chlorine combines with sulfur to form
SC14 but not SC16·
(g) Oxygen forms OF2, but not OF4 or OF6. Explain.
colors of the lines are red, blue-green, blue-violet, and violet, not necessarily in order.
(a) Calculate the frequency associated with the 410 nm
line.
(b) Calculate the energy of a single photon associated with
the 434 nm line.
(c) Calculate the energy of a mole of photons associated
with the 486 nm line.
(d) How may photons associated with the 656 nm line will
provide 1.00 kJ of energy?
(e) Match each colored line with its wavelength. Order the
lines by increasing energy and increasing frequency.
(f) Explain the origin of the four colored lines of the hydrogen spectrum. Explain why hydrogen does not display a continuous spectrum.
(g) Is it possible that the atomic emission spectrum of hydrogen has more than four lines? Explain.
2.2 Consider an atom of titanium.
(a) Write the complete electron configuration of titanium.
(b) Write the complete electron configuration of Ti 2+.
(c) Write the set of four quantum numbers for each valence electron in Ti 2+.
(d) Write the chemical formula for titanium(IV) oxide.
Would you expect titanium(IV) oxide to be colored?
Explain your answer.
(e) Predict the relative values of the first ionization energies of calcium and titanium. Explain the basis of your
prediction.
UNIT III. GASES,
INTERMOLECULAR
FORCES,
AND SOLUTIONS
2.3 The values of the first ionization energies of the period 3 elements are given in units of kJ/ mol.
Multiple-Choice Questions
(a)
(b)
(c)
(d)
(e)
Na = 495; Mg = 738; Al = 578; Si = 786;
P = 1012; S = 1000; Cl = 1251; Ar = 1521.
State the general trend and explain the trend using the
terms screening effect and effective nuclear charge.
Explain why the first ionization energy of aluminum is
lower than that of magnesium.
Explain why the first ionization energy of sulfur is
lower than that of phosphorus.
Predict the relative values of the second ionization
energies of sodium and magnesium. Explain your
reasoning.
Why is the first ionization energy of potassium lower
than that of sodium?
2.4 Write balanced net ionic equations for each of the following
laboratory situations. Then answer the questions. Assume
a reaction occurs in each case.
(a) Chlorine gas is bubbled into liquid water.
i. Identify the oxidizing agent and the reducing agent
in this reaction.
ii. Name a common use of gaseous chlorine.
(b) Fluorine gas is bubbled into liquid water.
i. Would you expect this reaction to be exothermic or
endothermic? Explain.
ii. Would the aqueous solution resulting from this reaction conduct electricity strongly, weakly, or not at
all. Explain.
(c) Hydrogen peroxide is allowed to stand at room
temperature.
i. When storing hydrogen peroxide what precautions
should be taken? Why?
ii. Assign oxidation numbers to each oxygen in the
equation and tell whether oxygen is oxidized or
reduced.
2.5 Four visible lines of the atomic emission spectrum of hydrogen have wavelengths of 410, 434, 486, and 656 nm. The
3.1 A given gas will show the greatest deviation from ideal behavior at which set of conditions of temperature and
pressure?
(a) 0 oc and 1 atm
(b) 100 oc and 1 atm
(c) 100 °C and 0.5 atm
(d) 0 oc and 0.5 atm
(e) - 100 oc and 1 atm
3.2 Equal numbers of moles of three gases are mixed in a 20.0 L
container at 25 oc. If the container has a pinhole leak, what
is the proper order of the partial pressures of the gases after
two hours?
(a) C02 > H2 > CH4
(b) H2 > C02 > CH4
(c) C02 > CH4 > H2
(d) H2 > CH4 > C02
(e) CH 4 > C02 > H 2
3.3 Which substance in the solid phase has the strongest intermolecular forces?
(a) Cl2
(b) Na
(c) C02
(d)
c
(e) CsH 12
3.4 Which gas is most soluble in water?
(a) carbon dioxide
(b) ammonia
(c) methane
(d) oxygen
(e) nitrogen
3.5 The kinetic-molecular theory predicts that two gases at the
same temperature will have the same
(a) average speed.
(b) average kinetic energy.
(c) pressure.
APPENDIX F
(d) rate of effusion.
(e) number of particles.
3.6 The density of a typical gas at normal atmospheric temper-
atures and pressures is
(a) 1gmL- 1
(b) 1 g L - 1
(c) 100 g L - 1
(d) 0.1 g mL- 1
(e) 0.01 g L- 1
3.7 Real gases tend to exhibit non-ideal behavior because their
particles possess which properties?
I. Attractive forces between molecules
II. Attractive forces between molecules and their
containers
III. Finite volumes
(a) I only
(b) II only
(c) III only
(d) I, II, and III
(e) I and II only
3.8 A solute dissolved in benzene lowers the freezing point of
the solution to a temperature that is lower than the freezing
point of pure benzene. The amount of change in freezing
point depends on
(a) the number of particles formed by the solute when
dissolved.
(b) the molar mass of the solvent.
(c) the freezing point of the solute.
(d) the atmospheric pressure.
(e) the temperature of the solvent.
3.9 Consider two solutions: a 0.25 molal solution of Fe(N03)3
and a 0.50 molal solution of NaCl. Which statement about
the solutions is correct?
(a) The sodium chloride solution has a lower freezing
point because the salt concentration is greater.
(b) The iron(III) nitrate solution has a higher boiling point
because the total ion concentration is greater.
(c) Both solutions freeze at approximately the same negative Celsius temperature because they have equal ion
concentrations.
(d) The iron(III) nitrate solution has a higher vapor pressure because the total ion concentration is greater.
(e) The iron(III) nitrate solution freezes at a higher temperature because it is more acidic.
3.10 When comparing carbon dioxide with oxygen under the
same conditions of temperature and pressure, what can be
said about carbon dioxide?
(a) C02 moves faster and effuses more slowly.
(b) C02 moves more slowly and effuses more slowly.
(c) C02 moves faster and effuses faster.
(d) C02 moves more slowly and effuses faster.
(e) C02 moves at the same average speed but effuses more
slowly.
3.11 Three balloons are filled with the same number of mole-
cules of 0 2, H 2, and C02, respectively, under the same conditions of temperature and pressure. Which is not the same
for each gas?
I. average kinetic energy
II. volume
III. average velocity of molecules
IV. density
(a)
(b)
(c)
(d)
(e)
AP Exam Practice Problems
1123
I and III only
III and IV only
III only
II and IV only
I, II, and III only
3.12 Which compound would be expected to be most soluble in
water?
(a) C6H6
(b) C2H4
(c) (C2HshO
(d) CHCl3
(e) (CH3hNH
3.13 Which aqueous solution will boil at the highest
temperature?
(a) 0.5 m C6H1206
(b) 1.0 m C 2H 50H
(c) 1.25 m NaCl
(d) 1.0 m CaCl2
(e) 0.5 m A1Cl3
3.14 How does the average velocity of molecules change when
the absolute temperature is halved?
(a) The average velocity stays the same.
(b) The average velocity decreases by 1/ 2.
(c) The average velocity decreases by 1/ 4.
(d) The average velocity doubles.
(e) The average velocity decreases by an amount depending on the masses of the molecules.
3.15 A given liquid would have which combination of
properties?
Vapor Pressure
(a) high
(b) low
(c) high
(d) low
(e) high
Heat of Vaporization
Attractive Forces
high
low
low
low
high
high
low
low
high
low
Free-Response Questions
3.1 A mixture of 0.300 mol each of hydrogen gas, oxygen gas,
and liquid water are present in a 20.00 liter container at
25 °C. The equilibrium vapor pressure of water at 25 °C is
23.76 torr.
(a) Calculate the total pressure inside the flask.
(b) Using principles of kinetic molecular theory, explain
which gas has the
i. highest average kinetic energy
ii. highest average velocity of molecules
iii. highest density
(c) The mixture is sparked, a reaction ensues consuming
one of the reactants entirely, and the resulting mixture
is allowed to come to equilibrium at 80 oc.
i. Write and balance a chemical equation to describe
the reaction.
ii. Which is the limiting reactant? Explain.
iii. Calculate the total pressure in the flask after thereaction is complete. The water vapor pressure at
80 oc is 355 torr.
iv. Calculate the number of moles of water present as
vapor when the reaction is complete.
1124
APPENDIX F
AP Exam Practice Problems
3.2 Consider the following 0.10 M solutions:
I. iron(III) chloride
II. copper(II) nitrate
III. hydrogen sulfide
(a) Describe the color of each solution.
(b) Predict whether each solution's conductivity would
measure high, low, or nonconducting and explain your
predictions.
(c) Which pair(s) of solutions, when mixed, would not
produce a detectable reaction? Why?
(d) Write a net ionic equation for each reaction produced
when the solutions are mixed in pairs.
(e) Which solution would have the:
i. highest boiling point? Explain.
ii. highest freezing point? Explain.
iii. lowest vapor pressure? Explain.
3.3 The empirical and molecular formulas of an unknown
compound are determined by combustion analysis and a
freezing point depression experiment.
(a) When a 0.8425 g sample of an unknown molecular
compound containing only carbon, hydrogen, and oxygen is combusted in excess oxygen, 1.8850 g of carbon
dioxide are produced and 0.8996 g of water is formed.
i. Calculate the mass in grams of oxygen required for
the combustion.
ii. Calculate the mass in grams of oxygen contained in
the sample of unknown compound.
iii. Determine the empirical formula for the unknown
compound.
(b) The unknown compound dissolves readily in chloroform, CHC13 . The freezing point of a solution prepared
by ~ixing 150.0 grams of CHC13 and 3.100 grams of the
unknown compound is -64.32 oc. The molal freezing. point depression constant of CHC13 is 4.68 oC/ molal
and its normal freezing point is -63.50 oc.
i. Calculate the molality of the unknown compound
in the chloroform solution.
ii. Calculate the molar mass of the unknown
compound.
iii. Determine the molecular formula of the unknown
compound.
iv. Write and balance an equation for the combustion
of the unknown compound.
3.4 Ethylene glycol, HOCH2CH20H, is a nonvolatile liquid
used as an antifreeze for automotive cooling systems. A solution is made by dissolving 250. grams of ethylene glycol
in 650. grams of water.
(a) Calculate the mass % of ethylene glycol in water.
(b) Calculate the molality of ethylene glycol in the
solution.
(c) Calculate the mole fraction of water in the solution.
(d) Calculate the theoretical freezing point of the solution.
The freezing point constant for water is 1.86 oc j m.
(e) Calculate the vapor pressure of the solution at 90 °C.
The vapor pressure of water at 90 oc is 525.8 torr.
(f) What quantity is needed to calculate the molarity of
ethylene glycol in the solution? Show how you would
do the calculation if you had this missing quantity.
(g) Explain how you would measure this missing quantity
in the laboratory.
3.5 Consider the following laboratory observations and answer the questions about them.
When solid ammonium chloride is added to liquid
water, the solid dissolves completely.
i. Distinguish between intramolecular forces of attraction and intermolecular forces of attraction.
Specify which give rise to chemical properties and
which are largely responsible for physical
properties.
ii. What are the forces of attraction in pure solid ammonium chloride?
iii. What are the forces of attraction in pure liquid
water?
iv. What intermolecular forces of attraction exist in an
aqueous solution of ammonium chloride that do
not exist in either pure ammonium chloride or pure
water?
(b) When an aqueous solution of silver nitrate is added to
an aqueous solution of ammonium chloride a white
precipitate forms.
i. Write and balance a net ionic equation to describe
the reaction.
ii. What forces of attraction exist within the white precipitate?
(c) When aqueous sodium hydroxide is added to the mixture in Part b, the white precipitate dissolves and the
heretofore odorless mixture now imparts a distinctive
odor.
i. Write and balance a net ionic equation to describe
the formation of the odiferous substance.
ii. Write and balance a net ionic equation to explain
the dissolution of the precipitate.
iii. Predict whether the odiferous substance is soluble
in water. Explain your prediction based on intermolecular forces of attraction.
(d) An aqueous solution of ammonium bromide is mixed
with a 3% aqueous solution of hydrogen peroxide. The
solution turns brown. The brown solution is then shaken with hexane and allowed to stand. Two distinct layers separate. The top layer is pink and the bottom layer
is colorless.
i. Predict the chemical formula of the brown substance.
ii. Identify the composition of the top layer and the
bottom layer. Explain why they do not dissolve in
each other.
iii. Discuss the intermolecular forces of attraction present in the top layer.
(a)
UNIT IV. KINETICS
AND EQUILIBRIUM
Multiple-Choice Questions
4.1 The half-life of mercury-203 is about 1.5 months. What
mass of a 64 gram sample of this isotope will remain after
nine months?
(a) 1 g
(b) 2 g
(c) 4 g
(d) 8 g
(e) 16 g
4.2 The rate constants for a forward reaction and its corresponding reverse reaction are generally expected to
APPENDIX F
be independent of temperature.
decrease with increasing temperature.
increase with increasing temperature.
increase with increasing temperature, only for the endothermic reaction.
(e) increase with increasing temperature, only for the
exothermic reaction.
(a)
(b)
(c)
(d)
4.3 The rate expression for a second-order reaction could be
(a) rate = k[A]
(b) rate = k[Af[B]
(c) rate = k[A][B]
(d) rate = k[Af[Bf
(e) rate = k[B]
4.4 The rate law of the reaction 2X + 2Y ~ 2XY is
rate = k[Xf[Y]. If [X] is doubled and [Y] is halved, the rate
of the reaction will
(a) increase by a factor of 4.
(b) remain the same.
(c) decrease by a factor of 4.
(d) increase by a factor of 2.
(e) decrease by a factor of 2.
4.5 What can be correctly said about the energy diagram for a
reversible endothermic reaction?
(a) The energy of activation is greater for the reverse reaction than for the forward reaction.
(b) The energy of activation is greater for the forward reaction than for the reverse reaction.
(c) The energy of activation is the same for the reaction in
both directions.
(d) The enthalpy of products is less than the enthalpy of
reactants.
(e) The forward reaction is faster than the reverse reaction.
4.6 An aqueous solution of sodium hydrogen carbonate has a
pH greater than 7 because:
(a) Sodium hydrogen carbonate donates a proton to water.
(b) Sodium hydrogen carbonate accepts a proton from
water.
(c) Hydrogen carbonate ion is acidic.
(d) Sodium ion is basic.
(e) Sodium ion accepts a proton from water.
4.7 Which species ionizes the least in water?
(a) HN03
(b) H2S04
(c) HC104
(d) HN02
(e) HBr
4.8 When one mole of sulfuric acid ionizes in water, the number of moles of ions present in solution is closest to which
value?
(a) 1
(b) 2
(c) 3
(d) 4
(e) 7
4.9 Which of these solutions can be used to prepare a buffer?
(a) HN03 and KOH
(b) HN03 and CH3COOH
(c) HN03 and NaCH3COO
(d) KOH and NH3
(e) KCl and NaCl
AP Exam Practice Problems
1125
4.10 The solubility of lead(II) carbonate is
(a) the same in water as it is in nitric acid.
(b) greater in water than it is in nitric acid.
(c) greater in water than it is in aqueous lead(II) nitrate.
(d) less in water than it is in aqueous sodium carbonate.
(e) the same in water as it is in aqueous sodium carbonate.
4.11 For the reaction, 2X(g) + Y(s) ~ X2Y(s), which factors
affect the value of the rate constant?
I. concentration
II. pressure
III. temperature
(a) I, II, and III
{b) I and II only
(c) II and III only
(d) I only
(e) III only
4.12 A certain reaction is believed to occur in the following steps:
1. A2 ~ 2A
2. A+ B ~ AB
3. A + AB ~ A2B slow
What is the most likely rate law?
(a) rate = k[A2][B]
(b) rate = k[Af[B]
(c) rate = k[A] 2
(d) rate = k[A] 112[B]
(e) rate = k[A2f[B]
4.13 Which is the strongest base in aqueous solution?
(a) HP042(b) H2P04(c) HC03(d)
co32-
<e> P0 43 4.14 A 0.1 M aqueous solution of which salt has the lowest pH?
(a) NH4Cl
(b) KCl
(c) CaCl2
(d) CuCl2
(e) AlCl3
4.15 If for the reaction 2A(g) ~ B(g), Kc = 4 at 25 °C, what is
KP at 25 oc for the following reaction? 1/2 B(g) ~ A (g )
(a) KP = 2(RT) 112
(b) KP = 4(RT) 112
(c) · KP = 2(RT) 2
(d) KP = 4(RT) 2
(e) Kp = 1/ 2(RT) 112
Free-Response Questions
4.1 Consider 3.00 liters of a saturated solution of calcium
hydroxide.
(a) The pH of the saturated solution is 12.370.
i. Write the chemical equation for the dissolution of
solid calcium hydroxide in water. Assume calcium
hydroxide dissociates completely.
ii. Calculate the concentration of hydroxide ion in a
saturated solution of calcium hydroxide.
iii. Calculate the solubility of calcium hydroxide in
water.
iv. Calculate the K sp of calcium hydroxide.
1126
(b)
APPENDIX F
AP Exam Practice Problems
The saturated solution is filtered to remove any solid
calcium hydroxide and separated into three 1.00 liter
parts.
i. The pH of one part is adjusted to 13.000. Calculate
the mass of the calcium hydroxide that will precipitate from this solution under these conditions.
ii. To a second 1.00 liter solution, 500 mL of 0.100 M
magnesium chloride is added. Write the balanced
equation for the dissolution of magnesium hydroxide, calculate the reaction quotient for the reaction
and predict whether a precipitate of magnesium
hydroxide will form. Explain your reasoning. The
Ksp of magnesium hydroxide is 1.8 X 10- 11 .
iii. To a third 1.00 liter saturated solution of calcium
hydroxide, 10.00 mL of 0.5000 M hydroazoic acid,
HN3, is added. Calculate the pH of the resulting solution. The Ka of hydroazoic acid is 1.9 X 10- 5 .
4.2 21.60 g of sodium benzoate, NaC 6H 5COO, is dissolved in
enough water to make 0.750 liters of solution. The Ka for
benzoic acid, C6H5COOH, is 6.3 X 10- 5 .
(a) Write a chemical equation for the reaction of benzoate
ion, C6H 5Coo- , and water.
(b) Calculate the percent ionization of benzoate ion.
(c) Calculate the pH of the sodium benzoate solution.
(d) Calculate the pH of a solution made by adding 6.100 g
of benzoic acid to 250.0 mL of the sodium benzoate solution. Assume no volume change.
(e) Calculate the pH of a solution made by adding 100.0 mL
of a 0.400 M solution of hydrochloric acid to 250.0 mL
of the original sodium benzoate solution. Assume volumes are additive.
(f) If an additional 25.0 mL of the hydrochloric acid solution is added to the solution produced in Parte, calculate the pH of the final solution.
4.3 Gaseous ammonia is produced in an exothermic reaction
when hydrogen gas and nitrogen gas are combined under
the right conditions.
3 H 2(g)
+ N2(g)
~ 2
NH3(g) ~ 3/ 2 H2(g) + 1/ 2 N2(g)
At another temperature, 1.700 g of ammonia is placed
in a 2.00 L flask and allowed to come to equilibrium.
At equilibrium, there are 0.120 grams of hydrogen gas
present in the mixture.
i. Calculate number of grams of nitrogen at
equilibrium.
ii. Calculate the equilibrium constant, K 0 for the
reaction:
2 NH3(g) ~ 3 H2(g)
4.4 Write balanced net ionic equations for each of the following
laboratory situations. Then answer the questions. Assume
a reaction occurs in each case.
(a) Two moles of a sodium hydroxide solution are added
to a solution containing one mole of phosphoric acid.
i. Can the mixture of products act as a buffer solution? Explain.
ii. Write three separate equations showing the successive ionization of phosphoric acid. In each equation, identify the conjugate acid-base pairs.
(b) Sodium fluoride is added to water.
i. Predict the pH of this solution relative to water.
ii. Suggest a substance that when added to the resulting mixture will produce a buffer solution.
(c) An aqueous solution of sodium hydroxide solution is
added to solid ammonium chloride.
OH- (aq)
+ NH4Cl(s)
~
H 20(l) + NH3(aq) + Cl- (aq)
i. Can the resulting solution act as buffer? Explain.
ii. One product of the reaction is exposed to hydrogen
chloride gas. Write and balance an equation for the
resulting reaction.
4.5 Use chemical principles to explain the following:
(a) The rates of chemical reactions generally increase with
an increase in temperature.
(b) Increasing concentrations of reactants increase reaction
rate.
(c) The orders of reactants in a rate equation cannot be obtained from the coefficients in the balanced overall
equation for a reaction.
(d) Upon mixing reactants, often no observable reaction is
observed until something is done to initiate the reaction. Cite a common example.
(e) Addition of a catalyst speeds up a chemical reaction.
NH3(g)
At 500 oc, KP for the reaction is 1.45 X 10- 5 .
(a) Calculate Kc for the reaction at 500 °C.
(b) If the temperature is decreased for the reaction, predict
whether the value of Kp will increase, decrease, or stay
the same. Explain your answer.
(c) Calculate KP for the following reaction at 500 °C:
(d)
hydrogen gas increase, decrease, or stay the same?
Explain your answer.
+ N2(g)
iii. Is the temperature of this equilibrium mixture
greater or less than 500 °C? Explain your answer.
iv. If the temperature of this equilibrium mixture were
returned to 500 oc, would the number of moles of
UNIT V. THERMODYNAMICS,
ELECTROCHEMISTRY,
NUCLEAR AND
ORGANIC CHEMISTRY
Multiple-Choice Questions
5.1 What is a product formed at the anode of the electrolysis of
an aqueous sodium sulfate solution?
(a) H2(g)
(b) 02(g)
(c) Na(s)
(d) S(s)
(e) S02(g)
5.2 What is a product formed at the cathode of the electrolysis
of an aqueous copper nitrate solution?
(a) H2(g)
(b) 0 2(g)
(c) Cu(s)
(d) N2(g)
(e) NO(g)
APPENDIX F
5.3 Carbon monoxide reacts with oxygen according to the following thermodynamic equation at 25 oc and 1 atmosphere pressure:
2 CO(g) + 0 2 (g)
~
2C0 2 (g)
L'lH = - 566 kJ
Which statement(s) is (are) true?
I. The reaction is endothermic
II. The heat of combustion of gaseous carbon monoxide is
-283 kJ/ mol.
III. The heat of standard formation of C02(g) is - 283 kJ/ mol.
(a) 1 only
(b) 2 only
(c) 3 only
(d) 2 and 3 only
(e) 1 and 2 only
5.4 Assume one mole of each of the following chemical
species. Which has the greatest absolute entropy under the
same conditions of temperature and pressure?
(a) I(g)
(b) 12 (g)
(c) lz(s)
(d) 1- (aq)
(e) Fz(g)
5.5 The specific heats of three unknown substances vary in the
following order: X > Y > Z. A 1.0 gram sample of substance X at 100 oc is added to 100 g of water at 20 oc and
the temperature change is recorded. The procedure is repeated with substance Y and then with substance Z. How
will the final temperatures of the water compare?
(a) X= Y = Z
(b) X > Y > Z
(c) Z > Y > X
(d) Y > Z > X
(e) Y > X > Z
5.6 Which change will increase the voltage of an electrochemical cell based on this reaction:
(a)
(b)
(c)
(d)
(e)
Fe(s) + Cl2(g) ~ Fe 2+(aq) + 2 Cl- (aq)
Increase the mass of Fe.
Increase the Rartial pressure of Cl2(g).
Increase [Fe +].
Increase [Cl- ].
All of the above changes will decrease the voltage.
5.7 Which two half reactions, when suitably coupled, will
make a voltaic cell that will produce the largest initial
voltage?
I. Fe 2+(aq) + 2 e- ~ Fe(s) Eo = - 0.440 volts
II. Cu2+(aq) + 2 e- ~ Cu(s) Eo = +0.337 volts
III. Fe 3+(aq) + 3 e- ~ Fe(s) Eo = - 1.660 volts
IV. Ag+(aq) + 1 e- ~ Ag(s) Eo = +0.799 volts
(a) I and II
(b) II and III
(c) I and III
(d) II and IV
(e) III and IV
5.8 At 25 oc, which change occurs with the largest increase in
entropy?
(a) H 20(Z) ~ H20(g)
(b) H20(s) ~ H 20(g)
(c) H20(Z) ~ HCl(g) ~ H 30 +(aq) + Cl- (aq)
(d) H 20(l) + 1/ 2 0 2(g) ~ H20 2(l)
(e) H 20(l) + NH3(g) ~ NH 4+(aq) + OH- (aq)
AP Exam Practice Problems
1127
5.9 What is the correct order when the following substances
are placed in increasing order of oxidation number for
sulfur?
(a) H2S < S < Na2S203 < KHS03 < Al2(S04h
(b) Al2(S04h < KHS03 < NazS203 < S < H zS
(c) S < H2S < KHS03 < NazS203 < Al2(S04h
(d) Al2(S04h < KHS03 < NazS203 < H2S < S
(e) H 2S < S < KHS03 < Na2S203 < Al2(S04h
5.10 The bond dissociation energy for N=N is 940 kJ/ mol.
What is the standard heat formation of the gaseous nitrogen molecule in kJ/ mol?
(a) +940
(b) - 940
(c) - 1880
(d) - 470
(e) 0
5.11 Which of these compounds have cis and trans isomers?
I. 1-pentene
II. 2-pentene
Ill. 2-methyl-2-pentene
(a) II only
(b) II and III only
(c) I and II only
(d) I and III only
(e) I, II, and III
5.12 Which set of reactants produces a gaseous product?
I. Cu + H 2S04
II. Cu + HN03
Ill. Cu + HCl
(a) I only
(b) II only
(c) I and II only
(d) I and III only
(e) I, II, and III
5.13 How many isomers exist for C6H14?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6
5.14 Which change will generally produce an increase in the en-
tropy of a system?
(a) decreasing the temperature
(b) formation of a precipitate from solution
(c) decreasing the volume
(d) sublimation
(e) condensation
5.15 What are the signs of tlH, tlG, and L'lS for the freezing of
liquid water at - 5 °C?
(a)
tlH
tlG
tlS
+
+
+
(b)
(c)
(d)
(e)
+
+
-
+
1128
AP Exam Practice Problems
APPENDIX F
FREE-RESPONSE QUESTIONS
5.1 The half-cell reactions for rechargeable nickel-cadmium
(nicad) batteries are:
Cd(OHh(s) + 2 e-
~
Cd(s) + 2 OH- (aq)
E0 = -0.809
NiOOH(s) + H 20(l) + e-
~
Ni(OHh(s) + OH- (aq)
E0
(a)
(b)
(c)
(d)
(e)
(f)
=
+0.490
Write a balanced equation for the overall process.
Identify the half-reaction that occurs at the cathode.
Calculate the cell potential.
If a nicad battery produces a current of 40.0 milliamps
for 5.00 hours, how many electrons are transferred?
How many grams of cadmium will be oxidized or reduced (specify which) under the conditions of Part d?
As the cell discharges, will the pH of each compartment increase, decrease, or stay the same? Explain.
5.2 Consider the reaction: C0 2(g)
+
2 HCl(g) ~ Cl 2CO(g)
+ H 20(g)
Draw the Lewis structure for each reactant and each
product.
(b) Using the table of bond enthalpies below, calculate .clH
for the reaction. Be sure to include units.
(a)
C-0
Bond
Bond
enthalpy
(kJ/ mol)
351
C=O C==O C-Cl H-Cl H-0
715
1073
331
Calculate the equilibrium constant, Keq, for the reaction
at 25 oc.
(f) At what temperature will the reaction come to
equilibrium?
(g) If the tetrachloroethane produced in this reaction
formed as a liquid rather than as a gas, would .clHrxn
change and if so, how would it change? Explain your
answer.
(e)
431
5.4 Write balanced net ionic equations for each of the following
laboratory situations. Then answer the questions. Assume
a reaction occurs in each case.
(a) Electricity is applied to an aqueous solution of sodium
sulfate.
H20(l) ~ H 2(g) + 1/ 2 02(g)
i. Write the half reactions that occur at the cathode
and anode. Specify at which electrode each half reaction occurs.
ii. In the presence of an acid-base indicator, specify
two observations you would make at each
electrode.
(b) An acidic solution of potassium dichromate is added to
a solution of hydrogen peroxide.
i. Identify the oxidizing agent and the reducing agent
in this reaction.
ii. Describe any color change you would observe.
(c) A copper half cell is suitably connected to a silver half
cell.
2 Ag +(aq) + Cu(s) ~ 2 Ag(s) + Cu2+(aq)
i.
Which electrode acts as the cathode and which acts
as the anode? In which direction do the electrons
flow?
ii. If a gold half cell replaced the copper half cell,
would the electrons flow in the same direction?
Explain?
464
(c) Is the reaction exothermic or endothermic? Explain.
Predict the sign of ilS for the reaction. Explain your
reasoning.
(e) Will the reaction be more spontaneous at high temperatures or at low temperatures? Explain.
(f) Given the standard heats of formation of the following
molecules, calculate the heat of formation of Cl2CO(g).
ilH'J of C0 2(g) = -393.5 kJ/ mol
(d)
ilH'J of HCl(g) = -92.30 kJ/ mol
ilH'J of H 20(g) = -241.8 kJ/ mol
5.3 Consider the reaction of gaseous ethyne, C2H 2(g), with
chlorine to produce tetrachloroethane, C 2H 2Cl4(g). Thermodynamic data at 25 oc for the reaction are:
tlH 0 = -405 KJ
tl5° = - 349 JK - 1
5.5 In separate experiments, five grams each of three salts are
dissolved in water and the temperature change of the
water is recorded. The results are summarized in the table.
Salt
sodium chloride
calcium chloride
ammonium chloride
(a)
Some thermodynamic data for selected reactants and products are:
(b)
Substance
AHJ(kJ mol- 1)
so (J mol- 1 K- 1)
C2H2(g)
Cl2(g)
C2H2Cl4(g)
227
201
(c)
+298
(d)
0
Write a balanced equation for the reaction assuming all
the reactants and products are gaseous.
(b) Calculate ilH'J for C2H2Cl4(g).
(c) Calculate sofor Cl2(g).
(d) Calculate .clGo for the reaction at 25 oc.
(a)
(e)
(f)
Initial H2 0 temp
Final H2 0 temp
22 oc
21 oc
45 oc
22 oc
10 oc
23 oc
Give the sign of ilH for the dissolving of calcium chloride and for the dissolving of ammonium chloride and
state whether each dissolves exothermically or
endothermic ally.
Give the sign of .clS for the dissolving of calcium chloride and ammonium chloride and state whether each
dissolves with an increase or decrease in entropy.
Give the sign of .clG for the dissolving of each of the
three salts. Explain your answers.
State what effect an increase in temperature will have
on the solubility of ammonium chloride. Explain using
thermodynamic principles.
For which salt is the relative magnitude of the lattice
energy significantly greater than the relative energy of
the hydration energy? Explain your reasoning.
What are the principle driving influences for the dissolution of each of the three salts?
lications and Essavs
I Strate ies in Chemistr
Estimating Answers 26
The Importance of Practice 28
Pattern Recognition 58
Problem Solving 89
How to Take a Test 106
Analyzing Chemical Reactions 143
Using Enthalpy as a Guide 180
Calculations Involving Many Variables 404
What Now? 1094
I Chemistr and Li e
The Battle for Iron in Living Systems 1024
Polycyclic Aromatic Hydrocarbons 1070
The Origins of Chirality in Living Systems 1085
~ Chemistr
Put to W'llrk
Chemistry and the Chemical Industry 4
Chemistry in the News 18
Antacids 135
The Hybrid Car 196
Explosives and Alfred Nobel 328
Orbitals and Energy 380
Gas Pipelines 409
Gas Separations 420
Supercritical Fluid Extraction 453
Cell Phone Tower Range 498
Recycling Plastics 501
Toward the Plastic Car 506
Liquid Crystal Displays 513
Methyl Bromide in the Atmosphere 590
Catalytic Converters 608
The Haber Process 631
Controlling Nitric Oxide Emissions 656
Amines and Amine Hydrochlorides 694
Direct Methanol Fuel Cells 874
Environmental Applications of Radioisotopes 921
Carbon Fibers and Composites 962
Gasoline 1061
Portrait of an Organic Chemical 1076
Elements Required by Living Organisms 57
Glucose Monitoring 102
Drinking Too Much Water Can Kill You 147
The Regulation of Human Body Temperature 185
Nuclear Spin and Magnetic Resonance Imaging 236
Ionic Size Makes a Big Difference 265
The Improbable Development of Lithium Drugs 280
The Chemistry ofVision 36 7
Blood Pressure 398
Fat- and Water-Soluble Vitamins 538
Blood Gases and Deep-Sea Diving 540
Sickle-Cell Anemia 559
Nitrogen Fixation and Nitrogenase 610
The Amphiprotic Behavior of Amino Acids 703
Blood as a Buffered Solution 729
Sinkholes 744
Tooth Decay and Fluoridation 74 7
Entropy and Life 815
Driving Nonspontaneous Reactions 830
Heartbeats and Electrocardiography 868
Medical Applications of Radiotracers 910
Radiation Therapy 922
How Much Perchlorate Is Too Much? 944
Nitroglycerin and Heart Disease 956
The Mass Spectrometer 48
Glenn Seaborg and Seaborgium 51
The Aura of Gold 143
Arsenic in Drinking Water 960
Energy, Enthalpy, and P- V Work 176
The Scientific Method 13
Basic Forces 45
1129
1130
CHEMICAL APPLICATIONS AND ESSAYS
The Speed of Light 214
Measurement and the Uncertainty Principle 225
Probability Density and Radial Probability Functions 230
Experimental Evidence for Electron Spin 234
Effective Nuclear Charge 260
Calculation of Lattice Energies: The Born-Haber Cycle 304
Oxidation Numbers, Formal Charges, and Actual Partial
Charges 318
Phases in Atomic and Molecular Orbitals 3 73
The Ideal-Gas Equation 416
The Clausius-Clapeyron Equation 456
X-Ray Diffraction by Crystals 465
The Third Form of Carbon 468
The Transistor 490
Hydrates 533
Ideal Solutions with Two or More Volatile Components 548
Colligative Properties of Electrolyte Solutions 554
Using Spectroscopic Methods to Measure Reaction
Rates 580
Limitations of Solubility Products 741
Other Greenhouse Gases 782
Water Softening 788
The Entropy Change when a Gas Expands
Isothermally 808
Entropy and Probability 812
What's "Free" About Free Energy? 822
The Dawning of the Nuclear Age 915
The Hydrogen Economy 937
Charles M. Hall 990
Shape-Memory Alloys 998
Entropy and the Chelate Effect 1021
Charge-Transfer Color 1040