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CHM 1045 - General Chemistry 1 (U05)
Fall 2013
Dr. Jeff Joens
Classroom: CP 145
Time: M, W, F 2:00pm to 3:15pm
Office: CP 331 phone 348-3121
email: [email protected]
web page: www.joenschem.com
Homework Problems
Chapter 1 Homework Problems: 6, 10, 12, 13, 18, 24, 26, 30, 36, 43,
44, 48, 50, 54, 58, 64, 74, 78, 86, 110
Note: Homework is not to be turned in. My solutions to the homework
problems are available at my website (www.joenschem.com). Answers
(but not detailed solutions) to the odd numbered end of chapter
problems are given at the end of the book.
Math Review
Appendix 1 of the textbook reviews several math concepts that you
need to be familiar with, including the following:
Scientific notation - Writing numbers in scientific notation,
converting to and from scientific notation, mathematical operations in
scientific notation.
Trigonometry - Basic relationships.
Logarithms and exponents - Use of base 10 and natural
logarithms, conversions involving logarithms.
Quadratic formula - Use in calculations.
CHAPTER 1
The Study of Chemistry
Basic Definitions
Chemistry - The study of the properties and transformation of
matter.
Matter - Possesses mass and occupies space.
Mass - A measure of the quantity of matter possessed by an
object. Measured in comparison to the standard kilogram.
Basic Definitions
Energy - The capacity to do work or provide heat.
Kinetic energy - Energy due to the motion of an object
EK = 1/2 (mv2)
Potential energy - Energy due to the position or composition of
an object (gravitational, electrical, chemical, nuclear…)
Conservation laws
Conservation of mass
Conservation of energy
States of Matter
There are three common states (phases) of matter.
Solid - State where the particles making up a substance occupy a
fixed volume and have fixed locations (do not move about).
There are two general types of solids:
Crystalline solid - Particles making up the solid have a regular
repeating arrangement (crystal structure)
Amorphous solid - Particles making up the solid do not have a regular
arrangement.
Liquid - State where the particles making up a substance occupy
a fixed volume but can freely move about within that volume.
Gas - State where the particles making up a substance occupy the
entire volume of their container and can freely move about within that
volume. The volume occupied by a gas strongly depends on the applied
pressure.
Solids and liquids are called condensed phases, and have little
unoccupied space. Gases, in contrast, consist of particles that are
generally far apart from one another. Liquids and gases, because they
can change their shape, are classified as fluids.
State of matter
Volume
Shape
solid
fixed volume
fixed shape
liquid
fixed volume
fluid shape
gas
volume depends
on pressure
fluid shape
ice
liquid water
water vapor
Types of Substances
Pure substance - A substance with fixed composition and
properties (both physical and chemical properties). For example,
methane is a pure substance that is 75% carbon and 25% hydrogen by
mass, that is a gas at room temperature, and which can react with oxygen
to form carbon dioxide and water.
Mixture - A combination of two or more pure substances that
have not chemically reacted. The composition of a mixture can be
continuously varied over a range of values.
Heterogeneous - Composition differs from place to place within
the mixture.
Homogeneous (solution) - Composition is the same throughout
the mixture.
Examples of Mixtures
A mixture of iron and sulfur (heterogeneous).
Mix
A solution of sugar dissolved in water.
(homogeneous)
A mixture of solid salt and sugar crystals (heterogeneous)
Air, a mixture of nitrogen (78%), oxygen (21%), argon (0.9%) and a
large number of additional trace gases (homogeneous).
Elements and Compounds
Element - A pure substance that cannot be decomposed into more
simple substances by chemical means.
Compound - A pure substance that can be decomposed into two
or more simple substances.
Copper (II) sulfate
pentahydrate
copper (II) sulfate
copper, sulfur, oxygen
water
hydrogen, oxygen
Atoms and Molecules
An atom is the smallest particle making up an element. When
two or more atoms combine they form a molecule. Molecules are the
smallest particles making up most pure chemical substances (exceptions
include ionic compounds such as sodium chloride).
Scientific Notation
Scientific notation is a convenient method for expressing very
large or very small numbers. (see Appendix I for a review of scientific
notation and other basic mathematical concepts)
Form: (mantissa) x 10power
mantissa - a number between 1 and 10
10power - a power of 10, related to the number of places the
decimal point must be shifted to the left (positive exponent) or right
(negative exponent)
Examples:
4135. = 4.135 x 103
0.00048 = 4.8 x 10-4
0.000000000074 m = 7.4 x 10-11 m (bond length in H2)
SI (Systeme Internationale) Units
SI units are the standard system of units used in science. Units are
divided into two type
Base (Fundamental) units (7 total)
length
meter
m
mass
kilogram
kg
time
second
s
electrical current
ampere
A
temperature
Kelvin
K
amount of substance mole
mol
light intensity
cd
candala
These units are sometimes called MKS (meter/kilogram/seconds) units
Derived units - Formed from combinations of one or more
fundamental units.
Examples:
Area = (length) . (width) = m2
Volume = (length) . (width) . (height) = m3
Density = mass/volume = kg/m3
Velocity = distance/time = m/s
Energy = Joule = kgm2/s2
In principle all physical quantities can be expressed in SI base
(fundamental) or derived units. In practice, other units (metric and nonmetric) are often used.
Metric System
In science, the units used to express values for physical properties
are usually metric units. In a metric system different units for the same
property are related in a regular manner.
Metric unit = (prefix) + (base unit)
prefix
factor
giga
1,000,000,000 or 109
mega
1,000,000 or 106
kilo
1,000 or 103
deci
0.1 or 10-1
centi
0.01 or 10-2
milli
0.001 or 10-3
micro
0.000001 or 10-6
nano
0.000000001 or 10-9
pico
0.000000000001 or 10-12
symbol
G
M
k
d
c
m

n
p
Metric System (Example)
The base unit for length is the meter (m).
So:
1 gigameter (Gm) = 1000000000 m = 109 m
1 megameter (Mm) = 1000000 m = 106 m
1 kilometer (km) = 1000 m = 103 m
1 decimeter (dm) = 0.1 m = 10-1 m
1 centimeter (cm) = 0.01 m = 10-2 m
1 millimeter (mm) 0.001 m = 10-3 m
1 micrometer (m) = 0.000001 m = 10-6 m
1 nanometer (nm) = 0.000000001 m = 10-9 m
1 picometer (pm) = 0.000000000001 m = 10-12 m
One can interconvert between any two metric units for the same
property simply by an appropriate change in the power of 10.
Volume
m3 (cubic meters; derived SI unit)
L (liters) volume occupied by a cube with 10 cm sides
cm3 (cubic centimeters) volume occupied by a cube with 1 cm
sides)
Conversions
1. m3 = 1000. L (exact)
1. L = 1000. mL (exact)
1. L = 1000. cm3 (exact)
1. mL = 1. cm3 (exact)
1. m3 = 106 cm3 (exact)
Temperature Scales
Centigrade (Celsius) 0 C (normal freezing point of water)
100 °C (normal boiling point of water)
Fahrenheit
32 F (normal freezing point of water)
212 F (normal boiling point of water)
Kelvin (SI unit)
0 K (absolute zero - lowest possible temperature)
273.15 K (normal freezing point of water)
373.15 K (normal boiling point of water)
Relationships Among Temperature Scales
Conversions
T(K) = T(C) + 273.15
T(°C) = T(K) - 273.15
T(°F) = 9/5 T(°C) + 32
T(°C) = 5/9 [ T(°F) - 32 ]
Example
The highest and lowest official recorded temperatures (1895 present) for Miami are:
high temperature
low temperature
100. °F (July 21, 1942)
27. °F (February 3, 1917)
Express these temperatures in °C.
Example
The highest and lowest official recorded temperatures (1895 present) for Miami are:
high temperature
low temperature
100. °F (July 21, 1942)
27. °F (February 3, 1917)
Express these temperatures in °C.
T(°C) = 5/9 [ T(°F) - 32 ]
So
high
T(°C) = 5/9 [ 100 - 32 ] = 37.8 °C (38. °C)
low
T(°C) = 5/9 [ 27 - 32 ] = - 2.8 °C (- 3. °C)
Chemical and Physical Property
Chemical property - A property involving the chemical transformation
of a substance.
Physical property - A property that does not involve the chemical
transformation of a substance
Examples:
The normal boiling point of benzene is 80.1  C (physical)
Carbon can react with oxygen to form carbon dioxide (chemical)
The density of liquid water is 1.00 g/mL (physical)
Iron metal rusts in the presence of oxygen and water (chemical)
Intensive and Extensive Property
Properties can often be divided into two categories
Extensive property - Value depends on the size of the system
Intensive property - Value does not depend on the size of the system
Extensive -
mass
volume
Intensive -
temperature
density (mass/volume)
Precision and Accuracy
Precision is a measure of how close successive independent
measurements of the same quantity are to one another.
Accuracy is a measure of how close a particular measurement (or
the average of several measurements) is to the true value of the measured
quantity.
Good precision; poor accuracy
Good precision, good accuracy
Significant Figures
The total number of digits in a number that provide information
about the value of a quantity is called the number of significant figures.
It is assumed that all but the rightmost digit are exact, and that there is
an uncertainty of ± a few in the last digit.
Example: The mass of a metal cylinder is measured and found to
be 42.816 g. This is interpreted as follows
42.816
error is ± 1 or 2
considered as certain
42.81623
Number of significant figures is 5
Result known to a higher degree of precision
Examples
Level of liquid = 4.58 mL
Temperature = 103.4 oC
Rules For Counting Significant Figures
1) All nonzero digits are significant
(28.548 = 5 sig figs; 189. = 3 sig figs))
2) All zeros located between nonzero digits are significant
(302.8 = 4 sig figs; 21.033 = 5 sig figs)
3) Zeros to the left of the first nonzero digit are not significant
(0.004108 = 4 sig figs; 0.075 = 2 sig figs)
4) Zeros to the right of the last nonzero digit are significant if the
number contains a decimal point
(3.80 = 3 sig figs; 18000. = 5 sig figs)
5) Zeros to the right of the last nonzero digit in a number without
a decimal point may or may not be significant
(6700 = 2, 3, or 4 sig figs, as zeros might be placeholders)
Note that exact numbers have an infinite number of significant
figures. Example: 1 dozen = 12 (exact)
Counting Significant Figures (Examples)
3.108
0.00175
7214.0
4000.
34000
Counting Significant Figures (Examples)
3.108
4 significant figures
0.00175
3 significant figures (zeros are placeholders)
7214.0
5 significant figures
4000.
4 significant figures
34000
2, 3, 4, or 5 significant figures
(some or all zeros may be placeholders)
We can always make clear how many significant figures are
present in a number by writing the number in scientific notation.
3.4 x 104
2 significant figure
3.40 x 104
3 significant figures
Significant Figures in Calculations
There are two general cases.
Multiplication and/or division - The number of significant figures
in the result is equal to the smallest number of significant figures present
in the numbers used in the calculation.
Example. For a particular sample of a solid, the mass of the solid
is 34.1764 g and the volume of the solid is 8.7 cm3. What is the value for
D, the density of the solid?
D = mass = 34.1764 g = 3.9283218 g/cm3 = 3.9 g/cm3
volume
8.7 cm3
Addition and/or subtraction. The result carries the same number
of decimal places as the quantity in the calculation with the fewest
decimal places.
Example. The masses for three rocks are 24.18 g, 2.7684 g, and
91.8 g. What is the combined mass of the rocks?
24.18
g
2.7684 g
91.8
g
118.7484 g = 118.7 g
Additional Cases
1) For calculations involving both addition/subtraction and multiplication/division the rules for significant figures are applied one at a
time, rounding off to the correct number of significant figures at the end
of the calculation.
Example.
(46.38 - 39.981) =
13.821
6.399 = 0.4629911 = 0.463
13.821
If we had stopped the above calculation after subtracting the two
numbers in parentheses we would have rounded the result to 6.40. While
you should keep track of significant figures as you do calculations it is a
good idea not to round off until you get to the final answer, to avoid
roundoff error.
2) Significant figures for other kinds of mathematical operations
(logarithm, exponential, etc.) will be discussed when appropriate.
Rounding Numbers
In the above calculations we had to round off the results to the
correct number of significant figures. The general procedure for doing
so is as follows:
1) If the first digit dropped is 4 or less, round down.
2) If the first digit dropped is 5 or more, round up.
Examples: Correctly round each of the following numbers as indicated.
3.4682
to 3 sig figs
18.4513
to 4 sig figs
1.4500
to 2 sig figs
6.3499
to 2 sig figs
Examples: Correctly round each of the following numbers as indicated.
3.4682
to 3 sig figs
3.47
18.4513
to 4 sig figs
18.45
1.4500
to 2 sig figs
1.5
6.3499
to 2 sig figs
6.3
Conversion Factors and Dimensional Analysis
A conversion factor converts a number from one set of units to
another set of units.
Dimensional analysis is the process used to check that the correct
final units are obtained in a calculation.
Example: Based on our metric relationships we know
1000. mL = 1. L
We can find two conversion factors from this relationship
1000. mL = 1. L
Divide by 1. L
1000. mL = 1. L = 1
1. L
1. L
Divide by 1000. mL
1. L = 1000. mL = 1
1000. mL 1000. mL
Since multiplying a number by 1 does not change the value of
that number, multiplying by 1000. mL/1. L or 1. L/1000. mL also does
not change the value of the number, only the units in which the value is
expressed.
For example, to convert 46.8 mL to L
# L = 46.8 mL
1L
= 0.0468 L = 4.68 x 10-2 L
1000. mL
We can also use relationships to convert between units that apply
to different types of quantities (mass and volume, for example).
Example. The density of silver iodide is 5.69 g/cm3. the mass of
a pure sample of silver iodide is 48.316 g. What is the volume occupied
by this sample?
V = 48.316 g 1. cm3 = 8.49 cm3
5.69 g
Notice in this case we used our conversion factor to go from one
type of quantity (mass) to a different type of quantity (volume).
Dimensional Analysis
Dimensional analysis is the process used to make sure the dimensions that appear in the result of a calculation are correct.
Example: How many inches are there in 75.8 cm?
Since 1 in = 2.54 cm, there are two conversion factors we can
construct.
1. in
2.54 cm = 1
2.54 cm
1. in
So
# in = 75.8 cm 1. in = 29.8425… = 29.8 in
2.54 cm
# in = 75.8 cm 2.54 cm = 192.532 = 193. cm2/in ?!?
1. in
Conversion Factors (Example)
The Washington Monument is 555.4 feet high. What is the height
of the monument in meters?
height(m) = 555.4 ft 12 in 2.54 cm 1 m = 169.28592 m = 169.3 m
1 ft
1 in
100 cm
(note all conversion factors are exact)
height(m) = 555.4 ft 12 in 2.54 cm 1 m  m
1 ft 1 in
100 cm
Practice Problems
1) The normal boiling point for nitrogen (N2) is - 195.8 °C. Express this
temperature in °F and K.
2) The density of liquid mercury (Hg) is 13.594 g/cm3. Give the density
in the appropriate SI units.
3) What is the conversion factor between in3 (cubic inches) and cm3
(cubic centimeters)?
1) The normal boiling point for nitrogen (N2) is - 195.8 °C. Express this
temperature in °F and K.
We use the equations for converting between temperature scales.
T(K) = T(C) + 273.15
= (- 195.8) + 273.15 = 77.35 = 77.4 K
T(°F) = 9/5 T(°C) + 32
= 9/5 (- 195.8) + 32 = - 320.44 = - 320.4 °F
2) The density of liquid mercury (Hg) is 13. 594 g/cm3. Give the density
in the appropriate SI units.
The SI unit for density (a derived unit) is kg/m3. Therefore
D = 13.594 g
cm3
1 kg 100 cm 100 cm 100 cm = 13594. kg/m3
1000 g 1 m
1m
1m
= 1.3594 x 104 kg/m3
3) What is the conversion factor between in3 (cubic inches) and cm3
(cubic centimeters)?
# cm3 = 1 in3 2.54 cm 2.54 cm 2.54 cm = 16.387064 cm3
1 in
1 in
1 in
Note that the above is an exact conversion factor, since the
relationship
1 in = 2.54 cm
is exact.
End of Chapter 1
Chemistry. From the word alchemy, from Old French alkemie,
from Middle Latin alkimia, from Arabic al-kimiya, from Greek khemeioa
(found about 300 AD in a decree of Diocletian against "the old writings
of the Egyptians"), all meaning "alchemy." Perhaps from an old name for
Egypt (Khemia, literally "land of black earth," found in Plutarch), or
from Greek khymatos "that which is poured out," from khein "to pour,"
related to khymos "juice, sap." The word seems to have elements of both
origins. - from The Online Etymology Dictionary
“A tidy laboratory means a lazy chemist.” - Jöns Jacob Berzelius
“Research is what I'm doing when I don't know what I'm doing.”
- Wernher Von Braun