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Module 1: Basic Concepts Matter, Mathematical Manipulation, Dimensional Analysis, Density, Specific

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Title: Module 1: Basic Concepts Matter, Mathematical Manipulation, Dimensional Analysis, Density, Specific


1
Module 1 Basic Concepts Matter, Mathematical
Manipulation, Dimensional Analysis, Density,
Specific Gravity, Temperature, and Heat Transfer
  • By Alyssa Jean-Mary
  • Source Modular Study Guide for First Semester
    Chemistry by Anthony J. Papaps and Marta E.
    Goicoechea-Pappas

2
Basic Ideas What is Chemistry?
  • Chemistry is the science that studies the
    composition, characterization, and transformation
    of matter
  • It started out as alchemy.

3
Basic Ideas What is the Scientific Method?
  • The Scientific Method is a systematic approach to
    research that involves collecting and analyzing
    data.
  • The first step is to formulate a problem.
  • The second step is to make observations and
    conduct experiments on that problem.
  • The third step is to interpret the observations
    and experiments from the second step.
  • Here, a hypothesis is first formed. A hypothesis
    is a tentative explanation for a set of
    observations that is made after the collection of
    enough information.
  • After the formation of a hypothesis, a more
    definite explanation is developed a law or a
    theory is made. A law is a concise verbal or
    mathematical statement of a relationship between
    phenomena that is always the same under the same
    conditions that is made after the collection of a
    large amount of information. A theory is a step
    further than a law. It is a unifying principle
    that explains a body of facts and those laws that
    are based on them.
  • The fourth step is testing the interpretation,
    making sure additional observations and
    experiments support the interpretation made is
    the thrid step.

4
Basic Ideas What is Matter and how is it
classified?
5
Basic Ideas States of Matter
  • The physical state that a sample of matter exists
    in depends on the temperature
  • There are three physical states of matter
  • Solid
  • Solids have a definite shape and volume, a high
    density, and are virtually incompressible.
  • Liquid
  • Liquids have a definite volume, but assume the
    shape of the container they are in. They also
    have a high density like solids, but are slightly
    compressible unlike solids.
  • Gas
  • Gases assume the volume and shape of the
    container they are in (i.e. no definite volume or
    shape), have a low density unlike solids and
    liquids, and are very compressible.
  • Solids have stronger forces of attraction and are
    more ordered than liquids, and liquids, in turn,
    have stronger forces of attraction and are more
    ordered than gases.

6
Basic Ideas Conversion between States of Matter
  • Matter can convert between the three physical
    states by changes in temperature and pressure
  • Gas to Liquid cool or increase pressure
    Condensation
  • Gas to Solid cool Deposition
  • Liquid to Gas heat or decrease pressure
    Vaporization (Evaporation) (Boiling)
  • Liquid to Solid cool Freezing
    (Solidification) (Crystallization)
  • Solid to Gas heat Sublimation
  • Solid to Liquid heat Melting (Fusion)

7
Basic Ideas Common Elements to Know
8
Basic Ideas Types of Solutions (i.e. -
Homogeneous Mixtures)
  • Every solution has two components a solute and a
    solvent.
  • The solute(s) are the component(s) that are
    present in the lesser amount.
  • The solvent is the component that is present in
    the greatest amount.
  • Liquid solutions are the most common, but there
    are also gas solutions and solid solutions. For
    example, an alloy is a solid solution. It is a
    homogeneous mixture of metals.

9
Basic Ideas Characteristics of Solutions
  • Solutions
  • have uniform distribution.
  • have components that do not separate upon
    standing.
  • have components that cannot be separated by
    filtration.
  • only vary their compositions within certain
    limits.
  • are almost always transparent (i.e. you cannot
    see through it).

10
Basic Ideas Energy
  • Energy is the capacity to do work or transfer
    heat. Two forms of energy are potential energy
    (PE) and kinetic energy (KE).
  • Potential energy is the energy an object
    possesses because of its position or composition.
    This is the kind of energy that is found in
    chemicals. For example, natural gas and gasoline
    contain PE.
  • Kinetic energy is the energy of motion.

11
Basic Ideas Properties and Changes
  • Properties
  • A physical property is a property that can be
    observed in the absence of any change in
    composition. Some examples are color, odor,
    taste, melting point, boiling point, freezing
    point, density, length, and specific heat.
  • A chemical property is a property that matter
    exhibits as it undergoes changes in composition.
    Some examples are that coal and gasoline burn in
    air to form carbon dioxide and water, iron reacts
    with oxygen in the air to form rust, and bleach
    turns hair blonde.
  • Changes
  • A physical change is a change that is observed
    without a change in composition. Some examples
    are cutting wood, melting a solid, and boiling a
    liquid.
  • A chemical change is a change that is observed
    only when a change in composition is occurring.
    Some examples are the burning of wood, the
    rusting of iron, and the dying of hair.

12
Basic Ideas Additional Properties
  • An extensive property is a property that depends
    on the amount of material present. Some examples
    are volume and mass.
  • An intensive property is a property that does not
    depend on the amount of material present. Some
    examples are melting point, boiling point,
    freezing point, color, and density.

13
Basic Ideas Laws
  • Law of Conservation of Mass There is no
    observable change in the quantity of matter
    during an ordinary chemical reaction. For
    example, 58.7g of Ni and 12.0g of C make 70.7g
    NiC when reacted together.
  • Law of Conservation of Energy Energy cannot be
    created or destroyed, but it can be converted
    from one form to another. For example, potential
    energy can be converted to kinetic energy, but if
    you have 10kJ of potential energy, then you are
    going to get 10kJ of kinetic energy.
  • Law of Definite Proportions Different samples of
    any pure compound contain the same elements, each
    in the same proportion by mass. For example, all
    samples of water (H2O) contain 11.1 hydrogen (H)
    by mass and 88.9 oxygen (O) by mass.

14
Basic Ideas Accuracy vs. Precision
  • Accuracy tells us how close a measurement is to
    the true value.
  • Precision tells us how closely two or more
    measurements agree with one another.
  • For example, Say you measured the density of a
    substance in two separate trials to be 1.05g/mL
    and 0.998g/mL, and the density of the substance
    is actually 1.00g/mL. The accuracy of the
    measurement is obtained by comparing it to
    1.00g/mL, the actual density, whereas the
    precision of the measurement is obtained by
    comparing the 1.05g/mL to the 0.998g/mL.

15
Rounding Off Numbers
  • The rounding off of a number depends on the
    identity of the digit after the cut-off point
    (i.e. the next digit). The digit before the
    cut-off point is known as the previous digit.
    The rules for rounding off are
  • Rule 1 If the next digit is less than 5, then
    the previous digit remains the same.
  • Rule 2 If the next digit is greater than 5 or
    5 followed by nonzeros, then the previous digit
    is increased by one.
  • Rule 3 If the next digit is 5 or 5 followed by
    all zeros, then the previous digit
  • A. remains the same if it is even OR
  • B. is increased by one if it is odd.
  • Steps to Round Off a Number
  • Step 1 Identify the next digit.
  • Step 2 Based on the next digit, identify the
    rule that should be followed for rounding off.
  • Step 3 Based on the rule, either keep the
    previous digit the same or increase it by one.

16
Examples of Rounding Off Numbers
  • Example 1 Round off 2.637 to the second decimal
    point.
  • Answer
  • Step 1 The next digit is 7.
  • Step 2 Since 7 is greater than 5, rule 2
    applies.
  • Step 3 Since rule 2 applies, the previous
    digit, 3, is increased by one, making it 4. So,
    the number rounded off is 2.64.
  • Example 2 Round off 4.45120 to the second
    decimal point.
  • Answer
  • Step 1 The next digit is 1.
  • Step 2 Since 1 is less than 5, rule 1 applies.
  • Step 3 Since rule 1 applies, the previous
    digit remains the same. So, the number rounded
    off is 4.45.
  • Example 3 Round off 1.67500 to the second
    decimal point.
  • Answer
  • Step 1 The next digit is 5 followed by zeros.
  • Step 2 Since the next digit is a 5 followed by
    zeros, rule 3 applies. And since the previous
    digit, 7, is odd, part B of rule 3 applies.
  • Step 3 Since part B of rule 3 applies, the
    previous digit, 7, is increased by one, making
    it 8. So, the number rounded off is 1.68.

17
Scientific Notation
  • The general from of scientific notation is
  • N x 10e
  • N is a number that is between /- 1 and /- 9. e
    is an exponent (i.e. a power of ten), and thus is
    always a whole number.
  • Some examples are 4.5 x 1011 or 8.7 x 10-6.
  • Steps to convert a number into scientific
    notation
  • Step 1 If your number is not in scientific
    notation, add 100 to it.
  • Step 2 Convert your number so that it is between
    /- 1 and /- 9.
  • If you need to move the decimal place to the left
    to do this, then the exponent needs to be
    increased by the same amount.
  • If you need to move the decimal place to the
    right to do this, then the exponent needs to be
    decreased by the same amount.

18
Examples of Scientific Notation
  • Example 1 What is 425630.5 in scientific
    notation?
  • Answer
  • Step 1 Since the number is not in scientific
    notation, it becomes 425630.5 x 100.
  • Step 2 To get the number between /- 1 and /-
    9, I have to move the decimal point to the left 5
    places. Since I moved the decimal point to the
    left, I have to increase my exponent by the same
    amount, 5. So, my number in scientific notation
    is 4.256305 x 105.
  • Example 2 What is -0.0000586 in scientific
    notation?
  • Answer
  • Step 1 Since the number is not in scientific
    notation, it becomes 0.00586 x 100.
  • Step 2 To get the number between /- 1 and /-
    9, I have to move the decimal point to the right
    3 places. Since I moved the decimal point to the
    right, I have to decrease my exponent by the same
    amount, 3. So, my number in scientific notation
    is 5.86 x 10-3.
  • Example 3 What is 625.366 x 105 in correct
    scientific notation?
  • Answer
  • Step 1 Since the number is already in scientific
    notation, nothing is added to it.
  • Step 2 To get the number between /- 1 and /-
    9, I have to move the decimal point to the left 2
    places. Since I moved the decimal point to the
    left, I have to increase my exponent by the same
    amount, 2. So, my number in scientific notation
    is 6.25366 x 107.

19
Significant Figures
  • The amount of significant figures indicates how
    accurate a measurement is.
  • Exact numbers have an infinite number of
    significant figures, which means that there is an
    infinite number of zeros after the number. These
    zeros are not shown for convenience. For example,
    the amount in 1 dozen, 12, is an exact number,
    but we dont write 12.00000… every time.
  • Steps to identify the amount of significant
    figures a number has
  • Step 1 Going from left to right, locate the
    first nonzero digit.
  • Step 2 Again going from left to right, count the
    amount of digits present in the number, starting
    with the first nonzero digit.
  • Note If there are zeros at the end of a number
    without a decimal point, they may or may not be
    significant. Thus, if the zeros are significant,
    a decimal point should be at the end of the
    number. For example, 300 could have 1 significant
    figure, 2 significant figures, or 3 significant
    figures, but 300. has 3 significant figures.
  • Example 1 How many significant figures are
    present in the number 564.32?
  • Answer
  • Step 1 The first nonzero digit is 5.
  • Step 2 Starting with the 5, there are 5
    significant figures.
  • Example 2 How many significant figures are
    present in the number 0.00042?
  • Answer
  • Step 1 The first nonzero digit is 4.
  • Step 2 Starting with the 4, there are 2
    significant figures.

20
Manipulating Powers of Ten
  • Three ways to manipulate powers of ten
  • If powers of ten are multiplied, the exponents
    are added.
  • If powers of ten are divided, the exponents are
    subtracted.
  • If powers of ten are raised to an exponent, the
    exponents are multiplied.
  • Example 1 What is 106 x 104?
  • Answer Since it is multiplication, the exponents
    are added together 6 4 10, so, it is 1010.
  • Example 2 What is 1013/10-3?
  • Answer Since it is division, the exponents are
    subtracted from each other 13 (-3) 16, so,
    it is 1016.
  • Example 3 What is (105)3?
  • Answer Since it is raised to an exponent, the
    exponents are multiplied together 5 x 3 15,
    so, it is 1015.

21
Numbers with Powers of Ten Multiplying and
Dividing
  • Steps when multiplying and dividing numbers with
    powers of ten
  • Step 1 Place the numbers (also called
    coefficients) together and the powers of ten
    together.
  • Step 2 Multiply or divide the numbers and add or
    subtract the powers of ten, depending on which
    operation is present.
  • Step 3 The final answer should
  • have the same amount of significant figures as
    the number with the least amount of significant
    figures.
  • have been rounded off correctly.
  • preferably be reported in scientific notation.

22
Examples of Multiplying and Dividing Numbers with
Powers of Ten
  • Example 1 Multiplication What is (3.443 x 106)
    x (0.43 x 104)?
  • Answer
  • Step 1 (3.443 x 0.43) x (106 x 104)
  • Step 2 1.48049 x 1010
  • Step 3 3.443 has 4 significant figures and 0.43
    has 2 significant figures, so the answer should
    have 2 significant figures. To round off the
    number to 2 significant figures, the previous
    digit, 4, should become 5 since the next digit
    is 8. So, it is 1.5 x 1010.
  • Example 1 Division What is (4.25 x 104)/(3.21 x
    102)?
  • Answer
  • Step 1 (4.25/3.21) x (104/102)
  • Step 2 1.32399 x 102
  • Step 3 4.25 has 3 significant figures and 3.21
    also has 3 significant figures, so the answer
    should also have 3 significant figures. To round
    off the number to 3 significant figures, the
    previous digit, 2, should stay the same since
    the next digit is 3. So, it is 1.32 x 102.

23
Numbers with Powers of Ten Adding and Subtracting
  • Steps when adding and subtracting numbers with
    powers of ten
  • Step 1 Make all of the powers of ten the same.
  • Step 2 Once all of the powers of ten are the
    same, add or subtract the numbers, depending on
    which operation is present, but keep the powers
    of ten the same
  • Step 3 The final answer should
  • have the same amount of decimal places as the
    number with the fewest decimal places at the time
    of the addition or subtraction.
  • have been rounded off correctly.
  • preferably be reported in scientific notation.

24
Examples of Adding and Subtracting Numbers with
Powers of Ten
  • Example 1 Addition What is 5.34 x 1043 4.2 x
    1044?
  • Answer
  • Step 1 To make the powers the same, either
    change 43 to 44 or 44 to 43. If 43 is turned into
    44, since the value is increased by one, the
    decimal point is moved to the left by one, making
    it 0.534 x 1044.
  • Step 2 (0.534 4.2) x 1044 4.734 x 1044.
  • Step 3 At the time of addition, 0.534 has 3
    decimal places and 4.2 has 1 decimal place, so
    the answer should have 1 decimal place. To round
    off the number to 1 decimal point, the previous
    digit, 7, should remain the same because the
    next digit is 3. So, it is 4.7 x 1044.
  • Example 1 Subtraction What is 0.98 x 1056
    3.12 x 1055?
  • Answer
  • Step 1 To make the powers the same, either
    change 56 to 55 or 55 to 56. If 56 is turned into
    55, since the value is decreased by one, the
    decimal point is moved to the right by one,
    making it 9.8 x 1055.
  • Step 2 (9.8 3.12) x 1055 6.68 x 1055.
  • Step 3 At the time of addition, 9.8 has 1
    decimal place and 3.12 has 2 decimal places, so
    the answer should have 1 decimal place. To round
    off the number to 1 decimal point, the previous
    digit, 6, should be increased to 7, because the
    next digit is 8. So, it is 6.7 x 1055.

25
Numbers with Powers of Ten Mixing
Multiplying/Dividing with Adding/Subtracting
  • When all operations are combined, make sure to
    carry out those in parenthesis first.
  • Example 1 What is
  • (2.63 x 105 x (3.64 x 10-4 1.22 x 10-3))/(7.36
    x 106)2?
  • Answer
  • (3.64 x 10-4 1.22 x 10-3) (0.364 x 10-3 -
    1.22 x 10-3) (0.364 1.22) x 10-3 -0.856 x
    10-3
  • (7.36 x 106)2 (7.36 x 106) x (7.36 x 106)
    (7.36 x 7.36) x (106 x 106) 54.1696 x 1012
  • (2.63 x 105 x -0.856 x 10-3) (2.63 x -0.856) x
    (105 x 10-3) -2.2513 x 102
  • -2.2513 x 102/54.1696 x 1012 (-2.2513/54.1696)
    x (102/1012) 0.04156 x 10-10 4.16 x 10-12

26
Units of Measurement Equalities in the English
System
  • Volume
  • 1 pint (pt) 16 fl oz (fluid ounce)
  • 1 quart (qt) 2 pt
  • 1 gallon (gal) 4 qt
  • Mass
  • 1 pound (lb) 16 ounces (oz)
  • 1 ton 2000 lb
  • Length
  • 1 foot (ft) 12 inches (in)
  • 1 yard (yd) 3 feet (ft)
  • 1 mile (mi) 5280 ft
  • Time
  • 1 minute (min) 60 seconds (sec)
  • 1 hour (hr) 60 minutes (min)
  • 1 day 24 hours (hr)

27
Units of Measurement The Metric System and the
International System of Units (SI Units)
  • These two systems are decimal systems, where the
    units are related to each other by powers of ten.
    Prefixes are used to indicate fractions and
    multiples of ten.
  • The basic units for these systems are
  • Volume liter (L)
  • Mass gram (g)
  • Length meter (m)
  • Time second (s)
  • The relation between length units and volume
    units 1 mL 1 cm3 1 cc
  • The table to the left illustrates the value of
    each prefix. The number in the table always gets
    placed in front of the base unit and a 1 always
    gets placed in from of the prefixed base unit.
    For example, 1 millimeter 10-3 meters or 1 mm
    10-3 m.

28
Units of Measurement Conversion between the
Metric and the English Systems
  • Volume
  • 1 qt 0.946 L
  • Mass
  • 1 lb 454 g
  • Length
  • 1 in 2.54 cm

29
Use of Conversion Factors in Calculations
  • Obtained from equalities, which show the
    relationship between two quantities that are
    measuring the same quantity (i.e. mass, volume,
    length, etc.)
  • From the equality, two different conversion
    factors can be obtained
  • When using a conversion factor in a problem, you
    use the one that cancels out the given units and
    leaves the answer units the given units need to
    be on the bottom of the conversion factor, with
    the answer units on the top of the conversion
    factor
  • Equality
  • x y,
    where x and y are different units and the s
    arent equal
  • Two conversion factors from the equality x/
    y and y / x
  • If you want to convert y to x, you need to use
    x / y
  • y ( x / y) x
  • If you want to convert x to y, you need to use
    y / x
  • x ( y / x) y

30
Problem Solving with Conversion Factors Factor
Label Method
  • Step 1 Write down the given quantity and unit(s)
    and the answer unit(s), with space between them
    for the conversion factors.
  • Step 2 Identify the equalities needed to change
    the given unit(s) to the answer unit(s) more
    than one equality may be needed.
  • Step 3 Write down the two conversion factors
    possible from each of the identified equalities.
  • Step 4 Arrange the conversion factors between
    the given quantity and unit and the answer unit,
    so that the given unit cancels, leaving the
    answer unit the given unit needs to be on the
    bottom of the first conversion factor and the
    answer unit needs to be on the top of the last
    conversion factor.
  • If the given quantity has two units, convert the
    unit on top, and then convert the unit on the
    bottom. Unlike when converting the unit on
    top, which is described above, when converting
    the unit on the bottom, the given unit needs to
    be on the top of the first conversion factor for
    the bottom and the answer unit needs to be on
    the bottom of the last conversion factor for the
    bottom.
  • Hint A quantity with two units, x/y, can be
    written as x / 1 y, since dividing by one
    doesnt change the value of the number. This
    will help to choose the correct conversion factor
    for the problem.

31
Examples of Using the Factor Label Method 1
  • Example 1 English to English Conversion How
    many feet are in 3 yards?
  • Answer
  • Step 1 3 yd.
    ____ ft.
  • Step 2 1 yd. 3 ft. (this covers all the units
    above, so no more equalities are needed)
  • Step 3 Conversion factors 1 yd. / 3 ft. OR 3
    ft. / 1 yd.
  • Step 4 3 yd. (3 ft. / 1 yd.) 9 ft. this
    conversion factor is needed to cancel yd. (given
    unit is on bottom) and get ft. (answer unit is on
    top)
  • Example 2 Metric to Metric Conversion How many
    kilograms are in 90 decigrams?
  • Answer
  • Step 1 90 dg.
    ____ kg.
  • Step 2 1 dg. 0.1 g. and 1 kg. 1000 g. (two
    equalities are needed here since one does not
    cover all of the units above )
  • Step 3 Conversion factors 1 dg. / 0.1 g. OR 0.1
    g. / 1 dg. and
  • 1 kg. / 1000 g. OR 1000 g. / 1 kg.
  • Step 4 90 dg. (0.1 g. / 1 dg.) (1 kg. / 1000
    g.) 0.0090 kg. the first conversion factor is
    needed to cancel dg (given unit is on bottom) and
    get g (unit is on top), which leads to the second
    conversion factor, which cancels g (unit is on
    bottom) to get kg (answer unit is on top)

32
Examples of Using the Factor Label Method 2
  • Example 3 Metric to English Conversion How many
    feet are in 5.85 centimeters?
  • Answer
  • Step 1 5.85 cm.
    ____ ft.
  • Step 2 2.54 cm. 1 in. and 12 in. 1 ft. (two
    equalities are needed here since one does not
    cover all of the units above the first equality
    converts between the english and the metric
    system and the second one converts within the
    english system)
  • Step 3 Conversion factors 2.54 cm. / 1 in. OR 1
    in. / 2.54 cm. and 12 in. / 1 ft. OR 1 ft. / 12
    in.
  • Step 4 5.85 cm. (1 in. / 2.54 cm.) (1 ft. /
    12 in.) 0.192 ft. the first conversion factor
    is needed to cancel cm. (given unit is on bottom)
    and get in. (unit is on top), which leads to the
    second conversion factor, which cancels in. (unit
    is on bottom) to get ft. (answer unit is on top)
  • Example 4 Using Square Units How many m2 are in
    105 in2?
  • Answer
  • Step 1 105 in2
    ____ m2
  • Step 2 2.54 cm. 1 in. and 1 cm. 0.01 m. (two
    equalities are needed here since one does not
    cover all of the units above the first equality
    converts between the english and the metric
    system and the second one converts within the
    metric system)
  • Step 3 Conversion factors 2.54 cm. / 1 in. OR 1
    in. / 2.54 cm. and 1 cm. / 0.01 m. OR 0.01 m. /
    1 cm.
  • Step 4 105 in.2 (2.54 cm. / 1 in.)2 (0.01 m.
    / 1 cm.)2 0.0677 m.2 the first conversion
    factor is needed to cancel in. (given unit is on
    bottom) and get cm. (unit is on top), which leads
    to the second conversion factor, which cancels
    cm. (unit is on bottom) to get m. (answer unit is
    on top) each conversion factor needs to be
    squared so that the given units are cancelled
    completely to give the answer units

33
Examples of Using the Factor Label Method 3
  • Example 5 Using Cubed Units How many m3 are in
    105 in3?
  • Answer
  • Step 1 105 in3
    ____ m3
  • Step 2 2.54 cm. 1 in. and 1 cm. 0.01 m. (two
    equalities are needed here since one does not
    cover all of the units above the first equality
    converts between the english and the metric
    system and the second one converts within the
    metric system)
  • Step 3 Conversion factors 2.54 cm. / 1 in. OR 1
    in. / 2.54 cm. and 1 cm. / 0.01 m. OR 0.01 m. /
    1 cm.
  • Step 4 105 in.3 (2.54 cm. / 1 in.)3 (0.01 m.
    / 1 cm.)3 0.00172 m.3 the first conversion
    factor is needed to cancel in. (given unit is on
    bottom) and get cm. (unit is on top), which leads
    to the second conversion factor, which cancels
    cm. (unit is on bottom) to get m. (answer unit is
    on top) each conversion factor needs to be
    cubed so that the given units are cancelled
    completely to give the answer units
  • Example 6 Using Double Units How many ft./sec.
    are in 731 in./min.?
  • Answer
  • Step 1 731 in./1 min.
    ____ ft./sec.
  • Step 2 For the top units, 12 in. 1 ft. (only
    one equality is needed) for the bottom units,
    1 min. 60 sec. (only one equality is needed)
  • Step 3 For the top units, 12 in. / 1 ft. OR 1
    ft. / 12 in. for the bottom units, 1 min. / 60
    sec. OR 60 sec. / 1 min.
  • Step 4 731 in./1 min. (1 ft. / 12 in.) (1
    min. / 60 sec.) 1.02 ft./sec. the first
    conversion factor (for the top units) is needed
    to cancel in. (given unit is on bottom) and get
    ft. (answer unit is on top), and the second one
    (for the bottom units) is needed to cancel min.
    (given unit is on top) and get sec. (answer unit
    is on bottom)

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Density (d) and Specific Gravity (sp.gr.)
  • Density mass/volume OR d m/V
  • The common units of density are
  • g/mL for liquids and solids
  • g/L for gases
  • The density of a substance shows the relationship
    between its mass and its volume. For example, if
    the density of a substance is 3.45 g/mL, the
    relationship between the mass and volume can be
    written as the equality 3.45 g 1 mL.
  • Specific Gravity (sp.gr.) (density of
    substance)/(density of water at 4?C) (density
    of substance in g/mL)/(1.00g/mL)
  • Since the density of a substance is divided by
    1.00 to obtain the specific gravity, the density
    and specific gravity are numerically equivalent
    (i.e., they are the same number since dividing
    any number by 1.00 gives the same number).
    Although they are numerically equivalent, they
    are not equal. Since both the density of a
    substance and the density of water have the same
    units, they are cancelled out when the specific
    gravity is obtained, making the specific gravity
    a unitless quantity, unlike density, which always
    has units.

35
To Obtain a Substances Density
  • Since density is mass divided by volume, you need
    to obtain both a substances mass and its volume
    to obtain its density.
  • To obtain the mass, measure the substance on a
    balance.
  • To obtain the volume
  • If it is a liquid, measure it with a graduated
    cylinder.
  • If it is a solid, one of two methods can be used
  • One is by water displacement. Here, a certain
    volume of water is placed in a graduated
    cylinder, and the value is recorded (Vwater). The
    solid is then dropped into the graduated cylinder
    with the water. The new volume of water is then
    recorded (Vwatersolid). To obtain the volume of
    the solid (Vsolid), the initial volume of the
    water is subtracted from the new volume of water
    (Vsolid Vwatersolid - Vwater).
  • The other is through mathematical equations,
    using one of the following equations
  • V(cubic solid) l x w x h (length (l) width
    (w) height (h))
  • V(rectangular solid) l x w x h
  • V(sphere) (4/3) pr3 (radius (r) diameter
    (d)/2)
  • V(cylinder) (pd2h)/4

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Steps to Solving a Problem
  • Step 1 Identify the information that is given in
    the problem.
  • Step 2 Identify what information the problem is
    looking for.
  • Step 3 Identify the equation that is needed to
    obtain the information you are looking for, while
    using the information you were given.
  • Step 4 Put the given information into the
    equation found in Step 3 and solve for the
    information you are looking for, making sure that
    all of the given information is expressed in the
    proper units.

37
Examples of Calculations of Density 1
  • Example 1 What is the density of a liquid that
    has a mass of 5.67 grams and a volume of 10.3 mL?
  • Step 1 5.67g m 10.3mL V
  • Step 2 density (d)
  • Step 3 d m/V
  • Step 4 d 5.67 g / 10.3 mL 0.550 g/mL
  • Example 2 What is the mass of a liquid if it
    has a density of 1.50 g/mL and a volume of 14 mL?
  • Step 1 1.50 g/mL d 14mL V
  • Step 2 mass (m)
  • Step 3 d m/V
  • Step 4 d m / V - m d V 1.50 g/mL 14
    mL 21 g
  • Example 3 What is the volume of a liquid if it
    has a mass of 14.6 grams and a density of 3.45
    g/mL?
  • Step 1 14.6g m 3.45 g/mL d
  • Step 2 volume (V)
  • Step 3 d m/V
  • Step 4 d m / V - V m / d 14.6 g / 3.45
    g/mL 4.23 mL

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Examples of Calculations of Density 2
  • Example 4 If a 24g solid was placed in a
    graduated cylinder containing 25.0mL of water and
    the water raised to 34.2mL, what is the density
    of the substance?
  • Answer
  • Step 1 24g m 25.0mL Vwater 34.2mL
    Vwatersolid
  • Step 2 density (d)
  • Step 3 d m/V, where V Vsolid Vwatersolid
    - Vwater
  • Step 4 V Vwatersolid Vwater 34.2mL-25.0mL
    9.2mL d m/V 24g/9.2mL 2.6g/mL
  • Example 5 What is the density of a wooden block
    that has a mass of 75g and measures 2.5cm by
    3.5cm by 6.1cm?
  • Answer
  • Step 1 75g m 2.5cm length (l) 3.5cm
    width (w) 6.1cm height (h)
  • Step 2 density (d)
  • Step 3 d m/V, where V V(rectangular solid)
    l x w x h
  • Step 4 V 2.5cm x 3.5cm x 6.1cm 53.375cm3
    53.375mL d m/V 75g/53.375mL 1.4g/mL

39
Examples of Calculations of Specific Gravity
  • Example 1 What is the specific gravity of a
    substance with a mass of 5.021 g and a density of
    1.21 g/mL?
  • Step 1 5.021 g m 1.21 g/mL d
  • Step 2 specific gravity (sp.gr.)
  • Step 3 sp.gr. (density of substance in
    g/mL)/(1.00g/mL)
  • Step 4 sp.gr. 1.21 g/mL / 1.00 g/mL 1.21
  • Example 2 What is the specific gravity of a
    substance with a mass of 5.021 g and a volume of
    7.99 mL?
  • Step 1 5.021g m 7.99mL V
  • Step 2 specific gravity (sp.gr.)
  • Step 3 sp.gr. (density of substance in
    g/mL)/(1.00g/mL), where d m/V
  • Step 4 d m/V 5.021 g / 7.99 mL 0.628 g/mL
    sp.gr. (density of substance in
    g/mL)/(1.00g/mL) 0.628 g/mL / 1.00 g/mL 0.628

40
Temperature Conversions
  • There are three temperature units degrees
    Fahrenheit (F), degrees Celsius (C), and Kelvin
    (K). (Note K does not have a sign.)
  • To convert C to F F (1.8 C) 32
  • To convert F to C C (F 32) / 1.8
  • To convert C to K K C 273
  • To convert K to C C K 273
  • Note For the Celsius scale and the Kelvin scale,
    there is a 100 difference between the freezing
    point and the boiling point of water, but on the
    Fahrenheit scale, the difference is 180.

41
Examples of Temperature Conversions
  • Example 1 How many degrees Fahrenheit are in 73
    degrees Celsius?
  • Answer F (1.8 C) 32 (1.8 73 C) 32
    163.4 F
  • Example 2 How many degrees Celsius are in 200
    degrees Fahrenheit?
  • Answer C (F 32) / 1.8 (200 F 32) /
    1.8 93.3 C
  • Example 3 How many Kelvin are there in 650
    degrees Celsius?
  • Answer K C 273 650 C 273 923 K
  • Example 4 How many degrees Celsius are there in
    543 Kelvin?
  • Answer C K 273 543 K 273 270 C
  • Example 5 How many degrees Fahrenheit are there
    in 321 Kelvin?
  • Answer
  • C ? K 273 321 K -273 48 C
  • F (1.8 C) 32 (1.8 48 C) 32 118.4
    F

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Heat Transfer
  • During chemical changes and physical changes,
    heat is transferred
  • If there is an evolution of heat (i.e. heat is
    lost or released), it is an exothermic process.
  • If there is an absorption of heat (i.e. heat is
    gained or absorbed), it is an endothermic
    process.
  • The units to express the amount of heat
    transferred are calories (cal) or joules (J),
    where 1 cal 4.184J.
  • Specific heat is the amount of heat necessary to
    raise the temperature of 1 g of substance by 1C.
    Specific heat is a physical intensive property,
    like density, melting point, and boiling point.
    Each substance has its own specific heat.
  • Using the specific heat of a substance, the heat
    that is absorbed or released in a given process
    can be obtained by
  • q m x s x ?T
  • where q is the heat energy (cal, kcal, J, or
    kJ), m is mass (g), s is specific heat
    (cal/gC), and ?T is the change in temperature
    (?T T2 T1)(C).

43
Examples of Calculations of Heat Transfer
  • Example 1 How much heat (in cal) is needed to
    heat 54g of a substance (specific heat 0.212
    cal/gC) from 72C to 98C?
  • Answer
  • Step 1 Given 54g m 0.212 cal/gC s 72C
    T1 98C T2
  • Step 2 Looking for heat (in cal) q
  • Step 3 Equation q m x S x ?T, where ?T T2
    T1
  • Step 4 ?T T2 T1 98C - 72C 26C q
    (54g) x (0.212 cal/gC) x (26C) 297.648 cal
    3.0 cal.
  • Example 2 How much of a substance is present if
    56J of heat is added when the substance (specific
    heat 0.532 cal/gC) is heated from 23C to
    54C?
  • Answer
  • Step 1 Given 56J q 0.532 cal/gC s 23C
    T1 54C T2
  • Step 2 Looking for mass m
  • Step 3 Equation q m x S x ?T, where ?T T2
    T1
  • Step 4 ?T T2 T1 54C - 23C 31C q m
    x S x ?T ? 56J (m) x (0.532 cal/gC) x
    (31C), but since there is J on one side and cal
    on the other side, the J have to be converted to
    cal before solving for m 56J x (1 cal /4.184J)
    13.384 cal 13.384 cal (m) x (0.532
    cal/gC) x (31C), so m 0.81156 g 0.81 g.
  • Example 3 If 86cal of heat is added to 10g of a
    substance (specific heat 0.411 cal/gC), and
    the final temperature was measured to be 152C,
    what is the initial temperature of the substance?
  • Answer
  • Step 1 Given 86cal q 10g m 0.411 cal/gC
    s 152C T2
  • Step 2 Looking for initial temperature T1
  • Step 3 Equation q m x S x ?T, where ?T T2
    T1
  • Step 4 86cal (10g) x (0.411 cal/gC) x (?T),
    so ?T 20.92C ?T T2 T1 ? 20.92C 152C
    T1, so T1 131.08C 1.3 x 102C

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Some Specific Heats
  • The larger the specific heat of the substance,
    the more heat it needs to raise its temperature.
  • The specific heat of water is 1.00 cal/gC,
    which is one of the largest specific heats. Since
    approx. 60 of our body weight is water, this
    large specific heat allows our body to maintain a
    constant body temperature (around 37C) much
    easier. So, our body can absorb or release a
    large amount of energy with little change in body
    temperature.
  • Examples of other specific heats
  • wood 0.421 cal/gC
  • gold 0.0306 cal/gC
  • graphite 0.172 cal/gC

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