CHAPTER 2 Atoms and Elements

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					               CHAPTER 2
               Atoms and Elements


Objectives
You will be able to do the following:
1. Given a periodic table, determine the group number for the column in which the
    element is found. This includes the 1-18 numbering and the common variations.
    For example, the second column can be numbered 2 or 2A.
2. Given a periodic table, determine the names associated with groups
    1 (alkali metals), 2 (alkaline earth metals), 17 (halogens), and 18 (noble gases).
3. Write or identify the characteristics of metals.
4. Given a periodic table, determine whether an element is a metal, nonmetal, or a
    metalloid (semimetal).
5. Given a periodic table, determine whether an element is a representative (or
    main-group) element, a transition metal, or an inner transition metal.
6. Given a periodic table, write or identify the number for the period on the table to
    which each element belongs.
7. Given the name or symbol for an element, identify whether it is a solid, liquid, or
    gas at room temperature.
8. Write or identify the symbols, charges, and relative sizes of protons, neutrons,
    and electrons.
9. Write a description of the nuclear model of the atom. Your description should
    include mention of where the proton, neutron, and electron are found, the
    relative size of the nucleus compared to the size of the atom, and the modern
    description of the electron.
10. Write a description of the carbon atom, including a rough sketch representing its
    electrons.
11. Write an explanation for why electrons affect the chemical characteristics of an
    atom.
12. Write an explanation for why protons affect the chemical characteristics of an
    atom.
13. Write an explanation for why neutrons do not affect the chemical characteristics
    of an atom.
14. Write an explanation for why atoms of the same element can have a different
    number of neutrons.
15. Convert between the atomic number and the number of protons in an atom of
    an isotope.
16. Given an isotope’s mass number, atomic number, and charge, write its symbol.
17. Given an isotope’s symbol, determine its mass number, atomic number, and
    charge.
18. Given the number of protons and neutrons in an atom of an isotope, determine
    its mass number.
19. Given the mass number and the atomic number of an isotope, determine the
    number of neutrons in an atom of the isotope.
                                                                                         7
8   Chapter 2   Atoms and Elements



                      20. Given two of the following three, determine the third: (1) the number of protons
                          in an atom, (2) the number of electrons in an atom, and (3) the charge on the
                          atom.
                      21. Write or identify the diatomic elements (H2, N2, O2, F2, Cl2, Br2, and I2).
                      22. Write a description of the hydrogen molecule.
                      23. Write a general description of the structure of the following: the noble gases,
                          hydrogen gas, nitrogen gas, oxygen gas, fluorine gas, chlorine gas, bromine liquid,
                          and iodine solid.
                      24. Write a brief description of the “sea of electrons” model for metallic bonding.
                      25. Write or identify the International System of Measurements (SI) standard units
                          and their abbreviations for length, mass, time, temperature, and amount of
                          substance.
                      26. Write a description of how the unit liter, L, is derived from the SI standard of
                          meter.
                      27. Write or identify the metric base units and their abbreviations for length, mass,
                          volume, energy, and gas pressure.
                      28. Convert between the prefix, its abbreviation, and its value for the following
                          metric prefixes: giga, mega, kilo, centi, milli, micro, nano, and pico.
                      29. Convert between metric derived units and their abbreviations for the units
                          derived from the SI base units and the metric prefixes. (For example, the
                          abbreviation for milligram is mg.)
                      30. Write the relationship between the SI base units and the units derived from the
                          metric prefixes.
                              For example, 103 mm = 1 meter
                      31. Write a description of the relationship between mass and weight.
                      32. Write or identify the two factors that cause the weight of an object to change.
                      33. Write an explanation for why the weight of an object on the moon is less than the
                          weight of the same object on the earth.
                      34. Write an explanation for why the mass of an object is the same on the moon and
                          the earth.
                      35. Write the relationship between kilograms and metric tons.
                      36. Write conversion factors that relate the SI base units and the units derived from
                          the metric prefixes.
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                              For example,
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                      37. Write the English-metric conversion factors listed on Table 2.9.
                      38. Write an explanation for why increased temperature usually leads to decreased
                          density for solids and liquids.
                      39. Write or identify the common units used to describe the density of solids, liquids,
                          and gases.
                      40. Given a percentage by mass or a percentage by volume, write the conversion
                          factor that comes from it.
                      41. Identify numbers in a calculation as exact or not exact.
                      42. Round off answers to calculations to report the correct significant figures.
                                                                                        9


43. Make the following types of unit conversions using the unit analysis technique.
      a. Convert from one English unit to another English unit of the same type of
         measurement; for example, in. to ft.
      b. Convert from one metric unit to another metric unit of the same type of
         measurement; for example, mg to kg.
      c. Convert between metric units and English units of the same type of
         measurement; for example, qt to mL.
      d. Convert between mass and volume using density as a conversion factor.
      e. Convert between a cubic length type volume unit (for example, cm3) and
         single unit type volume; for example, mL.
      f. Convert between units of the part and units of the whole using percentage
         as a conversion factor.
44. Convert between temperature in the Celsius, Fahrenheit, and Kelvin scales.
45. Convert between the definition and the term for the following words or phrases.

Chapter 2 Glossary
Group (on the periodic table) All the elements in a given column on the periodic
   table; also called a family.
Family (on the periodic table) All the elements in a given column on the periodic
   table; also called a group.
Alkali metals Group 1 on the periodic table.
Alkaline earth metals Group 2 on the periodic table.
Halogens Group 17 on the periodic table.
Noble gases Group 18 on the periodic table.
Representative elements The elements in groups 1, 2, and 13 through 18 (the “A”
   groups) on the periodic table; also called main-group elements.
Main-group elements The elements in groups 1, 2, and 13 through 18 (the “A”
   groups) on the periodic table; also called representative elements.
Transition metals The elements in groups 3 through 12 (the “B” groups) on the
   periodic table.
Inner transition elements The 28 elements at the bottom of the periodic table.
Period (on the periodic table) A horizontal row on the periodic table.
Atom The smallest part of an element that retains the chemical characteristics of the
   element.
Proton A positively charged particle found in the nucleus of an atom.
Electron A negatively charged particle found outside the nucleus of an atom.
Neutron An uncharged particle found in the nucleus of an atom.
Nucleus The extremely small, positively charged core of the atom.
Ion Any charged particle, whether positively or negatively charged.
Cation An ion formed from an atom that has lost one or more electrons and thus has
   become positively charged.
Anion An ion formed from an atom that has gained one or more electrons and thus
   has become negatively charged.
10   Chapter 2   Atoms and Elements



                     Isotopes    Atoms that have the same number of protons but different numbers of
                         neutrons. They have the same atomic number but different mass numbers.
                     Atomic mass unit (u or amu) Unit of measurement for the masses of particles; 1/12
                         the mass of a carbon atom that has 6 protons, 6 neutrons, and 6 electrons.
                     Atomic number          The number of protons in an atom’s nucleus. It establishes the
                         element’s identity.
                     Mass number           The sum of the number of protons and neutrons in an atom’s
                         nucleus.
                     Covalent bond A link between atoms that results from their sharing two electrons.
                     Molecule An uncharged collection of atoms held together with covalent bonds.
                     Diatomic Composed of paired atoms. The diatomic elements are H2, N2, O2, F2,
                         Cl2, Br2, and I2.
                     Allotropes Different forms of the same element.
                     Value   A number and unit that together represent the result of a measurement or
                         calculation. The distance of a particular race, for example, may be reported as a
                         value of 100 meters.
                     Unit A defined quantity based on a standard. For example, in the value 100 meters,
                         meter is the unit.
                     Base units The seven units from which all other units in the SI system of measurement
                         are derived.
                     Mass The amount of matter in an object. Mass can also be defined as the property of
                         matter that leads to gravitational attractions between objects and therefore gives
                         rise to weight.
                     Weight A measure of the force of gravitational attraction between an object and a
                         significantly large body, such as the earth or the moon.
                     Matter Anything that has mass and occupies space.
                     Absolute zero      Zero kelvins (0 K), the lowest possible temperature, equivalent to
                         −273.15 °C. It is the point beyond which motion can no longer be decreased.
                     Precision The closeness in value of a series of measurements of the same entity. The
                         closer the values of the measurements, the more precise they are.
                     Accuracy How closely a measured value approaches the true value of a property.
                     Mass density Mass divided by volume (usually called density).
                     Significant figures         The number of meaningful digits in a value. The number of
                         significant figures in a value reflects the value’s degree of uncertainty. A larger
                         number of significant figures indicates a smaller degree of uncertainty.
                     Unit (dimensional) analysis A general technique for doing unit conversions.
                     Conversion factor A ratio that describes the relationship between two units.
                                                                                                                                11


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                                                                                                  Figure 2.1 Periodic Table




EXERCISE 2.1 - Periodic Table
Complete the following table.

      Name             Symbol         Group          Metal,         Representative        Number        Solid,
                                      Number        Nonmetal     Element, Transition     for Period    Liquid,
                                                       or           Metal or Inner                     or Gas?
                                                    Metalloid?    Transition Metal?
                         Al
    silicon
                        Ni
    sulfur
                         F
    cesium
                        Hg
    uranium                            (No
                                      group
                                     number)
                        Mn
    strontium
                                       17                                                    4
                                       1B                                                    5
                                       VA            metal
                                       14           nonmetal
12    Chapter 2   Atoms and Elements



                      EXERCISE 2.2 - Group Names

                      What is the name of the group on the periodic table for (a) helium, (b) chlorine,
                      (c) magnesium, and (d) sodium?




     Table 2.1 Some of the Characteristics of the Particles Within the Atom

       Particle      Symbol         Relative   Mass in grams            Mass in atomic                  Location in the
                                    charges                             mass units                      atom
       neutron       n or n0        0          1.6750 x 10 −24 g        1.00867 u                       nucleus
       proton        p or p+        +1         1.6726 x 10 −24 g        1.00728 u                       nucleus
       electron      e−             -1         9.1096 x 10 −28 g        0.000549 u                      outside nucleus




                      Table 2.2 Symbols for Common Isotopes

                          Most common                1              Aluminum cation, Al3+                         27 3+
                          hydrogen isotope           1H                                                           13 Al

                          Most abundant isotope      238            Iodine anion, I−                              127 –
                          of uranium                  92U                                                          53 I

                          Sodium cation, Na+         23  +          Most common oxygen                            16 2–
                                                     11Na           anion, O2−                                     8O




     Figure 2.2 Carbon Atom

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You can see an animation that describes the structure of some of the chemical elements
at the following Web address:
     http://www.mpcfaculty.net/mark_bishop/element_properties.htm
14   Chapter 2   Atoms and Elements



                     Summary of New Skills
                     You will be asked to convert between the symbol for an isotope and the isotope’s
                     atomic number, mass number, ionic charge, and its number of protons, neutrons,
                     and electrons. The following describes the steps.
                             1. If you are given the isotope symbol, follow these guidelines to get the
                             atomic number, mass number, and ionic charge.
                                      a. The subscript on the left of the element symbol is the atomic
                                      number.
                                      b. The superscript on the left of the element symbol is the mass
                                      number.
                                      c. The superscript on the right of the element symbol is the ionic
                                      charge.
                             2. Follow these guidelines to convert between atomic number, mass number,
                             ionic charge, and the number of protons, neutrons, and electrons in the
                             atom.
                                      a. The atomic number and the number of protons are always equal.
                                      b. The mass number is the sum of the number of protons and
                                      neutrons, so the number of neutrons can be calculated by subtracting
                                      the atomic number (the number of protons) from the mass number.
                                      c. The charge on an atom is the number of protons minus the
                                      number of electrons.
                                             ♦   For a uncharged atom, the number of electrons and
                                                 protons are equal.
                                             ♦   For a positive ion, the number of electrons is equal to the
                                                 number of protons minus the size of the charge.
                                             ♦   For a negative ion, the number of electrons is equal to the
                                                 number of protons plus the size of the charge.

                 EXERCISE 2.3 - Isotope Symbolism
                 Complete the following table.
                  Symbol      Atomic        Mass        Number        Number        Number         Charge
                              number       number       protons       neutrons      electrons
                  59
                  28 Ni

                  32 2–
                  16 S

                                 82          207                                        80
                                                            33            42            33
                                                            35            44            36
                                                                                                              15


Table 2.3    Standards for the International System of Measurement

  Type of                  Standard      Abbreviation     Definition
  Measurement              Unit
  length                   meter              m           The distance that light travels in a vacuum in
                                                          1/299,792,458 of a second
  mass                     kilogram           kg          The mass of a platinum-iridium alloy cylinder
                                                          in a vault in France
  time                     second             s           The duration of 9,192,631,770 periods of
                                                          the radiation emitted in a specified transition
                                                          between energy levels of cesium-133
  temperature              kelvin             K           1/273.16 of the temperature difference
                                                          between absolute zero and the triple point
                                                          temperature of water
  amount of                mole              mol          The amount of substance that contains the
  substance                                               same number of chemical units as there are
                                                          atoms in 12 grams of carbon-12
  electric current         ampere             A           Current that, if maintained in two straight
                                                          parallel conductors of infinite length and
                                                          placed 1 meter apart in a vacuum, will produce
                                                          a force equal to 2 x 10−7 newton per meter.
  luminous intensity       candela            cd          The luminous intensity of a black body surface
                                                          1/600,000 m2 at the normal melting point of
                                                          platinum


Table 2.4    Derived Units in the International System of Measurements


  Type of            Calculated From       Derived unit        Redefined                        Abbreviation
  Measurement                              from Standards
  area               square length               m2            xxxx                            xxxx
  volume             cubic length                m3            liter = 1   dm3   = 10−3
                                                                                          m3   L or l
  velocity           length per time             m             xxxx                            xxxx
                                                   s
  acceleration       velocity per time           m             xxxx                            xxxx
                                                  s2
  force              mass times                    kg m        newton                          N
                     acceleration                   s2
  energy             force times                  kg m2        joule                           J
                     distance                       s2
  gas pressure       force per area                kg          pascal                          Pa
                                                   m s2
16   Chapter 2    Atoms and Elements



         Table 2.5 Some Base Units and Their Abbreviations for the International System of
         Measurement
            Type of Measurement              Base Unit       Abbreviation
            Length                           meter           m
            Mass                             gram            g
            Volume                           liter           L or l
            Energy                           joule           J
            Gas pressure                     pascal          Pa

         Table 2.6 Metric Prefixes
          Prefixes for Large Units                                        Prefixes for Small Units
            Prefix     Abbreviation              Value              Prefix      Abbreviation             Value
           giga            G           10 or 1,000,000,000
                                         9
                                                                  centi            c          10 −2 or 0.01
           mega            M           106 or 1,000,000           milli            m          10 −3 or 0.001
           kilo            k           103 or 1000                micro            µ          10 −6 or 0.000001
                                                                  nano             n          10 −9 or
                                                                                              0.000000001
                                                                  pico             p          10 −12 or
                                                                                              0.000000000001

          Table 2.7 Common Units and Their Abbreviations                  Notice that the abbreviation for inch
          (in.) is the only abbreviation that ends in a period.
            Type of            Unit          Abbreviation       Type of             Unit              Abbreviation
            Measurement                                         Measurement
            English Mass       ton               ton            Time                year                yr or year
                               pound              lb                                day                  d or day
                               ounce              oz                                hour                 h or hr
            English Length     mile           mi or mile                            minute                 min
                               yard               yd                                second               s or sec
                               foot               ft
                               inch              in.            Temperature         Degree                 °C
                                                                                    Celsius
            English Volume     gallon             gal                               Degree                 °F
                                                                                    Fahrenheit
                               quart              qt                                kelvin                  K
                               pint               pt
                               fluid              fl oz           Energy              joule                      J
                               ounce
                               cubic             cu ft                              calorie                cal
                               foot
                               cubic            cu in.                              dietary                Cal
                               inch                                                 calorie
          Table 2.8 Comparison of the Mass and Weight of a 143 Pound Person.
                                On Earth                Between Earth and Moon                On the Moon
            Mass                 65 kg                         65 kg                            65 kg
            Weight               637 N                         ≈O N                      1/6 (637 N) = 106 N
                                                                                                    17


EXERCISE 2.4         - Metric-Metric Conversion Factors
Write conversion factors that include the following metric units.

      a. joule and kilojoule
      b. meter and centimeter
      c. liter and gigaliter
      d. gram and microgram
      e. gram and megagram
      f. pascal and millipascal

Table 2.9 English-Metric Unit Conversion Factors

 Type of              Probably most useful   Also useful to know
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Table 2.10 Densities of Some Common Substances at 20 °C (unless otherwise stated)

  Substance                        Density g/mL          Substance                   Density g/mL
  air at sea level                 0.0012                sodium chloride (salt)      2.16
                                   (or 1.2 g/L)
  Styrofoam                        0.03                  sulfur, S                   2.07
  pine wood                        0.4-0.6               glass                       2.4-2.8
  gasoline                         0.70                  silicon, Si                 2.32
  ethanol                          0.7893                aluminum, Al                2.702
  olive oil                        0.92                  diamond                     3.0-3.5
  ice                              0.92                  titanium, Ti                4.5
  water, H2O, at 20 °C             0.998204              Earth (average)             5.25
  water, H2O, at 0 °C              0.999840              iron, Fe                    7.86
  water, H2O, at 3.98 °C           1.00000               lead, Pb                    11.34
  sea water                        1.025                 mercury, Hg                 13.59
  whole blood                      1.05                  platinum, Pt                21.45
  sucrose (white sugar)            1.58                  osmium, Os                  22.48
  bone                             1.5-2.0               atomic nucleus              ≈1014
  sulfuric acid (concentrated)     1.84                  black hole (not 20 °C)      ≈1016
18    Chapter 2   Atoms and Elements




Sample Study           TIP-OFF After calculating a number using multiplication and division, you need to
Sheet 2.1              round it off to the correct number of significant figures.
Rounding
                       GENERAL STEPS
Off Numbers
Calculated             STEP 1 Determine whether each value is exact or not, and ignore exact values.
Using                             Numbers that come from definitions are exact.
Multiplication                         Numbers in metric-metric conversion factors that are derived from
and Division
                                       the metric prefixes are exact, such as

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                                       Numbers in English-English conversion factors with the same type of
                                       unit (for example, both length units) top and bottom are exact, such
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                                       The number 2.54 in the following conversion factor is exact.

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                                  Numbers derived from counting are exact. For example, there are exactly
                                  five toes in the normal foot.

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                                  Values that come from measurements are never exact.
                                  We will assume that values derived from calculations are not exact unless
                                  otherwise indicated. (With one exception, the numbers relating English
                                  to metric units that you will see in this text have been calculated and
                                  rounded, so they are not exact. The exception is 2.54 cm/1 in. The 2.54
                                  comes from a definition.)
                       STEP 2 Determine the number of significant figures in each value that is not exact.
                              All non-zero digits are significant.

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       Zeros between nonzero digits are significant.

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       Zeros to the right of nonzero digits in numbers that include decimal points are
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STEP 3 When multiplying and dividing, round your answer off to the same number
       of significant figures as the value containing the fewest significant figures.
       If the digit to the right of the final digit you want to retain is less than 5,
       round down (the last digit remains the same).

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20   Chapter 2   Atoms and Elements



                            If the digit to the right of the final digit you want to retain is 5 or greater,
                            round up (the last significant digit increases by 1).

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                     EXAMPLE See Exercises 2.5, 2.6, and 2.7.



           Table 2.11    Numbers That Are Exact.

             General Category             More Specific Category                           Examples
                                                                                                  5 fingers
             Values from Counting                                                         5 in
                                                                                                   1 hand
                                          Numbers in English-English                               12 in.
             Defined Values                Conversion Factors (with units of the           12 in
                                                                                                    1 ft
                                          same type of measurement)
                                          Numbers in Metric-Metric                                  103 mm
                                          Conversion Factors (with units of the           103 in
                                                                                                      1m
                                          same type of measurement)
                                          Some Numbers in English-Metric                             2.54 cm
                                                                                          2.54 in
                                          Conversion Factors (rare)                                    1 in.

             Values Calculated from                                                       10 calculated from
             Exact Numbers and not                                                                 5 fingers
                                                                                          2 hands
             Rounded (rare)                                                                         1 hand


           Table 2.12    Numbers That Are Not Exact

             Category                     Example
             Values from                  185.0 lb from a measurement
             measurements
             Values calculated from                                             �����
             numbers that are not         ����������       ����������������                ����������
             exact                                                             ��������
             Values calculated from                  27 students with As
             numbers that are exact,      33 from                        x 100 = 33% with As
             but for which the                        82 students total
             answer is rounded off
                                                                                               21


EXERCISE 2.5       - Significant Figures
Identify whether each of the following values is exact or not. If it is not exact, write the
number of significant figures it has.

       a. 8.0 in 8.0 mL (derived from a measurement)
       b. 80 from 80 desks in a classroom (determined by counting them)
                     2000 lb
       c. 2000 in
                      1 ton

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       d. 453.6 in
                      ����
                    103 mg
       e. 103 in
                      1g
       f. 0.1067 in 0.1067 oz (from the mass of a penny calculated from its
          measured mass of 3.023 g)
       g. 0.006665 in 0.006665 lb (calculated from the mass in ounces of the penny
          described in part f.)
       h. 10 in 10% of the tablet desks in a room are for left handed people
          (determined by counting 8 left-handed desks and counting 80 desks total
          and then calculating the percentage)
       i. 21 from 21% of the desks have initials carved in them (determined by
          counting 17 desks with initials and counting 80 desks total and then
          calculating the percentage)
       j. 6.00 x 103 from the temperature of the surface of the sun, 6.00 x 103 °C.




EXERCISE 2.6 - Rounding Off Answers Derived from
               Multiplication and Division

A first-class stamp allows you to send letters weighing up to 1 oz. (There are 16 ounces
per pound.) You weigh a letter and find it has a mass of 10.5 g. Can you mail this
letter with one stamp? The unit analysis setup for converting 10.5 g to ounces is below.
Identify whether each value in the setup is exact or not. Determine the number of
significant figures in each inexact value, calculate the answer, and report it to the correct
number of significant figures.

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22     Chapter 2   Atoms and Elements



                         EXERCISE 2.7 - Rounding Off Answers Derived from
                                        Multiplication and Division

                         The re-entry speed of the Apollo 10 space capsule was 11.0 km/s. How many hours
                         would it have taken for the capsule to fall through 25.0 miles of the stratosphere? The
                         unit analysis setup for this calculation is below. Identify whether each value in the
                         setup is exact or not. Determine the number of significant figures in each inexact value,
                         calculate the answer, and report it to the correct number of significant figures.

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Sample Study             TIP-OFF After calculating a number using addition and subtraction, you need to
Sheet 2.2:               round it off to the correct number of decimal positions.
Rounding
                         GENERAL STEPS
Off Numbers              STEP 1 Determine whether each value is exact, and ignore exact values (see Study
Calculated                      Sheet 2.1).
Using Addition           STEP 2 Determine the number of decimal places for each value that is not exact.
and Subtraction          STEP 3 Round your answer to the same number of decimal places as the inexact value
                                with the fewest decimal places.


                         EXERCISE 2.8 - Rounding Off Answers Derived from
                                        Addition and Subtraction

                         Report the answers to the following calculations to the correct number of decimal
                         positions. Assume that each number is ±1 in the last decimal position reported.
                           a. 684 - 595.325 =                  b. 92.771 + 9.3 =

                         EXERCISE 2.9 - Rounding Off Answers

                         The mass of a liquid can be found by first weighing a container, adding the liquid
                         to the container, weighing the container and the liquid, and finding the mass of the
                         liquid by subtracting the mass of the container from the total mass of container and
                         liquid. A container is found to have a mass of 42.6 g. When 10.2 mL of a liquid
                         is added to the container, the mass increases to 50.7 g. What is the density of this
                         substance? The set-up for this problem is below. Do the calculation and report your
                         answer to the correct significant figures.

                                   ?g   50.7 g - 42.6 g
                                      =
                                   mL     10.2 mL
                                                                                                          23



TIP-OFF You wish to express a given value in terms of a different unit or units.            Sample Study
GENERAL STEPS                                                                              Sheet 2.3:
STEP 1 State your question in an expression that sets the unknown unit(s) equal to
                                                                                           Calculations
        one or more of the values given.
                                                                                           Using Unit
       To the left of the equals sign, show the unit(s) you want in your answer.
                                                                                           Analysis
       To the right of the equals sign, start with an expression composed of the
        given unit(s) that parallels in kind and placement the units you want in your
        answer.
          If you want a single unit in your answer, start with a value that has a single
          unit.
          If you want a ratio of two units in your answer, start with a value that has
          a ratio of two units, or start with a ratio of two values, each of which has
          one unit. Put each type of unit in the position you want it to have in the
          answer.
STEP 2 Multiply the expression to the right of the equals sign by conversion factors
        that cancel unwanted units and generate the desired units.
        If you are not certain which conversion factor to use, ask yourself, “What is
        the fundamental conversion the problem requires and what conversion factor
        do I need to make that type of conversion?” Figure 2.5 provides a guide to
        useful conversion factors.
STEP 3 Do a quick check to be sure you used correct conversion factors and that your
        units cancel to yield the desired unit(s).
STEP 4 Do the calculation, rounding your answer to the correct number of
        significant figures and combining it with the correct unit.
24        Chapter 2    Atoms and Elements




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      Figure 2.5
      Types of Unit Conversions
      Here is a summary of some of the basic types of conversions that are common in chemistry
      and the types of conversion factors used to make them.
                                                                                                       25


  Here are more examples of the most useful types of unit analysis conversions.

EXAMPLE 2.1 - Metric-Metric Unit Conversions
Convert 4567.36 micrograms to kilograms.

Solution
When converting from one metric unit to another, convert from the given unit to the
base unit and then from the base unit to the unit that you want.
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EXAMPLE 2.2 - English-Metric Unit Conversions
Convert 475 miles to kilometers.

Solution
The conversion factor 2.54 cm/in. can be used to convert from an English to a metric
unit of length.
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Memorizing other English-metric conversion factors will save you time and effort. For
example, if you know that 1.609 km = 1 mi, the problem becomes much easier.
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EXAMPLE 2.3 - Unit Conversions Using Density
What is the volume in liters of 64.567 pounds of ethanol at 20 °C?

Solution
Pound is a mass unit, and we want volume. Density provides a conversion factor that
converts between mass and volume. You can find the density of ethanol on a table like
Table 2.10. It is 0.7893 g/mL at 20 °C.
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26   Chapter 2   Atoms and Elements



                     EXAMPLE 2.4 - Unit Conversions Using Percentage
                     The label on a can of cat food tells you there are 0.94 lb of cat food per can with 0.15%
                     calcium. If there are three servings per can, how many grams of calcium are in each
                     serving?
                     Solution
                     Note that two phrases in this question can be read as “something per something” and
                     therefore can be used as a unit analysis conversion factors. The phrase “three servings
                     per can” leads to the first conversion factor used below, and “0.94 lb of cat food per
                     can” leads to the second.
                     Percentages also provide ratios that can be used as unit analysis conversion factors.
                     Because percentages are assumed to be mass percentages unless otherwise indicated,
                     they tell us the number of mass units of the part for each 100 mass units of the whole.
                     The ratio can be constructed using any unit of mass as long as the same unit is written
                     in both the numerator and denominator. This leads to the third conversion factor in
                     our setup. The fourth conversion factor changes pounds to grams.
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                     EXAMPLE 2.5 - Converting a Ratio of Two Units
                     When 2.3942 kg of the sugar glucose are burned (combusted), 37.230 kJ of heat are
                     evolved. What is the heat of combustion of glucose in J/g? (Heat evolved is described
                     with a negative sign.)
                     Solution
                     When the answer you want is a ratio of two units, start your unit analysis setup with a
                     ratio of two units. Put the correct type of unit in the correct position in the ratio. For
                     this problem, we put the heat unit on the top and the mass unit on the bottom.
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                     EXAMPLE 2.6 - Cubic Length
                     The volume of a hydrogen atom is about 1.4 x 105 pm3. What is its volume in liters?

                     Solution
                     Squared or cubed units can often be converted by thinking about how to convert the
                     single unit and squaring or cubing the conversion factors necessary to convert the
                     single unit.
                                                                     3            3
                                                           1m            102 cm           1L
                          ? L = 1.4 ×    105   pm3                                                = 1.4 × 10 –26 L
                                                         1012   pm        1m          103   cm3
                                                                                              27


For each of the following exercises, write the unit analysis set-up, calculate your answer,
and report your answer with the correct significant figures and units.

EXERCISE 2.10 - UNIT ANALYSIS The average human body contains 13 gallons of
water. What is this volume in quarts?



EXERCISE 2.11 - UNIT ANALYSIS The diameter of a proton is 2 x 10 −15 meters.
What is this diameter in nanometers?



EXERCISE 2.12 - UNIT ANALYSIS The mass of an electron is 9.1093897 x 10 −31 kg.
What is this mass in nanograms?



EXERCISE 2.13 - UNIT ANALYSIS There are 2035 tons of sulfuric acid used to make
Jell-O each year. What is this mass in kilograms?



EXERCISE 2.14 - UNIT ANALYSIS A piece of Styrofoam has a mass of 88.978 g and
a volume of 2.9659 L. What is its density in g/mL?



EXERCISE 2.15 - UNIT ANALYSIS The density of blood plasma is 1.03 g/mL.
A 70 kg adult has about 2.5 L of blood plasma. What is the mass in kilograms of the
blood plasma in this person?



EXERCISE 2.16 - UNIT ANALYSIS Pain information is transferred through the
nervous system between 12 and 30 meters per second. If a student drops a textbook
on her toe, how long will it take for the pain information with a velocity of 18 m/s to
travel 6.0 feet to reach the brain?



EXERCISE 2.17 - UNIT ANALYSIS An electron takes 6.2 x 10 −9 seconds to travel
across a TV set that is 22 inches wide. What is the velocity of the electron in km/hr?
28   Chapter 2   Atoms and Elements



                     EXERCISE 2.18 - UNIT ANALYSIS The mass of the ocean is about 1.8 x 1021 kg.
                     If the ocean contains 0.041% by mass calcium ions, Ca2+, what is the mass in tons of
                     Ca2+ in the ocean?




                     EXERCISE 2.19 - UNIT ANALYSIS While you are at rest, your heart pumps
                     about 5.0 liters of blood per minute. Your brain gets about 15% by volume of your
                     blood. What volume of blood in liters is pumped through your brain in 1.0 hour of
                     rest?




                     EXERCISE 2.20 - UNIT ANALYSIS A normal adult has from 4 to 6 million red
                     blood cells per mm3 of blood. Consider a person with 5.5 L of blood and 5 x 106 red
                     blood cells per mm3 of blood. How many red blood cells does this person have?




     Figure 2.6 Temperature Scales

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The following is a summary of the steps for making temperature conversions.
       STEP 1 Write down the memorized equation for the conversion. Include the
       units.
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       STEP 2 Check your equation using the following criteria.
               •    To check when converting between Celsius and Fahrenheit:
                        Do the units cancel to yield the correct unit?
                        Would your equation show that 32 °F equals 0 °C?
               •    To check when converting between the Kelvin and Celsius scales,
                    be sure that your equation will lead to a kelvin value that is larger
                    than the degree Celsius value.
       STEP 3 Do the calculation and report your answer with the correct significant
       figures and unit.
               •    Remember to put the subtraction for the degree Fahrenheit to
                    degree Celsius conversion in parentheses when you push the
                    buttons on the calculator.
               •    Be careful with significant figures.


EXERCISE 2.21 - Temperature Conversions

  a. N,N-dimethylaniline, C6H5N(CH3)2, melts at 2.5 °C. What is
     N,N-dimethylaniline’s melting point in °F and K?



  b. Benzenethiol, C6H5SH, melts at 5.4 °F. What is benzenethiol’s melting point
     in °C and K?



  c. The hottest part of the flame on a Bunsen burner is found to be 2.15 × 103 K.
     What is this temperature in °C and °F?
30   Chapter 2   Atoms and Elements



                     Having Trouble?
                     The skills in this chapter build on each other. For example, to do unit conversions using
                     unit analysis, you need to be able to write conversion factors, and to write conversion
                     factors, you need to be familiar with units and their abbreviations for different types of
                     measurement. Here is a list of the major categories of tasks you need to be able to do
                     in order to work the problems in this chapter. You should go through the list in order
                     and be sure you have mastered each skill before you go on to the next one. You should
                     be able to do the following.
                     1. Convert between the type of measurement, the SI base unit for that type of
                        measurement, and the abbreviation for the units for length, mass, volume,
                        energy, and gas pressure. See Table 2.5.
                     2. Convert between the metric prefixes, their abbreviations, and their values for the
                        prefixes listed on Table 2.6.
                     3. Convert between the type of measurement, the units for that type of
                        measurement, and the abbreviations for the units for the units listed on Table
                        2.7.
                     4. Write metric-metric conversion factors from you knowledge of the metric
                        prefixes. See Table 2.8.
                             For example, knowing the milli(m) means 10 −3 leads to the following
                             conversion factor.
                                   103 mm
                                      1m
                     6. Write the English-metric conversion factors listed on Table 2.9.
                     7. Write percentage values as conversion factors.
                           For example, the fact that water is 88.81% oxygen leads to the following
                           conversion factor.
                                      88.81 g
                                   100 g H2O
                     8. Use the dimensional analysis format to work unit conversion problems. Be sure
                         you can use the strategies listed in Steps 2 and 3. These will help you to do more
                         difficult problems later.
                     9. Use your calculator efficiently to calculate answers from dimensional analysis
                         set-ups. This includes knowing how to input numbers described with scientific
                         notation, knowing how to raise values to a power, and knowing when to use your
                         parentheses buttons.
                     10. Recognize whether numbers are exact on not.
                     11. Round your answers to calculations to reflect the correct significant figures.