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Chapter 1 Matter,Measurement, and Problem Solving


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Title: Chapter 1 Matter,Measurement, and Problem Solving

Chapter 1Matter,Measurement, and Problem
Classification of Matter
  • matter is anything that has mass and occupies
  • we can classify matter based on whether its
    solid, liquid, or gas
  • Fixed keeps shape when placed in a container
  • Indefinite takes the shape of the container

  • the particles in a solid are packed close
    together and are fixed in position
  • though they may vibrate
  • incompressible
  • the inability of the particles to move around
    results in solids retaining their shape and
    volume when placed in a new container, and
    prevents the particles from flowing

Crystalline vs. Amorphous solids
  • some solids have their particles arranged in an
    orderly geometric pattern we call these
    crystalline solids
  • salt and diamonds
  • some solids have their particles randomly
    distributed without any long-range pattern we
    call these amorphous solids
  • plastic
  • glass
  • charcoal

  • the particles in a liquid are closely packed, but
    they have some ability to move around
  • Incompressible
  • take the shape of their container and to flow
  • however, they dont have enough freedom to escape
    and expand to fill the container

  • in the gas state, the particles have complete
    freedom from each other
  • the particles are constantly flying around,
    bumping into each other and the container
  • Compressible
  • because there is a lot of empty space, the
    particles can be squeezed closer together
    therefore gases are compressible
  • because the particles are not held in close
    contact and are moving freely, gases expand to
    fill and take the shape of their container, and
    will flow

Classification of Matterby Composition
  1. made of multiple types of particles
  2. samples may show different intensive properties
  1. made of one type of particle
  2. all samples show the same intensive properties

Classification of Pure Substances
  1. made of one type of molecule, or array of ions
  2. molecules contain 2 or more different kinds of
  1. made of one type of atom (some elements found as
    multi-atom molecules in nature)
  2. combine together to make compounds

Classification of Mixtures
  1. made of multiple substances, whose presence can
    be seen
  2. portions of a sample have different composition
    and properties
  1. made of multiple substances, but appears to be
    one substance
  2. all portions of a sample have the same
    composition and properties

Separation of Mixtures
  • separate mixtures based on different physical
    properties of the components
  • Physical change

Changes in Matter
  • changes that alter the state or appearance of the
    matter without altering the composition are
    called physical changes
  • state changes
  • boiling / condensing
  • melting / freezing
  • subliming

Physical change vs. Chemical change
  • changes that alter the composition of the matter
    are called chemical changes
  • during the chemical change, the atoms that are
    present rearrange into new molecules, but all of
    the original atoms are still present
  • rusting
  • processes that release lots of energy
  • burning

Burning propane gas
  • changes in matter, both physical and chemical,
    result in the matter either gaining or releasing
  • energy is the capacity to do work
  • work is the action of a force applied across a
  • a force is a push or a pull on an object
  • electrostatic force is the push or pull on
    objects that have an electrical charge

  • kinetic energy is energy of motion
  • motion of the atoms, molecules, and subatomic
  • potential energy is energy that is stored in the
  • due to the composition of the matter and its
    position in the universe
  • chemical potential energy arises from
    electrostatic forces between atoms, molecules,
    and subatomic particles
  • Law of Conservation of Energy
  • energy is neither created nor destroyed. It is
    converted from one form to another

  • measure of the average amount of kinetic energy
  • higher temperature larger average kinetic
  • heat flows from the matter that has high thermal
    energy into matter that has low thermal energy
  • until they reach the same temperature
  • heat is exchanged through molecular collisions
    between the two materials

Temperature Scales
  • Fahrenheit Scale, F
  • used in the U.S.
  • Celsius Scale, C
  • used in all other countries
  • Kelvin Scale, K
  • absolute scale
  • no negative numbers
  • directly proportional to average amount of
    kinetic energy
  • 0 K absolute zero

Fahrenheit vs. Celsius
  • a Celsius degree is 1.8 times larger than a
    Fahrenheit degree
  • the standard used for 0 on the Fahrenheit scale
    is a lower temperature than the standard used for
    0 on the Celsius scale
  • the size of a degree on the Kelvin scale is the
    same as on the Celsius scale
  • so 1 kelvin is 1.8 times larger than 1F
  • the 0 standard on the Kelvin scale is a much
    lower temperature than on the Celsius scale

TC (TF 32)
TF 1.8 TC 32
K C 273.15
  • The melting point of gallium is 85.6oF. What is
    this temperature on
  • Celsius scale
  • Kelvin scale

The Standard Units
  • Scientists have agreed on a set of international
    standard units for comparing all our measurements
    called the SI units
  • Système International International System

Quantity Unit Symbol
length meter m
mass kilogram kg
time second s
temperature kelvin K
Common Prefix Multipliers in the SI System
All units in the SI system are related to the
standard unit by a power of 10 The power of 10 is
indicated by a prefix multiplier The prefix
multipliers are always the same, regardless of
the standard unit Report measurements with a unit
that is close to the size of the quantity being
Prefix Symbol Decimal Equivalent Power of 10
mega- M 1,000,000 Base x 106
kilo- k 1,000 Base x 103
deci- d 0.1 Base x 10-1
centi- c 0.01 Base x 10-2
milli- m 0.001 Base x 10-3
micro- m or mc 0.000 001 Base x 10-6
nano- n 0.000 000 001 Base x 10-9
pico p 0.000 000 000 001 Base x 10-12
Common Units and Their Equivalents
1 kilogram (km) 2.205 pounds (lb)
1 pound (lb) 453.59 grams (g)
1 ounce (oz) 28.35 grams (g)
1 liter (L) 1000 milliliters (mL)
1 liter (L) 1000 cubic centimeters (cm3)
1 liter (L) 1.057 quarts (qt)
1 U.S. gallon (gal) 3.785 liters (L)
1 kilometer (km) 0.6214 mile (mi)
1 meter (m) 39.37 inches (in.)
1 meter (m) 1.094 yards (yd)
1 foot (ft) 30.48 centimeters (cm)
1 inch (in.) 2.54 centimeters (cm) exactly
  • Derived unit
  • any length unit cubed
  • Measure of the amount of space occupied
  • SI unit cubic meter (m3)
  • Commonly measure solid volume in cubic
    centimeters (cm3)
  • Commonly measure liquid or gas volume in
    milliliters (mL)

Mass Volume
  • two main physical properties of matter
  • mass and volume are extensive properties
  • the value depends on the quantity of matter
  • extensive properties cannot be used to identify
    what type of matter something is
  • Large iceberg and small ice cube
  • even though mass and volume are individual
    properties, for a given type of matter they are
    related to each other!

  • Ratio of massvolume is an intensive property
  • value independent of the quantity of matter
  • Solids g/cm3
  • 1 cm3 1 mL
  • Liquids g/mL
  • Gases g/L
  • Volume of a solid can be determined by water
    displacement Archimedes Principle
  • Density solids gt liquids gtgtgt gases
  • except ice is less dense than liquid water!
  • For equal volumes, denser object has larger mass
  • For equal masses, denser object has smaller
  • Heating an object generally causes it to expand,
    therefore the density changes with temperature

A Measurement
  • the unit tells you what standard you are
    comparing your object to
  • the number tells you
  • what multiple of the standard the object
  • the uncertainty in the measurement
  • scientific measurements are reported so that
    every digit written is certain, except the last
    one which is estimated
  • If the length is reported as 3.26 cm,
  • the digits 3 and 2 are certain (known).
  • the final digit, 6, is estimated (uncertain).
  • all three digits (2, 7, and 6) are significant,
    including the estimated digit.

Known Estimated Digits
For the following volume readings, what would be
measured values?
E.g l8. . . . l . . . . l9. . . . l . . . .
l10. . cm What is the length of the line? 1)
9.2 cm 2) 9.13 cm 3) 9.19 cm
Uncertainty in Measured Numbers
  • accuracy is an indication of how close a
    measurement comes to the actual value of the
  • precision is an indication of how reproducible a
    measurement is

Accuracy, Precision, and Significant Figures
  • Significant figures The number of meaningful
    digits in a measured or calculated quantity. They
    come from uncertainty in any measurement.
  • Generally the last digit in a reported
    measurement is uncertain (estimated).
  • Exact numbers and relationships (7 days in a
    week, 30 students in a class, etc.) effectively
    have an infinite number of significant figures.

  • Classify each of the following as (1) exact or
    (2) measured
  • numbers.
  • A.__Gold melts at 1064 C.
  • B.__1 yard 3 feet
  • C.__The diameter of a red blood cell is 6 x 10-4
  • D.__There are 6 hats on the shelf.
  • E.__A can of soda contains 355 mL of soda.

Accuracy, Precision, and Significant Figures
  • Rules for counting significant figures
  • Zeros in the middle of a number are like any
    other digit they are always significant.
  • 4.803 cm 4 sf
  • 2. Rules for counting significant figures
  • Zero at the beginning of a number are not
    significant (placeholders).
  • 0.00661 g 3 sf or 6.61 x 10-3 g
  • 3. Zeros at the end of a number and after the
    decimal point are always significant.
  • 55.220 K 5 sf
  • 4. Zeros at the end of a number without a written
    decimal point are ambiguous and should be avoided
    by using scientific notation
  • if 150 has 2 sig. figs. then 1.5 x 102
  • but if 150 has 3 sig. figs. then 1.50 x 102

Rounding Numbers
  • If the first digit you remove is 4 or less, it
    and all following digits are dropped from the
  • 5.664 425 5.664 (4 s.f)
  • If the digit you remove is 5 or greater, the
    last digit of the number is increases by 1
  • 5.664 525 5.665 (4 s.f)
  • Sometimes, a calculator displays a small whole
    number. To give an answer with the correct
    number of significant figures, significant zeros
    may need to be written after the calculator
  • E.g 8.00 2.00 4 ?
  • 3 s.f 3 s.f calculator
    2 zeros are needed

  • result to give 3 s.f

Significant figures in calculation
  • When multiplying or dividing
  • the final answer must have the same number of
    significant figures as the measurement with the
    fewest significant figures.
  • Example
  • 110.5 x 0.048 5.304 5.3
  • 4 SF 2 SF calculator
    2 SF
  • When adding or subtracting
  • the final answer must have the same number of
    decimal places as the measurement with the fewest
    decimal places.
  • 25.2 one decimal place
  • 1.34 two decimal places
  • 26.54 calculated answer
  • 26.5 final answer with one decimal

Both Multiplication/Division and
Addition/Subtraction with Significant Figures
  • when doing different kinds of operations with
    measurements with significant figures, do
    whatever is in parentheses first, evaluate the
    significant figures in the intermediate answer,
    then do the remaining steps
  • 3.489 (5.67 2.3)
  • 2 dp 1 dp
  • 3.489 3.37 12
  • 4 sf 1 dp 2 sf 2 sf

Metric Equalities
  • An equality
  • states the same measurement in two different
  • can be written using the relationships between
    two metric units.
  • Example 1 meter is the same as 100 cm and 1000
  • 1 m 100 cm
  • 10-2 m 1cm
  • 1 m 1000 mm
  • 10-3m 1 mm

Conversion Factors
  • A conversion factor is
  • obtained from an equality.
  • E.g Metric U.S system
  • Equality 1 in. 2.54 cm
  • written as a fraction (ratio) with a numerator
    and denominator.
  • inverted to give two conversion factors for every
  • 1 in. 1 2.54 cm
  • 2.54 cm 1 in.

Arrange conversion factors so given unit
cancels Arrange conversion factor so given unit
is on the bottom of the conversion factor
Using Two or More Factors
  • Often, two or more conversion factors are
    required to obtain the unit needed for the
  • Unit 1 Unit 2 Unit 3
  • Additional conversion factors are placed in the
    setup problem to cancel each preceding unit.
  • Given unit x factor 1 x factor 2
    needed unit
  • Unit 1 x Unit 2 x Unit 3
    Unit 3
  • Unit 1 Unit 2

  • If a ski pole is 3.0 feet in length, how long is
    the ski pole in m?
  • Convert 288.0 cm to yard
  • Convert 9255 cm3 to gallons

1.8 Density
  • Density
  • compares the mass of an object to its volume.
  • is the mass of a substance divided by its volume.
  • Density Expression
  • Density mass g or g g/cm3
  • volume mL cm3
  • Note 1 mL 1 cm3
  • Can we use density as a conversion factor to
    calculate mass or volume?

  • What is the density (g/cm3) of 48.0 g of a metal
    if the level of water in a graduated cylinder
    rises from 25.0 mL to 33.0 mL after the metal is
  • A drop of gasoline has a mass of 22.0 mg and a
    density of 0.754 g/cm3. What is its volume in

33.0 mL
25.0 mL
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