Download Chapter 2

Introductory Chemistry:
A Foundation, 6th Ed.
Introductory Chemistry,
6th Ed.
Basic Chemistry, 6th Ed.
by Steven S. Zumdahl, Donald
J. DeCoste
University of Illinois
Chapter 2
Measurements
and
Calculations
Measurement
• Quantitative observation
• Comparison based on an accepted scale
– e.g. Meter stick
• Has 2 parts – number and unit
– Number tells comparison
– Unit tells scale
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Scientific Notation
• Technique used to express very large or
very small numbers
• Based on powers of 10
• To compare numbers written in scientific
notation
– First compare exponents of 10
– Then compare numbers
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Writing Numbers
in Scientific Notation
1 Locate the decimal point
2 Move the decimal point to the right of the nonzero digit in the largest place
– The new number is now between 1 and 10
3 Multiply the new number by 10n
– Where n is the number of places you moved the
decimal point
4 Determine the sign on the exponent n
– If the decimal point was moved left, n is +
– If the decimal point was moved right, n is –
– If the decimal point was not moved, n is 0
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Writing Numbers in Standard Form
1 Determine the sign of n of 10n
– If n is + the decimal point will move to the
right
– If n is – the decimal point will move to the left
2 Determine the value of the exponent of 10
– Tells the number of places to move the decimal
point
3 Move the decimal point and rewrite the
number
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Related Units in the Metric System
• All units in the metric system are related to
the fundamental unit by a power of 10
• Power of 10 is indicated by a prefix
• Prefixes are always the same, regardless of
the fundamental unit
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Some Fundamental SI Units
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Prefixes
• All units in the metric system utilize the
same prefixes
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Length
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Volume
• Measure of the
amount of 3-D space
occupied by a
substance
• SI unit = cubic meter
(m3)
• Commonly measure
solid volume in cubic
centimeters (cm3)
• 1 mL = 1 cm3
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Mass
• Measure of the amount of matter present in
an object
• SI unit = kilogram (kg)
• Commonly measure mass in grams (g) or
milligrams (mg)
– 1 kg = 2.2046 pounds, 1 lb = 453.59 g
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Uncertainty in Measured Numbers
• A measurement always has some amount of
uncertainty
• Uncertainty comes from limitations of the
techniques used for comparison
• To understand how reliable a measurement
is, we need to understand the limitations of
the measurement
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Reporting Measurements
• Significant figures: system used by
scientists to indicate the uncertainty of a
single measurement
• Last digit written in a measurement is the
number that is considered uncertain
• Unless stated otherwise, uncertainty in the
last digit is ±1
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Rules for Counting Significant Figures
• Nonzero integers are always significant
• Zeros
– Leading zeros never count as significant figures
– Captive zeros are always significant
– Trailing zeros are significant if the number has
a decimal point
• Exact numbers have an unlimited number of
significant figures
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Rules for Rounding Off
• If the digit to be removed
– Is less than 5, the preceding digit stays the same
– Is equal to or greater than 5, the preceding digit
is increased by 1
• In a series of calculations, carry the extra
digits to the final result, then round off
• Don’t forget to add place-holding zeros if
necessary to keep value the same!!
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Exact Numbers
• Exact numbers: numbers known with
certainty
– Counting numbers
• number of sides on a square
– Defined numbers
• 100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm
• 1 minute = 60 seconds
• Have unlimited number of significant figures
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Calculations with Significant Figures
• Calculators/computers do not know
about significant figures!!!
• Exact numbers do not affect the number of
significant figures in an answer
• Answers to calculations must be rounded to
the proper number of significant figures
– Round at the end of a calculation
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Multiplication/Division with
Significant Figures
• Result has the same number of significant
figures as the measurement with the smallest
number of significant figures
• Count the number of significant figures in
each measurement
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Multiplication/Division
with Significant Figures (cont.)
• Then round the result so it has the same
number of significant figures as the
measurement with the smallest number of
significant figures
4.5 cm
2 sig figs
x
0.200 cm = 0.90 cm2
3 sig figs
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2 sig figs
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Adding/Subtracting
Numbers with Significant Figures
• Result is limited by the number with the
smallest number of significant decimal places
• Find last significant figure in each
measurement
• Find which one is “left-most”
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Adding/Subtracting
Numbers with Significant Figures (cont.)
• Then round answer to the same decimal place
450 mL + 27.5 mL =
precise to 10’s place
precise to 0.1’s place
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480 mL
precise to 10’s place
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Problem Solving
and Dimensional Analysis
• Many problems in chemistry involve using
equivalence statements to convert one unit of
measurement to another
• Conversion factor = relationship between
two units
– May be exact or measured
– Both parts of the conversion factor should have
the same number of significant figures
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Problem Solving and
Dimensional Analysis (cont.)
• Conversion factors generated from
equivalence statements
2.54cm
– e.g. 1 inch = 2.54 cm can give
1in
1in
or
2.54cm
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Problem Solving and
Dimensional Analysis (cont.)
• Arrange conversion factors so starting unit
cancels
– Arrange conversion factor so starting unit is on
the bottom of the conversion factor
• May string conversion factors
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Converting One Unit to Another
• Find the relationship(s) between starting and
goal units. Write equivalence statement for
each relationship.
• Write a conversion factor for each equivalence
statement.
• Arrange the conversion factor(s) to cancel with
starting unit and result in goal unit.
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Converting One Unit to Another (cont.)
• Check that units cancel properly
• Multiply and divide the numbers to give the
answer with the proper unit.
• Check significant figures
• Check that your answer makes sense!
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Temperature Scales
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Density
• Density = property of matter representing
the mass per unit volume
Mass
Density 
Volume
• Volume of a solid can be determined by
water displacement
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Density (cont.)
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Using Density in Calculations
Mass
Density 
Volume
Mass
Volume 
Density
Mass  Density  Volume
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