Transcript Chapter 2

Chapter 2
Measurements
and
Calculations
Scientific Notation
• Technique used to express very large or
very small numbers: for example,
2,009,345,234 or 0.00000045723
• Expressed as a product of a number
between 1 and 10 and a power of 10
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Writing Numbers
in Scientific Notation
1 Locate the decimal point.
2 Count the number of places the decimal point must
be moved to obtain a number 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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Write the following numbers in scientific notation:
A.
2,009,345,234
B.
0.00000045723
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Converting from Scientific Notation to
Standard Form
1 Determine the sign of n in 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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Convert from Scientific Notation to Standard Form:
2.0684 x 105
3.28409 x 10-4
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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.
• A power of 10 is indicated by a prefix.
• Prefixes are always the same, regardless of
the fundamental unit.
• Examples:
kilogram = 1000 grams
kilometer = 1000 meters
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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 3D 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)
1 kg = 2.205 pounds, 1 lb = 453.59 g
68 kg = 150 lbs
• Commonly measure mass in grams (g) or
milligrams (mg)
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Uncertainty in Measured Numbers
• A measurement always has some amount of
uncertainty.
• To understand how reliable a measurement
is, we must understand the limitations of the
measurement.
• Example:
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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.
example: 4.675 = 4 sig figs
• Zeros
– Leading zeros never count as significant figures.
example: 0.000748 = 3 sig figs
– Captive zeros are always significant.
example: 2.0087 = 5 sig figs
– Trailing zeros are significant if the number has a
decimal point.
example: 6.980 = 4 sig figs
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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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Rules for Rounding Off
• If the digit to be removed:
– is less than 5, the preceding digit stays the same.
example:
– is equal to or greater than 5, the preceding digit is
increased by 1.
example:
In a series of calculations, carry the extra digits to the final result,
then round off.
example:
• When rounding off use only the first number to the right of
the last significant figure.
example:
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Round these numbers to four significant figures:
•
•
•
•
157.387
443,678
80, 332
7.8097
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Multiplication/Division with
Significant Figures
• Result must have the same number of significant figures as
the measurement with the smallest number of significant
figures:
example: 3.5 x 3.5609 =
example: 4.98/11.76 =
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Adding/Subtracting
Numbers with Significant Figures
• Result is limited by the number with the
smallest number of significant decimal places
example:
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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 factors are generated from
equivalence statements.
– e.g. 1 mi = 5,280. ft can give:
1 mi/5280. ft or
5280. ft/1 mi
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Converting One Unit to Another
• Find the relationship(s) between starting and
goal units. Write equivalence statement for
each relationship.
Given quantity x unit factor = desired quantity
• 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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Convert the following: (Use Table 2.7)
• 180 lbs to kg
• 12.3 mi to in.
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Temperature Scales
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Some facts concerning the temperature scales:
• The size of each degree is the same for the
Celsius and Kelvin scales.
• The Fahrenheit degree is smaller than the
Celsius and Kelvin unit.
F – 180 degrees between freezing and boiling point of water
C – 100 degrees between freezing and boiling point of water
• All three scales have different zero points.
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Converting between Kelvin and Celsius Scales
ToC + 273 = K
• Celsius to Kelvin: add 273 to C temperature
example: Convert 46o C to K
• Kelvin to Celsius: subtract 273 from K temperature
example: Convert 4 K to C
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Converting from Celsius to Fahrenheit
• Requires two adjustments:
1. Different size units; 180 F degrees = 100 C degrees
2. Different zero points
ToF = 1.80(ToC) + 32
Convert 30oC to oF
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Converting from Fahrenheit to Celsius
ToC = (ToF – 32)/1.80
Convert 102oF to oC
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Density
Mass
Density 
Volume
• Volume of a solid can be determined by
water displacement.
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Using Density in Calculations
Mass
Density 
Volume
Mass
Volume 
Density
Mass  Density  Volume
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Using Density in Calculations
• Calculate the density of an object which weighs 35.7 g and occupies a
volume of 21.5 mL.
• Calculate the mass of a piece of copper which occupies
2.86 cm3. (density = 8.96 g/cm3)
• Calculate the volume of an object with a density of 4.78 g/mL
and mass of 20.6 grams.
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