Transcript Figure 5.9

Zumdahl • Zumdahl • DeCoste
World of
CHEMISTRY
Chapter 5
Measurements
and Calculations
Goals of Chapter 5:
Measurement & Calculations
• Express numbers in scientific notation
• Learn English, metric, & SI system of
measurement
• Use metric system to measure length,
volume, and mass
• Significant digits
• Dimensional Analysis
• Temperature Scales
• Density/Specific Gravity
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Qualitative vs. Quantitative
• Qualitative: the substance was a white
powder
• Quantitative: The substance had a
mass of 5.6 grams
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Why are measurements important?
• Pay for gasoline by the gallon
• Construction: must have accurate
measurements
• Welding: measurements must be accurate
• Automobiles: Most items on cars have a
measurement
• Landscaping: Measurements important for
spatial relationships
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Measurements: 2 Parts
• Number + Unit
• Number alone is meaningless
• If I tell you a 2 x 4 is 5 long – what does this
mean: 5 feet, 5 inches, 5 meters?
• Unit alone is meaningless
• If I tell you the 2 x 4 is feet long – what does
this mean: 2 ft, 4 ft, 8 ft?
• ALWAYS INCLUDE BOTH NUMBER
AND UNIT!
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Scientific Notation
• Used to express very large or very small
numbers
• Express using number between 1 & 10
multiplied by a power of 10
• 10 is to positive power for large numbers
• 10 is to a negative number for small
numbers (decimals)
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Large Numbers
Decimal point moved to left
Power of 10 = # places moved = + number
125 = 1.25 x 100 = 1.25 x 102
Decimal point moved 2 places left
1700 = 1.7 x 1000 = 1.7 x 103
Decimal point moved 3 places left
93,000,000 = 9.3 x 107
Decimal point moved 7 places left
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Small Numbers (Decimals < 1.0)
Decimal point moved to the right
Power of 10 = # places moved = negative number
0.010 = 1.0 x 0.010 = 1.0 x 10-2
Decimal point moved right 2 places
0.000167 = 1.67 x 10-4
Decimal point moved right 4 places
0.089 = 8.9 x 10-2
Decimal point moved right 2 places
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Units
• Tell us what scale or standard is being used
to represent measurement
• Scientists need common units to represent
quantities like mass, length, time, and
temperature
• If everyone had own set of units – chaos
would result
• US uses English system, most of world (&
scientists) use metric system, also SI system
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BASIC UNITS
Physical Quantity
English System
Metric System
Mass
Pound or slug
Gram or kilogram
Length
inch, foot, yard
Centimeter or meter
Volume
Quart or gallon
Liter, milliliter, or cm3
Hours, minutes, seconds
Seconds
Degrees Fahrenheit
°C or Kelvin
Time
Temperature
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Metric Prefixes
Kilok
hecto-
deka-
h
dk
Move decimal point left
UNIT
deci-
centi-
milli-
d
c
m
Move decimal point right
Power of 10 between each increment
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Examples
1000 meters = 1 km (decimal moved 3 places left)
1 meter = 100 cm (decimal moved 2 places right)
10 mm = 1 cm (decimal moved 1 place left)
1 Liter = 1000 mL (decimal moved 3 places to right)
600 grams = 0.6 kg (decimal moved 3 places left)
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Table 5.2
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Table 5.3
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Figure 5.1: Comparison of English
and metric units.
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Figure 5.2:
Cube
representations.
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Figure 5.3:
A 100 mL
graduated cylinder.
1 mL = 1 cm3
1 milliliter = 1 cubic centimeter
100 mL = 100 cm3
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Uncertainty of Measurement
• When using instrument to measure
(such as a ruler or graduated cylinder),
we visualize divisions between
markings and estimate
• When making measurement, record all
certain numbers and first uncertain
number
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Figure 5.5: Measuring a pin.
Reading is between
2.8 cm & 2.9 cm
These divisions
were visualized
2.85 cm is
measurement
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“5” is uncertain
Significant Figures
• Includes all numbers recorded in a
measurement
• For pin, length = 2.85 cm: 3 significant
figures
• All certain numbers plus first uncertain
• Assume to be accurate to ± 1 in last #
• Pin length is 2.85 ± 0.01 cm
• Pin is somewhere between 2.84 & 2.86 cm
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Rules for Counting Significant Figures
• Significant & Non-significant zeros
• Leading zeros, precede non-zero digits =
nonsignificant
• Example: 0.0025 = 2 s.f. - zeros are non-significant
• Captive zeros (between nonzero digits) =
significant
• Example: 1.008 (4 s.f. - all numbers are significant)
• Trailing zeros (right end of number)
• Significant if bar is placed over zero or over zero to right
• Example: 200 (only #2 is significant = 1 s.f.)
2Ō0 (2 s.f. - 2 & Ō both significant)
20Ō (3 s.f. - 2 and both zeros are significant)
• Following decimal to right of nonzero digit =
significant
• 5.00 = 3 s.f.
Rules for counting significant figures
(continued)
• All nonzero integers are significant
• Example: 1457 has 4 s.f.
• Exact numbers have unlimited number of s.f.
• Determined by counting
• 8 apples, 21 students
• Not obtained from measuring devices
• From definitions
• 1 inch is exactly 2.54 cm
• Will not limit numbers in calculations
• Use same rules for scientific notation (10x
not s.f.)
To give answer with correct number
of significant figures – round off
• Look at number to right of last s.f.
• If number is <5 round down
• If number is ≥5 round up
• Do not round off until end of calculations
Rules for s.f. in calculations
• Multiplication & Division
• Answer should have same number of s.f. as
measurement with smallest number of s.f.
• Example: 4.56 x 1.4 = 6.384 → 6.4
(3 s.f.) (2 s.f.)*
(2 s.f.)*
• Addition & Subtraction
• Limited by smallest number of decimal places
• Example: 12.11
(2 decimal places)
18.0
(1 decimal place)*
+
1.013 (3 decimal places)
31.123 → 31.1 (1 decimal place)*
Figure 5.6: The three major temperature scales.
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Temperature Scales
Temperture Scale
Fahrenheit
Celsius
Kelvin
Abbreviation
°F
°C
K
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Boiling point H2 0 Freezing Point H 2O
212°F
32°F
100°C
0°C
373 K
273 K
Converting between Kelvin &
Celsius
To convert from Kelvin to Celsius:
T°C = TK – 273
Liquid Nitrogen boils at 77K, what is this in Celsius?
T°C = 77 – 273 = -196 °C
To convert from Celsius to Kelvin:
TK = T°C + 273
The bp of water on top of Mt. Everest is 70 °C. Convert to K.
TK = 70 + 273 = 343 K
Figure 5.7:
Converting 70
degrees
Celsius to Kelvin
units.
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Fahrenheit/Celsius Conversions
To convert from Celsius to Fahrenheit:
T°F = 1.80(T°C) + 32
If the temperature is 28°C, what is this in °F?
T°F = 1.80(28) + 32 = 50.4 + 32 = 82°F (2 s.f.)
To convert from Fahrenheit to Celsius:
T°C = (T°F – 32)/1.80
If you have a temperature of 101°F, what is this in °C?
T°C = (101 – 32)/1.80 = 69/1.8 = 38°C
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Figure 5.8: Comparison of the Celsius and Fahrenheit
scales.
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Density: amount of matter in a
given volume of substance
Density = mass / volume
•Determine mass using a balance
•Determine volume by calculations,
graduated cylinder, or water displacement
•Units are in g/cm3, g/mL, kg/L, lb/gal
Determining volume by water
displacement
• Place water in graduated cylinder &
record level
• Add object
• Record volume after addition of object
• Volume is difference between second
volume and first volume
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Figure 5.9: Tank of water.
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Figure 5.9: Person submerged in the tank.
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