1. Zumdahl • Zumdahl • DeCoste
World of
CHEMISTRY
Zumdahl • Zumdahl • DeCoste

2. Measurements and Calculations
Chapter 5
Measurements and Calculations

3. 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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4. Qualitative vs. Quantitative
Qualitative: appearance.
the substance was a white powder
Quantitative: Measurement
The substance had a mass of 5.6 grams
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5. 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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7. Copyright © Houghton Mifflin Company
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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9. Small Numbers (Decimals < 1.0)
Decimal point moved to the right
Power of 10 = # places moved = negative number
0.010 = 1.0 x = 1.0 x 10-2
Decimal point moved right 2 places
= 1.67 x 10-4
Decimal point moved right 4 places
0.089 = 8.9 x 10-2
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10. Copyright © Houghton Mifflin Company
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
Time
Hours, minutes, seconds
Seconds
Temperature
Degrees Fahrenheit
°C or Kelvin
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Metric Prefixes
Kilo- hecto deka- UNIT deci centi- milli-
k h dk d c m
Move decimal point left
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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16. Figure 5.1: Comparison of English and metric units.
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17. Figure 5.2: Cube representations.
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18. 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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19. Copyright © Houghton Mifflin Company
Dimensional Analysis
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20. 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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21. Figure 5.5: Measuring a pin.
Reading is between 2.8 cm & 2.9 cm
These divisions were visualized
2.85 cm is measurement
“5” is uncertain
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22. Significant Figures Ex.
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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23. Rules for Counting Significant Figures
Captive zeros (between nonzero digits)
Example: (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)

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Following decimal to right of nonzero digit = significant
5.00 = 3 s.f.
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25. Non-significant zeros
Leading zeros, precede non-zero digits
Example: = 2 s.f. - zeros are non-significant
Both: some numbers are sig. some are not
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26. 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

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Use same rules for scientific notation (10x not s.f.)
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28. 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

29. 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 = → 6.4
(3 s.f.) (2 s.f.)* (2 s.f.)*

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Addition & Subtraction
Limited by smallest number of decimal places
Example: (2 decimal places)
(1 decimal place)*
(3 decimal places)
→ (1 decimal place)*
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31. Figure 5.6: The three major temperature scales.
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32. Copyright © Houghton Mifflin Company
Temperature Scales
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33. 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
The bp of water on top of Mt. Everest is 70 °C. Convert to K.
TK = = 343 K

34. Figure 5.7: Converting 70 degrees Celsius to Kelvin units.
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35. 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 = = 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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36. Figure 5.8: Comparison of the Celsius and Fahrenheit scales.
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37. 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

38. 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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39. Copyright © Houghton Mifflin Company
Figure 5.9: Tank of water.
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40. Figure 5.9: Person submerged in the tank.
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