Chapter 2: Scientific Measurements

1
Chapter 2 Scientific Measurements

• Chemistry The Molecular Nature of Matter, 6E
• Jespersen/Brady/Hyslop

2
Properties

• Characteristics used to classify matter
• Physical properties
• Can be observed without changing chemical makeup
  of substance
• Ex. Gold metal is yellow in color
• Sometimes observing physical property causes
  physical change in substance
• Ex. Melting point of water is 0 C
• Measuring melting temperature at which solid
  turns to liquid

3
States of Matter

• Solids
• Fixed shape volume
• Particles are close together
• Have restricted motion
• Liquids
• Fixed volume, but take container shape
• Particles are close together
• Are able to flow
• Gases
• Expand to fill entire container
• Particles separated by lots of space
• Ex. Ice, water, steam

4
States of Matter

• Physical Change
• Change from 1 state to another
• Physical States
• Important in chemical equations
• Ex. 2C4H10(g) 13O2(g) ? 8CO2(g) 10H2O(g)
• Indicate after each substance with abbreviation
  in parentheses
• Solids (s)
• Liquids (l)
• Gases (g)
• Aqueous solutions (aq)

5
Chemical Properties

• Chemical change or reaction that substance
  undergoes
• Chemicals interact to form entirely
  differentsubstances with different chemical
  physical properties
• Describes behavior of matter that leads to
  formation of new substance
• Reactivity" of substance
• Ex. Iron rusting
• Iron interacts with oxygen to form new substance

6
Learning Check Chemical or Physical Property?
Chemical Physical




X
Magnesium metal is grey
X
Magnesium metal tarnishes in air
X
Magnesium metal melts at 922 K
Magnesium reacts violently with hydrochloric acid
X
7
Your Turn!

• Which one of the following represents a physical
  change?
• when treated with bleach, some dyed fabrics
  change color
• grape juice left in an open unrefrigerated
  container turns sour
• when heated strongly, sugar turns dark brown
• in cold weather, water condenses on the inside
  surface of single pane windows
• when ignited with a match in open air, paper burns

8
Intensive vs. Extensive Properties

• Intensive properties
• Independent of sample size
• Used to identify substances
• Ex. Color
• Density
• Boiling point
• Melting point
• Chemical reactivity
• Extensive properties
• Depend on sample size
• Ex. volume mass

9
Identification of Substances by Their Properties

• Ex. Flask of clear liquid in lab. Do you drink
  it?
• What could it be?
• What can we measure to determine if it is safe
  to drink?

Density
Melting Point
Boiling Point
Electrical conductivity
1.00 g/mL
0.0 C
100 C
None
10
Gold or Fools Gold?

• Can test by heating in flame
• Real gold
• Nothing happens
• Pyrite (Fools Gold)
• Sputters
• Smokes
• Releases foul-smelling fumes
• Due to chemical ability to react chemically with
  oxygen when heated

11
Your Turn!

• Which of the following is an extensive property?
• Density
• Melting point
• Color
• Temperature
• Mass

12
Observations

• Fall into 2 categories
• Quantitative observations
• Numeric data
• Measure with instrument
• Ex. Melting point, boiling point, volume, mass
• Qualitative observations
• Do not involve numerical information
• Ex. Color, rapid boiling, white solid forms

13
Measurements Include Units!!

• Measurements involve comparison
• Always measure relative to reference
• Ex. Foot, meter, kilogram
• Measurement number unit
• Ex. Distance between 2 points 25
• What unit? inches, feet, yards, miles
• Meaningless without units!!!
• Measurements are inexact
• Measuring involves estimation
• Always have uncertainty
• The observer instrument have inherent physical
  limitations

14
International System of Units (SI)

• Standard system of units used in scientific
  engineering measurements
• Metric ? 7 Base Units

15
SI Units

• Focus on 1st six in this book
• All physical quantities will have units derived
  from these 7 SI base units
• Ex. Area
• Derived from SI units based on definition of area
• length width area
• meter meter area
• m m m2
• SI unit for area square meters m2
• Note Units undergo same kinds of mathematical
  operations that numbers do!

16
Learning Check

• What is the SI unit for velocity?
• What is the SI unit for volume of a cube?
• Volume (V) length width height
• V meter meter meter
• V m3

17
Your Turn!

• The SI unit of length is the
• millimeter
• meter
• yard
• centimeter
• foot

18
Table 2.2 Some Non-SI Metric Units Commonly Used
in Chemistry
19
Table 2.3 Some Useful Conversions
20
Decimal Multipliers
21
Using Decimal Multipliers

• Use prefixes on SI base units when number is too
  large or too small for convenient usage
• Only commonly used are listed here
• For more complete list see Table 2.4 in textbook
• Numerical values of multipliers can be
  interchanged with prefixes
• Ex. 1 mL 103 L
• 1 km 1000 m
• 1 ng 109 g
• 1,130,000,000 s 1.13 109 s 1.13 Gs

22
Laboratory Measurements

• 4 common
• Length
• Volume
• Mass
• Temperature

23
Laboratory Measurements

• Length
• SI Unit is meter (m)
• Meter too large for most laboratory measurements
• Commonly use
• Centimeter (cm)
• 1 cm 102 m 0.01 m
• Millimeter (mm)
• 1 mm 103 m 0.001 m

24
2. Volume (V)

• Dimensions of (length)3
• SI unit for Volume m3
• Most laboratory measurements use V in liters (L)
• 1 L 1 dm3 (exactly)
• Chemistry glassware marked in L or mL
• 1 L 1000 mL
• What is a mL?
• 1 mL 1 cm3

25
3. Mass

• SI unit is kilogram (kg)
• Frequently use grams (g) in laboratory as more
  realistic size
• 1 kg 1000 g 1 g 0.1000 kg g
• Mass is measured by comparing weight of sample
  with weights of known standard masses
• Instrument used balance

26
4. Temperature

• Measured with thermometer
• 3 common scales
• Fahrenheit scale
• Common in US
• Water freezes at 32 F and boils at 212 F
• 180 degree units between melting boiling points
  of water

27
4. Temperature

• Celsius scale
• Rest of world (aside from U.S.) uses
• Most common for use in science
• Water freezes at 0 C
• Water boils at 100 C
• 100 degree units between melting boiling points
  of water

28
4. Temperature

• C. Kelvin scale
• SI unit of temperature is kelvin (K)
• Note No degree symbol in front of K
• Water freezes at 273.15 K boils at 373.15 K
• 100 degree units between melting boiling points
• Only difference between Kelvin Celsius scale is
  zero point
• Absolute Zero
• Zero point on Kelvin scale
• Corresponds to natures lowest possible
  temperature

29
Temperature Conversions

• How to convert between F and C?
• Ex. 100 C ? F
• tF 212 F

30
Temperature Conversions

• Common laboratory thermometers are marked in
  Celsius scale
• Must convert to Kelvin scale
• Amounts to adding 273.15 to Celsius temperature
• Ex. What is the Kelvin temperature of a solution
  at 25 C?

298 K
31
Learning Check T Conversions

• 1. Convert 100. F to the Celsius scale.
• 2. Convert 100. F to the Kelvin scale.
• We already have in C so

38 C
TK 311 K
32
Learning Check T Conversions

• 3. Convert 77 K to the Celsius scale.
• 4. Convert 77 K to the Fahrenheit scale.
• We already have in C so

196 C
321 F
33
Your Turn!

• In a recent accident some drums of uranium
  hexafluoride were lost in the English Channel.
  The melting point of uranium hexafluouride is
  64.53 C. What is the melting point of uranium
  hexafluoride on the Fahrenheit scale?
• 67.85 F
• 96.53 F
• 116.2 F
• 337.5 F
• 148.2 F

34
Uncertainties in Measurements

• Measurements all inexact
• Contain uncertainties or errors
• Sources of errors
• Limitations of reading instrument
• Ways to minimize errors
• Take series of measurements
• Data clusters around central value
• Calculate average or mean values
• Report average value

35
Limits in Reading Instruments

• Consider 2 Celsius thermometers
• Left thermometer has markings every 1 C
• T between 24 C 25 C
• About 3/10 of way between marks
• Can estimate to 0.1 C uncertainty
• T 24.3 ? 0.1 C
• Right thermometer has markings every 0.1 C
• T reading between 24.3 C 24.4 C
• Can estimate 0.01 C
• T 24.32 ? 0.01 C

36
Limits in Reading Instruments

• Finer graduations in markings
• Means smaller uncertainties in measurements
• Reliability of data
• Indicated by number of digits used to represent
  it
• What about digital displays?
• Mass of beaker 65.23 g on digital balance
• Still has uncertainty
• Assume ½ in last readable digit
• Record as 65.230 ? 0.005 g

37
Significant Figures

• Scientific convention
• All digits in measurement up to including 1st
  estimated digit are significant.
• Number of certain digits plus 1st uncertain digit
• Digits in measurement from 1st non-zero number on
  left to 1st estimated digit on right

38
Rules for Significant Figures

• All non-zero numbers are significant.
• Ex. 3.456
• has 4 sig. figs.
• Zeros between non-zero numbers are significant.
• Ex. 20,089 or 2.0089 104
• has 5 sig. figs
• Trailing zeros always count as significant if
  number has decimal point
• Ex. 500. or 5.00 102
• has 3 sig. figs

39
Rules for Significant Figures

• Final zeros on number without decimal point are
  NOT significant
• Ex. 104,956,000 or 1.04956 108
• has 6 sig. figs.
• Final zeros to right of decimal point are
  significant
• Ex. 3.00 has 3 sig. figs.
• 6. Leading zeros, to left of 1st nonzero digit,
  are never counted as significant
• Ex. 0.00012 or 1.2 104
• has 2 sig. figs.

40
Learning Check

• How many significant figures does each of the
  following numbers have?
• scientific notation of Sig. Figs.
• 413.97
• 0.0006
• 5.120063
• 161,000
• 3600.

4.1397 102
5
6 104
1
5.120063
7
1.61 105
3
3.6 103
2
41
Your Turn!

• How many significant figures are in 19.0000?
• 2
• 3
• 4
• 5
• 6

42
Rounding to Correct Digit

• If digit to be dropped is greater than 5, last
  remaining digit is rounded up.
• Ex. 3.677 is rounded up to 3.68
• If number to be dropped is less than 5, last
  remaining digit stays the same.
• Ex. 6.632 is rounded to 6.63
• If number to be dropped is 5, then if digit to
  left of 5 is
• Even, it remains the same.
• Ex. 6.65 is rounded to 6.6
• Odd, it rounds up
• Ex. 6.35 is rounded to 6.4

43
Scientific Notation

• Clearest way to present number of significant
  figures unambiguously
• Report number between 1 10 followed by correct
  power of 10
• Indicates only significant digits
• Ex. 75,000 people attend a concert
• If rough estimate?
• Uncertainty ?1000 people
• 7.5 104
• Number estimated from aerial photograph
• Uncertainty ?100 people
• 7.50 104

44
Learning Check

• Round each of the following to 3 significant
  figures. Use scientific notation where needed.
• 37.459
• 5431978
• 132.7789003
• 0.00087564
• 7.665

37.5 or 3.75 101
5.43 106
133 or 1.33 102
8.77 104
7.66
45
Accuracy Precision

• Accuracy
• How close measurement is to true or accepted true
  value
• Measuring device must be calibrated with standard
  reference to give
• correct value
• Precision
• How well set of repeated measurements of same
  quantity
• agree with each other
• More significant figures more
• precise measurement

46
Significant Figures in Calculations

• Multiplication and Division
• Number of significant figures in answer number
  of significant figures in least precise
  measurement
• Ex. 10.54 31.4 16.987
• 4 sig. figs. 3 sig. figs. 5 sig. figs 3
  sig. figs.
• Ex. 5.896 0.008
• 4 sig. figs. 1 sig. fig. 1 sig. fig.

5620 5.62103
700 7102
47
Your Turn!

• Give the value of the following calculation to
  the correct number of significant figures.
• 1.21213
• 1.212
• 1.212132774
• 1.2
• 1

48
Significant Figures in Calculations

• Addition and Subtraction
• Answer has same number of decimal places as
  quantity with fewest number of decimal places.
• Ex.
• Ex.

4 decimal places 1 decimal place 3 decimal
places 1 decimal place
12.9753 319.5 4.398
336.9
0 decimal places 2 decimal places 0 decimal place
397 273.15
124
49
Your Turn!

• When the expression,
• 412.272 0.00031 1.00797 0.000024 12.8
• is evaluated, the result should be expressed as
• 424.06
• 424.064364
• 424.1
• 424.064
• 424

50
Exact Numbers

• Number that come from definitions
• 12 in. 1 ft
• 60 s 1 min
• Numbers that come from direct count
• Number of people in small room
• Have no uncertainty
• Assume they have infinite number of significant
  figures.
• Do not affect number of significant figures in
  multiplication or division

51
Learning Check

• For each calculation, give the answer to the
  correct number of significant figures.
• 10.0 g 1.03 g 0.243 g
• 19.556 C 19.552 C
• 327.5 m 4.52 m
• 15.985 g 24.12 mL

11.3 g or 1.13 101 g
0.004 C or 4 103 C
1.48 103 m
0.6627 g/mL or 6.627 g/mL
52
Learning Check

• For the following calculation, give the answer to
  the correct number of significant figures.
• 1.
• 2.

2 104 m/s2
0.87 cm3/s
53
Your Turn!

• For the following calculation, give the answer to
  the correct number of significant figures.
• 179 cm2
• 1.18 cm
• 151.2 cm
• 151 cm
• 178.843 cm2

54
Dimensional Analysis

• Factor-Label Method
• Not all calculations use specific equation
• Use units (dimensions) to analyze problem
• Conversion Factor
• Fraction formed from valid equality or
  equivalence between units
• Used to switch from one system of measurement
  units to another

55
Conversion Factors

• Ex. How to convert a persons height from 68.0 in
  to cm?
• Start with fact
• 2.54 cm 1 in.
• Dividing both sides by 1 in. or 2.54 cm gives 1
• Cancel units
• Leave ratio that equals 1
• Use fact that units behave as numbers do in
  mathematical operations

1
1
56
Dimensional Analysis

• Now multiply original number by conversion factor
  that cancels old units leaves new
• Dimensional analysis can tell us when we have
  done wrong arithmetic
• Units not correct

173 cm
26.8 in2/cm
57
Using Dimensional Analysis

• Ex. Convert 0.097 m to mm.
• Relationship is 1 mm 1 103 m
• Can make 2 conversion factors
• Since going from m to mm use one on left.

173 cm
58
Learning Check

• Ex. Convert 3.5 m3 to cm3.
• Start with basic equality 1 cm 0.01 m
• Now cube both sides
• Units numbers
• (1 cm)3 (0.01 m)3
• 1 cm3 1 106 m3
• Can make 2 conversion factors

or
3.5 106 Cm3
59
Non-metric to Metric Units

• Convert speed of light from 3.00108 m/s to mi/hr
• Use dimensional analysis
• 1 min 60 s 60 min 1 hr
• 1 km 1000 m 1 mi 1.609 km

1.08 1012 m/hr
6.71 108 mi/hr
60
Your Turn!

• The Honda Insight hybrid electric car has a gas
  mileage rating of 56 miles to the gallon. What
  is this rating expressed in units of kilometers
  per liter?
• 1 gal 3.784 L 1 mile 1.609 km
• 1.3 102 km L1
• 24 km L1
• 15 km L1
• 3.4 102 km L1
• 9.2 km L1

61
Law of Multiple Proportions

• If 2 elements form more than 1 compound they
  combine in different ratios by mass
• Same mass of 1 element combines with different
  masses of 2nd element in different compounds
• Experimentally hard to get exactly same mass of 1
  element in 2 or more experiments
• Can use dimensional analysis to calculate

62
Applying Law of Multiple Proportions

• Titanium forms 2 different compounds with
  bromine. In compound A we find that 4.787 g of Ti
  are combined with 15.98 g of bromine. In compound
  B we find that 6.000 g of Ti are combined with
  40.06 g of bromine. Determine whether these data
  support the law of multiple proportions.
• Analysis
• Need same mass of 1 element compare masses of
  2nd element
• 6.000 g Ti for each
• How much Br?

63
Applying Law of Multiple Proportions

• Know
• In compound A 4.787 g Ti ? 15.98 g Br
• In compound B 6.000 g Ti ? 40.06 g Br
• Must find
• 6.000 g Ti ? ? g Br (compound A)
• Solution

20.03 g Br
Compare

• Ratio of small whole numbers
• Supports law of multiple proportions

64
Density

• Ratio of objects mass to its volume
• Intensive property (size independent)
• Determined by taking ratio of 2 extensive
  properties (size dependent)
• Frequently ratio of 2 size dependent properties
  leads to size independent property
• Sample size cancels
• Units
• g/mL or g/cm3

65
Learning Check

• A student weighs a piece of gold that has a
  volume of 11.02 cm3 of gold. She finds the mass
  to be 212 g. What is the density of gold?

19.3 g/cm3
66
Density

• Most substances expand slightly when heated
• Same mass
• Larger volume
• Less dense
• Density ? slightly as T ?
• Liquids Solids
• Change is very small
• Can ignore except in very precise calculations
• Density useful to transfer between mass volume
  of substance

67
Learning Check

• 1. Glass has a density of 2.2 g/cm3. What is
  the volume occupied by 22 g of glass?
• 2. What is the mass of 400 cm3 of glass?

10. g/cm3
880 g
68
Your Turn!

• Titanium is a metal used to make artificial
  joints. It has a density of 4.54 g/cm3. What
  volume will a titanium hip joint occupy if its
  mass is 205 g?
• 9.31 102 cm3
• 4.51 101 cm3
• 2.21 102 cm3
• 1.07 103 cm3
• 2.20 101 cm3

69
Your Turn!

• A sample of zinc metal (density 7.14 g cm-3)
  was submerged in a graduated cylinder containing
  water. The water level rose from 162.5 cm3 to
  186.0 cm3 when the sample was submerged. How
  many grams did the sample weigh?
• 1.16 103 g
• 1.33 103 g
• 23.5 g
• 1.68 102 g
• 3.29 g

70
Specific Gravity

• Ratio of density of substance to density of water
• Unitless
• Way to avoid having to tabulate densities in all
  sorts of different units

71
Learning Check

• Concentrated sulfuric acid is sold in bottles
  with a label that states that the specific
  gravity at 25 C is 1.84. The density of water at
  25 C is 0.995 g cm3. How many cubic centimeters
  of sulfuric acid will weigh 5.55 kilograms?
• Analysis
• 5.55 kg sulfuric acid ? cm3 sulfuric acid
• Solution
• density sulfuric acid specific gravity
  density water
• dsulfuric acid 1.84 0.995 g/cm3 1.83

5.58 cm3
72
Your Turn!

• Liquid hydrogen has a specific gravity of 7.08
  102. If the density of water is 1.05 g/cm3 at
  the same temperature, what is the mass of
  hydrogen in a tank having a volume of 36.9 m3?
• 7.43 102 g
• 2.74 g
• 274 g
• 2.74 106 g
• 2.61 106 g

7.43 102 g/cm3
73
Importance of Reliable Measurements

• To trust conclusions drawn from measurements
• Must know they are reliable
• Must be sure they are accurate
• Measured values must be close to true values
• Otherwise cant trust results
• Cant make conclusions based on those results
• Must have sufficient precision to be meaningful
• So confident that 2 measurements are same for 2
  samples
• Difference in values must be close to uncertainty
  in measurement

74
Learning Check

• You have a ring? Is it made of 24K gold?
• Calculate density compare to known
• Density of 24 K gold 19.3 g/mL
• Use inaccurate glassware
• Volume of ring 1.0 mL
• Use kitchen balance
• Mass of ring 18?? 1 g
• Anywhere between 17 19 g
• Density range is 17 19 g/mL
• Could be 24 k gold or could be as low as 18K gold
  (density 16.9 g/mL)

75
Learning Check (cont)

• Use more precise laboratory balance
• Mass of ring 18.153 ? 0.001 g
• Use more precise glassware
• Volume of ring 1.03 mL
• Density of ring 18.153 g/1.03mL 17.6 g/mL
• Calculate difference between d24K gold dring
• 19.3 g/mL 17.6 g/mL 1.7 g/mL
• Larger than experimental error in density
• ? 0.1 g/mL
• Conclude ring NOT 24 K gold!