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
2.1 | Physical and Chemical Properties

3. States of Matter Solids: Liquids: Gases: Ex. Ice, water, steam
Fixed shape & volume
Particles are close together
Have restricted motion
Liquids:
Fixed volume, but take container shape
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 Physical States
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)
H2O in solid, liquid & gas forms

5. Chemical Properties
Chemical change or reaction that substance undergoes
Chemicals interact to form entirely different substances 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
2.1 | Physical and Chemical Properties

6. Learning Check: Chemical or Physical Property?
Magnesium metal is grey X
Magnesium metal tarnishes in air X 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 “Fool’s Gold?” Can test by heating in flame Real gold
Nothing happens
Pyrite (Fool’s 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
2.2 Measurement of Physical and Chemical Properties

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
Some older units still in use
Need conversions to SI

19. Table 2.3 Some Useful Conversions
English Units
Mostly used in United States

20. Decimal Multipliers
Table 2.4 SI Prefixes—Their meanings and values

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 = 10–3 L
1 km = 1000 m
1 ng = 10–9 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 = 10–2 m = 0.01 m
Millimeter (mm)
1 mm = 10–3 m = 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 g = 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 K & boils at 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 nature’s 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 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 °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
2.3 | The Uncertainty of Measurements

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 =  0.01 °C
Fig. 2.12

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 = g on digital balance
Still has uncertainty
Assume ½ in last readable digit
Record as  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
has 4 sig. figs.
Zeros between non-zero numbers are significant.
Ex. 20, or × 104
has 5 sig. figs
Trailing zeros always count as significant if number has decimal point
Ex or × 102
has 3 sig. figs

39. Rules for Significant Figures
Final zeros on number without decimal point are NOT significant
Ex. 104,956, or × 108
has 6 sig. figs.
Final zeros to right of decimal point are significant
Ex has 3 sig. figs.
6. Leading zeros, to left of 1st nonzero digit, are never counted as significant
Ex or 1.2 × 10–4
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
161,000
3600.
× 102 5
6 × 10–4 1 7
1.61 × 105 3
3.6 × 103 2

41. Your Turn!
How many significant figures are in ? 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 is rounded up to 3.68
If number to be dropped is less than 5, last remaining digit stays the same.
Ex 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 is rounded to 6.6
Odd, it rounds up
Ex 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
7.665
37.5 or × 101
5.43 × 106
133 or × 102
8.77 × 10–4
7.66

45. Accuracy & Precision Accuracy Precision
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 × 31.4 ×
4 sig. figs. × 3 sig. figs. × 5 sig. figs = 3 sig. figs.
Ex ÷ 0.008
4 sig. figs. ÷ 1 sig. fig. = 1 sig. fig.
= 5620 = 5.62×103
= 700 = 7×102

47. Your Turn!
Give the value of the following calculation to the correct number of significant figures.
1.212
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.
319.5
4 decimal places
1 decimal place
3 decimal places
336.9
397 –
0 decimal places
2 decimal places
0 decimal place
124

49. Your Turn! When the expression,–
is evaluated, the result should be expressed as:
424.06
424.1
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 g g =
°C – °C =
327.5 m × 4.52 m =
g ÷ mL =
11.3 g or
1.13 × 101 g
0.004 °C or 4 × 10–3 °C
1.48 × 103 m
g/mL
or g/mL

52. Learning Check
For the following calculation, give the answer to the correct number of significant figures
= 2 × 10–4 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
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
Given Quantity
Desired Quantity
Conversion Factor × =

55. Conversion Factors
Ex. How to convert a person’s 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
Given Quantity
Desired Quantity
Conversion Factor × =
= 173 cm
= 26.8 in2/cm

57. Using Dimensional Analysis
Ex. Convert m to mm.
Relationship is 1 mm = 1 × 10–3 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 cm = 0.01 m
Now cube both sides
Units & numbers
(1 cm)3 = (0.01 m)3
1 cm3 = 1 × 10–6 m3
Can make 2 conversion factors or
3.5 × 106 Cm3

59. Non-metric to Metric Units
Convert speed of light from 3.00×108 m/s to mi/hr
Use dimensional analysis
1 min = 60 s 60 min = 1 hr
1 km = 1000 m 1 mi = 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 = L mile = km
1.3 × 102 km L–1
24 km L–1
15 km L–1
3.4 × 102 km L–1
9.2 km L–1

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 g of Ti are combined with g of bromine. In compound B we find that g of Ti are combined with 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: g Ti ⇔ g Br
In compound B: g Ti ⇔ g Br
Must find:
6.000 g Ti ⇔ ? g Br (compound A)
Solution:
= g Br
Compare
Ratio of small whole numbers
Supports law of multiple proportions

64. Density Ratio of object’s 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
2.5 | Density and Specific Gravity

65. Learning Check
A student weighs a piece of gold that has a volume of 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 × 10–2 cm3
1.07 × 10–3 cm3
2.20 × 10–1 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 cm3 to 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 The density of water at 25 °C is g cm–3. How many cubic centimeters of sulfuric acid will weigh kilograms?
Analysis:
5.55 kg sulfuric acid = ? cm3 sulfuric acid
Solution:
density sulfuric acid = specific gravity × density water
dsulfuric acid = 1.84 × g/cm3 = 1.83
Underline indicates number of significant digits. Round at end to avoid rounding errors in calculations.
5.58 cm3

72. Your Turn!
Liquid hydrogen has a specific gravity of × 10–2. 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 × 10–2 g
2.74 g
274 g
2.74 × 106 g
2.61 × 106 g
= 7.43 × 10–2 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 can’t trust results
Can’t 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 =  g
Use more precise glassware
Volume of ring = 1.03 mL
Density of ring = 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!