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Chapter 2 Scientific Measurements

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

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

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

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)

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

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

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

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

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

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

Your Turn!

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

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

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

International System of Units (SI)

- Standard system of units used in scientific

engineering measurements - Metric ? 7 Base Units

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!

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

Your Turn!

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

Table 2.2 Some Non-SI Metric Units Commonly Used

in Chemistry

Table 2.3 Some Useful Conversions

Decimal Multipliers

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

Laboratory Measurements

- 4 common
- Length
- Volume
- Mass
- Temperature

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

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

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

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

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

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

Temperature Conversions

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

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

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

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

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

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

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

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

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

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

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.

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

Your Turn!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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)

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!