Analyzing Data

1
Chapter 2

• Analyzing Data

2
Chapter 2 Introduction

• 2.1 Units Measurements
• 2.2 Scientific Notation Dimensional Analysis
• Factor-Label Method a.k.a. Conversion Factors
  or Dimensional Analysis
• 2.3 Uncertainty in Data
• Sig Figs, Sig Digs

3
Chapter 2 Learning Targets

• By the end of Chapter 2 I am able to
• Identify the SI base units of measurements for
  mass, time, length, temperature volume (2.1)
• Distinguish between qualitative quantitative
  observations and give examples of each. (2.1)
• Explain the meanings of the SI prefixes (2.1)
• Compare contrast mass and weight (2.1)
• State the derived units used to represent speed,
  area density. (2.1)
• Analyze a problem, solve for an unknown and
  evaluate my answer (2.1)

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Chapter 2 Learning Targets

• Express numbers in scientific notation (2.2)
• Convert between units using dimensional
  analysis/factor-label method (2.2)
• Define compare accuracy precision (2.3)
• Describe the accuracy of experimental data using
  error percent error (2.3)
• Apply the rules of Sig Figs to express
  uncertainty in measured calculated values (2.3)

5
2.1 Units Measurements Learning Targets

• Identify the SI base units of measurements for
  mass, time, length, temperature volume (2.1)
• Distinguish between qualitative quantitative
  observations and give examples of each. (2.1)
• Explain the meanings of the SI prefixes (2.1)
• Compare contrast mass and weight (2.1)
• State the derived units used to represent speed,
  area density. (2.1)
• Analyze a problem, solve for an unknown and
  evaluate my answer (2.1)

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2.1 Units Measurements

• Système Internationale d'Unités (SI) is an
  internationally agreed upon system of
  measurements.
• Chemistry involves both measuring and calculating
• Two types of observations in science
• Qualitative (no measurements, no numbers)
• Quantitative (actual measurements)

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2.1 Units Measurements

• There are 7 base units in SI
• Measurements based on an object or event (a
  physical standard).
• See p. 33 in text.
• YOU NEED TO KNOW THESE!

8
2.1 Units Measurements

• To better describe the range of possible
  measurements, scientists add prefixes to base
  units
• Based on factors of 10 metric system

KNOW THESE p 33 in text
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2.1 Units Measurements

• Mass vs. Weight
• Weight is a measure of force of gravity between
  two objects (wt. changes w/respect to gravity)
• Scales are for weighing
• Mass is a measure of the amount of matter an
  object contains
• A balance is used for finding mass
• The SI unit for mass is the Kilogram (kg)

10
The Physical Standard for Mass (FYI)

• The international prototype of the kilogram is
  inside three nested bell jars at the Bureau
  International des Poids et Mesures in Paris.

http//www.npr.org/templates/story/story.php?story
Id112003322
11
In search of a new Standard

• Physicist Richard Steiner adjusts the watt
  balance. This extremely sensitive scale can
  detect changes as small as ten-billionths of a
  kilogram.

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2.1 Units Measurements

• Temperature quantitative measurement of the
  average kinetic energy of the particles w/in an
  object.
• A thermometer is used to measure temperature
• Three temperature scales
• Fahrenheit, Celsius, Kelvin
• SI base unit - Kelvin

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2.1 Units Measurements

• Kelvin scale developed by William Thomson (a.k.a.
  Lord Kelvin)
• Zero Kelvin is the point at which all molecular
  motion stops Absolute Zero
• The size of the Celsius degree (oC) is the same
  as a Kelvin (K)
• To convert between the two
• K ? C -273
• C ? K 273
• Water boils at 100 oC, to convert to Kelvin add
  273. What is waters BP in K?
• 373 K

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2.1 Units Measurements

• Derived Units combination of base units
• Volume SI unit is cubic meter (m3)
• Usually the liter (L) is used
• 1 L equals 1 dm3
• For laboratory use the cubic centimeter is often
  used (cm3 or cc)
• 1 cm3 1 mL (See Figure 2.4 p. 36)

15
Figure 2.4 p. 36
The three cubes show volume relationships between
m3 dm3 cm3. as you move from left to right,
the volume of each cube gets 10 x 10 x 10, or
1000 (103) times smaller.
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2.1 Units Measurements

• Derived Units continued
• Density a physical property of matter
• defined as amount of mass per unit volume
  (density mass/volume)
• Common units
• g/cm3 for solids
• g/ml for liquids gases

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Application

• Question 116 g of sunflower oil is used in a
  recipe. The density of the oil is 0.925 g/ml.
  What is the volume of the sunflower oil in ml?
• What are you being asked to solve for?
• volume of sunflower oil
• What do you know, what are you given?
• Density mass/volume
• Density 0.925 g/ml
• Mass 116 g
• What is the unknown?
• volume
• Write the equation and isolate the unknown
  factor.
• density mass/volume
• rearrange to solve for unknown volume
  mass/density
• Substitute known quantities into equation
  solve.
• volume 116g/0.925g/ml
• volume 125 ml

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Homework

• 2.1 2-6 pgs. 38-39
• Chapter Assessment 66-67 p. 62
• Read 2.2 pgs. 41-46 Look at notes on-line
• 2nd 6th periods only
• PLEASE PUT CHAIRS UP BEFORE YOU LEAVE ? Thanks!!

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2.2 Scientific Notation Dimensional Analysis
Learning Targets

• Express numbers in scientific notation (2.2)
• Convert between units using dimensional
  analysis/factor-label method (2.2)

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2.2 Scientific Notation Dimensional Analysis

• Scientific notation used for short-handing very
  large and very small measurements.
• Very large number - the number of atoms in a
  sample might be something like 124,500,000,000,000
  atoms.
• Very small number - the size of an molecule in
  meters might be something like 0.0000000000238
  meters.

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2.2 Scientific Notation Dimensional Analysis

• The number of places moved equals the value of
  the exponent.
• The exponent is positive when the decimal moves
  to the left and negative when the decimal moves
  to the right.
• Example
• 800 8.0 ? 102
• 0.0000343 3.43 ? 105

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2.2 Application

• Question Each cell in the human body contains a
  complete genome which is composed of base pairs.
  Each base pair is 0.000,000,034m in length.
  There are 6,000,000,000 base pairs in each human
  cell. Change the above information into
  scientific notation.
• a.) 3.4 x 10-8 m
• b.) 6 x 109 base pairs

23
2.2 Scientific Notation Dimensional Analysis

• Addition Subtraction of numbers in scientific
  notation
• Exponents must be the same.
• Add or subtract coefficients.
• (7.35 x 102 m) (2.43 x 102 m) 9.78 x 102 m

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Application

• Add 3.5 x 103 m to 6.8 x 103 m
• (3.5 x 103) (6.8 x 103) 10.3 x 103
• Why??? Answer must be 1.03 x 104 because proper
  scientific notation states that you must have one
  whole number to the left of the decimal

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2.2 Scientific Notation Dimensional Analysis

• What if the exponents are NOT the same?
• Rewrite values with the same exponent.
• Example Consider amounts of energy produced by
  renewable energy sources in the U.S. in 2004
• Hydroelectric 2.840 x 1018 J
• Biomass 3.146 x 1018 J
• Geothermal 3.60 x1017 J
• Wind 1.50 x 1017 J
• Solar 6.9 x 1016 J

6.565 x 1018 J
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Application

• Subtract 7.9 x 102 km from 1.0 x 103 km
• (1.0 x 103) (0.79 x 103)
• Remember you must write as 2.1 x 102 (one whole
  number to the left of the decimal!!)

0.21 x 103
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2.2 Scientific Notation Dimensional Analysis

• Multiplication and division, exponents do NOT
  need to be the same
• To multiply, multiply the coefficients, then add
  the exponents.
• (4.6 x 1023 atoms) (2x10-23 g/atom)
• To divide, divide the coefficients, then subtract
  the exponent of the divisor from the exponent of
  the dividend.
• (9 x 108) / (3 x 10-4)
• Divide coefficients 9/3 3
• Subtract the exponents 8 (-4) 84 12
• Combine the parts 3 x 1012

9.2 x 100 g 9.2 g
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Math Skill Review

• Can you multiply these fractions? Complete the
  following in your notebook. Remember MATH IN
  PENCIL! ?
• 2/3 x 5/7
• 2/3 x 3/9
• a/b x c/d
• a2/b x b3/a
• 5 x 2/15

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2.2 Scientific Notation Dimensional Analysis

• Factor-Label Method (Dimensional Analysis
  Conversion factors book name)
• Problem solving consists of three parts
• Known ? Conversion Factor ? Desired
• 
  Answer

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2.2 Scientific Notation Dimensional Analysis

• Conversion factors are ratios with a value equal
  to one
• Example 1 4 quarters
• 1km 1000m
• The ratios are written as follows
• 1 and 4 quarters
• 4 quarters 1
• 1 km and 1000 m
• 1000 m 1 km

31
2.2 Application

• An object is traveling at a speed of 7500
  centimeters per second. Convert the value to
  kilometers per minute.
• Known 7500 cm /sec
• Desired ? km/min
• What relationships are known between cm km?
  Between sec min? Write them down
• 100 cm 1m 1000 m 1 km 60 s 1 min
• Use these relationships as ratios in such a way
  that s, cm, m all divide out
• km
• min

32
Open Note Quiz

1. How many seconds in a class at SKHS? Class
   periods are 98 minutes.
2. Convert 78 seconds to hours
3. Convert 2.5 x 106 g to kg
4. Convert 37.5g/ml to kg/L
5. Convert 7.56 mm3/s to dm3/min
6. Convert 9.06 km/hr to m/s

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2.2 HW

• 11-16, 19-20, 25, 76-80
• Conversion Lab

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2.3 Uncertainty in Data Learning Targets

• Define compare accuracy precision (2.3)
• Describe the accuracy of experimental data using
  error percent error (2.3)
• Apply the rules of Sig Figs to express
  uncertainty in measured calculated values (2.3)

35
2.3 Uncertainty in Data

• Accuracy Precision
• Accuracy refers to how close a measured value is
  to an accepted value
• Precision refers to how close measurements are to
  one another.

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2.3 Uncertainty in Data
Figure 2.10 on p. 47
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2.3 Uncertainty in Data Application

• Open your books and consider the data table, p.
  48.

38
2.3 Uncertainty in Data Application - continued

• Students were asked to determine the density of
  an unknown white powder.
• Each student measured the volume and mass of
  three samples.
• They calculated the densities and averaged the
  three.

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2.3 Uncertainty in Data Application - continued

• Which student collected the most accurate data?
• Student A
• Why?
• closest to the accepted value.
• Who collected the most precise data?
• Student C
• Why?
• closest to one another.

40
2.3 Uncertainty in Data

• Error Percent Error
• Error is defined as the difference between an
  experimental value (values measured during an
  experiment) and an accepted value
• Error Equation
• Error experimental value accepted value

41
2.3 Uncertainty in Data

• Error Percent Error (cont)
• Percent Error expresses error as a percentage of
  the accepted value.
• Percent Error Equation

42
2.3 Application do this in your notebook as
part of your notes

• The melting point of paradichlorobenzene is 53oC.
  In a laboratory activity two students tried to
  verify this value.
• Student 1 records 51.5oC, 53.5oC, 55.0oC,
  52.3oC, and 54.2oC
• Student 2 records 52.3oC, 53.2oC, 54.0oC,
  52.5oC, and 53.5oC
• Calculate the average value for the two students
• Calculate the percent error for each student
• Which of the students is most precise? Accurate?
  Explain.

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Calculate the average value for the two students

• Student 1 51.5oC 53.5oC 55.0oC 52.3oC
  54.2oC 266.5/5 53.3oC
• Student 2 52.3oC 53.2oC 54.0oC 52.5oC
  53.5oC 53.1oC

44
Calculate the percent error for each student

• Student 1
• Percent error
• Student 2
• Percent error

45
Which of the students is most precise?
Accurate? Explain.

• Student 2 is the most precise with a range of
  values from 52.3 to 54.0.
• Student 2 is also most accurate with a 0.189
  error.

46
2.3 Uncertainty in Data

• Significant Figures include all known digits
  plus one estimated digit.
• Often precision is limited by the tools
  available.

5.00 cm
47
2.3 Uncertainty in Data

• Rules for Significant Figures
• Rule 1 Nonzero numbers are always significant.
• Example 72.3 g
• 9.4567
• Rule 2 Zeros between nonzero numbers are always
  significant.
• Example 60.5 g
• 5005.05
• Rule 3 All final zeros to the right of the
  decimal are significant.
• Example 6.2000

How many sig figs?
3
How many sig figs?
5
How many sig figs?
3
How many sig figs?
6
How many sig figs?
5
48
2.3 Uncertainty in Data

• Rules for Significant Figures
• Rule 4 Placeholder zeros are not significant.
  To remove placeholder zeros, rewrite the number
  in scientific notation.
• Example 0.0253g and 4320 (3 sig figs each)
  Rewritten in Scientific notation
• 2.53 x 10-2 4.32 x 103
• 0.000601
• 50000

How many sig figs?
3
6.01 x 10-4
How many sig figs?
1
5 x 104
49
2.3 Uncertainty in Data

• Rules for Significant Figures
• Rule 5 Counting numbers and defined constants
  have an infinite number of significant figures.
• Example 6 molecules
• 60s 1 min

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2.3 Uncertainty in Data

• How many Sig Figs
• 4 Rule 1
• 5 Rules 2 3
• 5 Rules 2 3
• 4 Rules 2 3
• 1 Rule 4

• Examples using the 4 Rules
• 5465
• 0.60750
• 0.020020
• 500.0
• 300

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2.3 Uncertainty in Data

• Rules for Significant Figures
• What happens when your calculator gives you a
  funky number, how do you know how many sig figs
  to report in your answer?
• Rule 6 Addition Subtraction, answer will have
  the number of sig figs from the number with the
  least amount of decimal places in the problem.

Example 10.21
0.2 256
266.41 So my answer should have 0 decimal places
Decimal Places 2 1 0 266
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2.3 Uncertainty in Data

• Rules for Significant Figures
• Rule 7 Multiplication Division The answer will
  have the number of sig figs from the number with
  the least amount of sig figs.

Example 4675 x 625 ________ Which has the
least of sig figs? 625 has 3, so your answer
must have 3 4675 x 625 2921875 ? 2920000 2.92
x 106
YOU WILL USE THIS RULE A LOT!!!!!
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2.3 Homework

• 32-36, 40, 42-43, 47 51, 87, 91, 93-94