Data Analysis for General Chemistry

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Data Analysis for General Chemistry

• Introduction

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Contact Information

• Dr. Randa Roland
• UCSC 459-5486 Thimann 317
• e-mail roland_at_chemistry.ucsc.edu
• website chemistry.ucsc.edu course homepage
• syllabus, powerpoints, etc.

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General Procedures

• Come to lab on time and prepared
• Complete prelab
• Appropriate attire
• Lab writeups due the following lab session
• Late lab penalty 25 off for each day late
• All writeups must be turned in no matter what
• Makeup labs
• Same week or following week only
• See me and your TA

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Prelab includes

• Title and date
• Definitions
• Answers to prelab questions
• Procedure
• Data tables
• Prelabs are done PRIOR to lab in your notebook
• TA must sign off at start of lab session

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Summary includes

• Title and date
• Results (tables, graphs, values, errors, etc.)
• Primary souces of errors
• Sample calculations
• Summaries are due one week after lab completion
• Templates/guides are available (manual and web)

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Lab Reports Includes

• Abstract
• Results/sample calculations
• Discussion/conclusions
• Answers to postlab questions
• Write-ups must be neat
• Your TA decides whether your work is acceptable
• Grading rubric is a guideline for you

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Equation/Concept List

• At the end of lab notebook, divide page(s) in
  half vertically
• For each lab
• Left side List primary equation(s) used
• Define symbols
• Right side Indicate linked concept
• Example
• M ?V mol Finding moles of reactant M
  molarity (mol/L) or product in solutions
• V volume (L) Reactants and products are
  mol moles related through mole ratio

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Data Measurement

• How do we record data?
• What is the best value to report?
• What is uncertainty (precision)?

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Precision, Accuracy, Error

• Precision reproducibility
• Accuracy trueness
• Error standard deviation (uncertainty)

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Accuracy vs. Precision

• Precise
• Not Accurate

Better Accuracy Not Precise
Precise Accurate
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Types of Error 1

• Systematic Accuracy

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Types of Error 2

• Random Reproducibility / precision

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Reporting Data
Average
Standard deviation
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Examples of Precision

• 100 150 200
• 140 150 160
• 149 150. 151
• 149.5 150.0 150.5
• 149.9 150.0 150.1
• and so on
• Average 150
• Precision very different

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Examples of Precision/Standard Deviation

• 100 150 200 50
• 140 150 160 10
• 149 150. 151 1
• 149.5 150.0 150.5 0.5
• 149.9 150.0 150.1 0.1
• and so on
• Average 150
• Standard deviation reflects measuring device

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Reporting Data Example
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Example continued
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Example continued

• Report
• 10.01 0.02 g

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Significant Figures

• Which numbers are meaningful?
• 1. Mathematical
• 2. Standard Deviation

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Mathematical Sig. Figs.

• Multiplication/Division
• Round answer to fewest sig. figs.
• Addition/Subtraction
• Round answer to fewest decimal places.
• Standard deviation takes precedence over these
  rules.

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Example
3 sig. figs./2 decimal places
4 sig. figs./2 decimal places
Report 10.01 0.02 mL
Standard deviation takes precedence
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Direct vs. Derived Values

• Direct
• Measured /no calculations required
• Derived
• Must be calculated from data
• How do we account for our uncertainty?

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Uncertainty in Measuring Devices
Ruler
1.38 cm 0.01 cm
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Uncertainty in Measuring Devices
Graduated cylinders

0.4

0.3

0.364 0.001 mL
3.60 0.01 mL
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Error Propagation / Calculated Values

• Addition

Subtraction
Standard deviations are additive
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Error Propagation

• Multiplication

Division
Relative errors are used
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Addition
12.5 g s1 0.1 g 2.05 g s2
0.01g 12.55 g s 0.11 g
Report 12.6 0.1 g
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Subtraction
12.5 g s1 0.1 g 2.05 g s2
0.01g 10.45 g s 0.11 g
Report 10.4 0.1 g
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Multiplication
12.5 cm s1 0.1 cm ? 2.05 cm s2
0.01cm 25.625 cm2 s ?
0.1 cm 12.5 cm
0.01 cm 2.05 cm

0.33 cm2
s 25.625 cm2
Report 25.6 0.3 cm2
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Division
12.5 g s1 0.1 g 2.05 cm3 s2
0.01cm3 6.09756 g s ?
cm3
s 6.09756 g cm3
0.1 g 12.5 g
0.01 cm 2.05 cm
0.0785g/cm3

Report 6.10 0.08 g/cm3
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Example
Measured diameter length
diameter, d
length, l
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Example Density mass/Volume
diameter, d
Measured mass diameter length
length, l
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Density Calculation

• A 218.44 0.01 g metal cylinder has diameter of
  2.50 0.01 cm and is 5.00 0.01 cm long.
• What is the density of the metal?
• Mass 218.44 0.01 g
• Diameter 2.50 0.01 cm
• Length 5.00 0.01 cm
• Volume ¼pd2l Density m/V

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Density of a Cylinder

• Formula

Density
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Density continued

• Standard deviation

Final answer
Report D 8.90 0.02 g/cm3
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Density of a cylinder, take 2
Volume
Standard deviation
Volume 24.5 0.2 cm3
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Density continued
Volume 24.5 0.2 cm3 Mass 218.440.01 g
Density
Standard deviation
Note difference D 8.90 0.07 g/cm3
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Summary

• Multiple measurements required
• Average
• Standard deviation
• Direct uncertainty device dependent
• Calculated uncertainty error propagation
• Review sig. fig. rules

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Graphing / Visualizing Data
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Graphing

• For a plot of mass vs. volume
• y-axis mass in g
• x-axis volume in mL

Density linear relationship of mass to volume
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Densities
Increasing density Increasing heaviness