Data Analysis for General Chemistry

Introduction

Contact Information

Dr. Randa Roland

UCSC: 459-5486 Thimann 317

e-mail: roland@chemistry.ucsc.edu

website:chemistry.ucsc.edu course homepage

syllabus, powerpoints, etc.

General ProceduresCome 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

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

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)

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

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

Data Measurement

How do we record data?

What is the best value to report?

What is uncertainty (precision)?

Precision, Accuracy, Error

Precision: reproducibility

Accuracy: trueness

Error: standard deviation (uncertainty)

Accuracy vs. Precision

Precise

Not Accurate

Better Accuracy

Not PrecisePrecise

Accurate

Types of Error 1

Systematic: Accuracy

Trial Mass (g)1 10.222 10.233 10.194 10.175 10.22

Mass of Water

9.90

10.00

10.10

10.20

10.30

1 2 3 4 5

Trial

Mas

s (g

)

Types of Error 2

Random: Reproducibility / precision

Trial Mass (g)1 10.022 10.033 9.994 9.975 10.02

Mass of Water

9.80

9.90

10.00

10.10

10.20

1 2 3 4 5

Trial

Mas

s (g

)

Reporting Data

Average:

n

xxxx n21

Standard deviation:

1-n

x-xx-xx-x2

n

2

2

2

1

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

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

Reporting Data Example

3

99.903.0100.01V

mL

Trial #

Volume (mL)

1 10.002 9.993 10.03

mL10.01V mL006666.10

Example continued

1- 3

9.99-10.0110.03-10.0110.00-10.01 2222 mL

mL0.02σ mL021213.0

Trial #

Volume (mL)

1 10.002 9.993 10.03

Average 10.01

Example continued

Report:

10.01 ± 0.02 g

%2.0%100g 10.01

g 0.02 error relative

Trial #

Volume (mL)

1 10.002 9.993 10.03

Average 10.01

Significant Figures

Which numbers are meaningful?

1. Mathematical

2. Standard Deviation

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.

Example

3 sig. figs./2 decimal places4 sig. figs./2 decimal places

Trial #

Volume (mL)

1 10.002 9.993 10.03

Average 10.01St. Dev. 0.02

Standard deviation takes precedence

Report: 10.01 ± 0.02 mL

Direct vs. Derived Values

Direct:

Measured /no calculations required

Derived:

Must be calculated from data

How do we account for our uncertainty?

Uncertainty in Measuring Devices

0 1 2

Ruler

1.38 cm ± 0.01 cm

Uncertainty in Measuring DevicesGraduated

cylinders

0.364 ± 0.001 mL

3.60 ± 0.01 mL

0.3

0.4

3

4

Error Propagation / Calculated Values

Addition:

)()()()( baba BABA

Subtraction:

)()()()( baba BABA

Standard deviations are additive

Error Propagation

Multiplication

BAABABBA ba

ba

)()())((

Division

BAB

A

B

A

B

A ba

b

a

)(

)(

Relative errors are used

Addition

12.5 g = 0.1 g

+ 2.05 g = 0.01g

12.55 g = 0.11 gReport: 12.6 ± 0.1 g

Subtraction

12.5 g = 0.1 g

– 2.05 g = 0.01g

10.45 g = 0.11 gReport: 10.4 ± 0.1 g

Multiplication

12.5 cm = 0.1 cm

2.05 cm = 0.01cm

25.625 cm2 = ?

Report: 25.6 ± 0.3 cm2

= 25.625 cm2

0.1 cm

12.5 cm

0.01 cm

2.05 cm

+ = 0.33 cm2

Division 12.5 g = 0.1 g

2.05 cm3 = 0.01cm3

6.09756 g = ? cm3

Report: 6.10 ± 0.08 g/cm3

= 6.09756 g

cm3

0.1 g 12.5 g

0.01 cm

2.05 cm

+ = 0.0785g/cm3

Example sidecirclecylinder LAV

diameter, d

length, l

lddldldV

ldldlrV

ldd

ld

22

222

44

44

Measured: diameter

length

Example Density = mass/Volume

)()(

)(4

4

2

2 ld

m

ld

m

ld

mD

lddmld

m

ld

mD lddm

22

44

diameter, d

length, l

Measured: mass

diameter

length

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 = ¼d2l Density = m/V

Density of a Cylinder

3290005.8

)00.5()50.2(

)44.218(4

cm

g

cmcm

gD

lddmld

m

ld

mD lddm

22

44

Formula:

Density:

Density continued

Standard deviation:

Report: D = 8.90 ± 0.02 g/cm3

33

3

0182.0002046.090005.8

00.5

01.0

50.2

01.0

50.2

01.0

44.218

01.090005.8

cm

g

cm

g

cm

cm

cm

cm

cm

cm

g

g

cm

gD

Final answer:

Density of a cylinder, take 2

32 5437.24)00.5()50.2(4

cmcmcmV

Volume: 24.5 ±0.2 cm3

Standard deviation:

33

3

24544.001.05437.24

00.5

01.0

50.2

01.0

50.2

01.05437.24

cmcm

cm

cm

cm

cm

cm

cmcmV

Volume:

Density continued

333

3

30732.0008209.09159.8

5.24

2.0

44.218

01.09159.8

cm

g

cm

g

cm

cm

g

g

cm

gD

339159.8

5.24

44.218

cm

g

cm

gD

Note difference: D = 8.90 ± 0.07 g/cm3

Volume: 24.5 ±0.2 cm3

Mass: 218.44±0.01 g

VmV

m

V

mD Vm

Standard deviation:

Density:

Summary

Multiple measurements required

Average

Standard deviation

Direct uncertainty: device dependent

Calculated uncertainty: error propagation

Review sig. fig. rules

Graphing / Visualizing Data

Volume (mL) Mass (g)5.00 4.93

10.00 9.6215.00 14.9920.00 21.0225.00 24.8930.00 29.77

Density of Water

Density of Water

y = 1.0028x

0

10

20

30

0.00 10.00 20.00 30.00

Volume (mL)

Mas

s (g

)

OHdensitymL

g

xx

yylope

20028.1s

12

12

Graphing

For a plot of mass vs. volume

y-axis: mass in g

x-axis: volume in mL

mL

gdensity

volume

masslope 00.1s

Density: linear relationship of mass to volume

Densities

Substance Density

(g/mL)

wood 0.35

water 1.00

quartz 2.65

diamond 3.51

Ti 4.5

Ag 10.5

Au 19.3

Os 22.4

Increasing density

=

Increasing “heaviness”