Physical Chemistry Lab - University of Massachusetts Boston

Properties of Umass Boston

Analytical Chemistry Lab(CHEM313)

Drs. Robert Carter and Deyang QuChemistry Department


Objectives: Bridging the basic the analytical chemistry concepts with hand-on experimental work

• Review the basic analytical chemistry theories.

• Introduce analytical methods and statistical means

• Develop the skill of design, carrying out analytical experiments, most importantly the ability to extract information


Course Materials

• http://alpha.chem.umb.edu/chemistry/ch313/– Syllabus– Lab Schedule– Lab Manual

• Grading– Lab reports (due in two weeks)– Notebooks, bound– Final Exam

http://alpha.chem.umb.edu/chemistry/ch313/


Before the laboratory

• Review the analytical chemical concepts involved in the experiment

• Be familiar with the experimental procedures.

• Bring your lab book


While in the lab

• Safety! Safety! Safety!• On time.• Work with your partner.• Record the experimental procedures and

obtained data in detail.• Keep the working bench clean.• Clean the glassware.


After Laboratory

• Analysis YOUR data carefully with proper tools (e.g. software).

• Finish and hand in your report on time by email ([email protected]).

mailto:[email protected]

Lab Report• Due in two weeks by email ([email protected]). NO

late report will be graded!!• Full report:

– Two files: last name.first name_lab#.docx (word document for the report); last name.first name_lab#.xls (Excel file for data and calculation).

• Short report:– One file: ); last name.first name_lab#.xls (Excel file

for data and calculation).

• USE different Excel Templates for full and short report.


mailto:[email protected]


Introduction of the Evaluation of Experimental Error and Statistics

(1)


Precision and Accuracy• Precision:

Description of reproducibility.• Accuracy

Description of how close a measured value is to the “true” value.


Types of Error• Random or indeterminate error:

– Resulting from the impact of the environment e.g. operator, fluctuation of air flow, temperature etc.

– The value can not be predict at any given time, random and non-reproducible.

– Treated with statistical methods.• Systematic or determinate error:

– Sources• Instrument Error.• Method Error.• Personal Error.

– Predicable and reproducible.– Can not be treated with statistical method


Mean and Standard Deviation

1)()(tan

)()(tan

)(

))((

2

2

−−

=

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∑

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nmxsorssampleofdeviationdards

Nxsorpopulationofdeviationdards

n

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N

xmeantrueormeanpopulation

ie

i

ii

ii

ησ

ημ

•Population: a very large of N observations from which the sample can be imagined to com

•Sample: a small group of observation actually available

Population mean can well represent true value. Does the Population Mean=True Value? Depends on the accuracy


Estimating μ and σ

• But I do not usually know μ or σ. • Instead I measure a small sample of an

infinite distribution and calculate m and se (sample mean and SD).

• m ≈ μ; se ≈ σ• se is a reasonable estimate of σ.


What does Standard Deviation mean?

Titration, repeat 10 times by two students

Trial student A student B1 9.98 9.902 10.02 10.103 9.93 9.834 9.99 9.915 10.00 10.106 10.01 10.217 9.99 9.798 10.00 10.029 10.01 10.09

10 10.01 9.99

Mean 9.99 9.99SD 0.025473 0.134759

9.759.809.859.909.95

10.0010.0510.1010.1510.2010.25

0 2 4 6 8 10 12

Student A

Student B

Which student deserves better grade?


Gaussian DistributionFr

eque

ncy

10.0

410

.02

10.0

09.

989.96

9.94

3.0

2.5

2.0

1.5

1.0

0.5

0.0

10.3

10.2

10.1

10.0

9.9

9.8

9.7

3.0

2.5

2.0

1.5

1.0

0.5

0.0

student A student BMean 9.994StDev 0.02547N 10

student A

Mean 9.994StDev 0.1348N 10

student B

Histogram of student A, student BNormal

3 out of 10 (30%) measurements were within 10.00-10.01.


After a lot of measurements

Data

Freq

uenc

y

10.310.210.110.09.99.89.7

8

7

6

5

4

3

2

1

0

9.994 0.02547 109.994 0.1348 10

Mean StDev N

student Astudent B

Variable

Histogram of student A, student BNormal

μ

The area represents the fraction of measurements expected between 9.80-9.90


Normal Distribution• Gaussian distribution is defined by μ and σ,

analogous to mean and standard deviation. An universal Gaussian distribution can be applied to any case?

2

2)(

2

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z

x

eythus

sxxxzdefine

ey

curveGaussian

−

−−

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πσ

σμ

πσσ

μ

Percentage of measurements within μ-σ to μ-2σ


•μ±σ: 0.3413 x 2 =0.6826

•μ±2σ: 0.4773 x 2 =0.9546

•μ±3σ: 0.4986 x 2 =0.9973


Confidence Intervals• Most often we want to report the mean and the

statistical error in the mean to a certain level of confidence

tsx

meantheoferrordardsn

ss

tablefromtsstudenttnobservatioofnumbern

deviationdardssamplesn

tsx

ernalconfidence

m

m

±=

=

±=

μ

μ

tan

'::

tan:

int


Student’s t table

Degrees of Freedom: n-1


What level of confidence I have for students A and B?

Bstudent

Astudent

ntsx

−±=×

±=

−±=×

±=

±=

096.099.910

134759.0262.299.9

018.099.910

025472.0262.299.9

μ

• 10 observations: n=10• Degrees of freedom: n-1=9• For 95% CL, check t table

t=2.262•

• Student A: 10.01 – 9.97Student B: 10.09 – 9.89

Titration, repeat 10 times by two students

Trial student A student B1 9.98 9.902 10.02 10.103 9.93 9.834 9.99 9.915 10.00 10.106 10.01 10.217 9.99 9.798 10.00 10.029 10.01 10.09

10 10.01 9.99

Mean 9.99 9.99SD 0.025473 0.134759

Physical Chemistry Lab - University of Massachusetts Boston

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