Tools of the Trade Laboratory Notebook Objectives of a Good Lab Notebook (a)State what was done (b)State what was observed (c)Be easily understandable

Tools of the Trade Laboratory Notebook

Objectives of a Good Lab Notebook(a) State what was done(b) State what was observed(c) Be easily understandable to

someone else

Laboratory Notebook

Bad Laboratory Practice (A Recent Legal Case)Medichem Pharmaceuticals v. Rolabo Pharmaceuticals

Tools of the Trade

Two Patents describe a method for making the antihistamine drug Loratidine (Claritin) - US sales of $2.7 billion - the two patents are essentially identical- Medichem sued to invalidate Rolabo patent and claimed priority- Medichem had to prove it used the method to make loratidine before Rolabo did

A co-inventor’s lab notebook was a primary piece of evidence to support Medichem’s claim- documented analysis of a sample claimed to be made using the patented method - NMR spectral data confirmed the production of loratidine

The evidence was not enough to support Medichem's claim of reduction to practice- NMR data do not show the process by which loratidine was made- lab books were not witnessed

Rolabo Pharmaceuticals won the case (and the rights to make Loratidine) because of problems with a Lab Notebook!!

Nature Reviews Drug Discovery (2006) 5, 180

Tools of the Trade ALL Measurements have an Associated Error

Essential to understand instrument limitations

- Use proper procedures to minimize source of errors- Have to accept a certain level of instrumental errors - Only counting can lack an error

Balance

Grams error mg error

500 1.2 500 0.010

200 0.5 200 0.010

100 0.25 100 0.010

50 0.12 50 0.010

20 0.074 20 0.010

10 0.050 10 0.010

5 0.034 5 0.010

2 0.034 2 0.010

1 0.034 1 0.010

Buret

Vol. (ml) Error (mL)

5 ± 0.01

10 ± 0.02

25 ± 0.03

50 ± 0.05

100 ± 0.10

Volumetric Flask

Vol. (mL) Error (mL)

1 ± 0.02

2 ± 0.02

5 ± 0.02

10 ± 0.02

25 ± 0.03

50 ± 0.05

100 ± 0.08

200 ± 0.10

250 ± 0.12

500 ± 0.20

1000 ± 0.30

2000 ± 0.50

Transfer Pipet

Vol. (mL) Error (mL)

0.5 ±0.006

1 ±0.006

2 ±0.006

3 ±0.01

4 ±0.01

5 ±0.01

10 ±0.02

15 ±0.03

20 ±0.03

25 ±0.03

50 ±0.05

100 ±0.08

Tools of the Trade Weight Measurements

1.) Methods of Weighing:(i) Basic operational rules

Chemicals should never be placed directly on the weighing pan - corrode and damage the pan may affect

accuracy - not able to recover all of the sample

Balance should be in arrested position when load/unload pan Half-arrested position when dialing weights

- dull knife edge and decrease balance sensitivity accuracy

(ii) Weight by difference: Useful for samples that change weight upon exposure to the

atmosphere- hygroscopic samples (readily absorb

water from the air)

Weight of sample = ( weight of sample + weight of container) – weight of container

(iii) Taring: Done on many modern electronic balances Container is set on balance before sample is added Container’s weight is set automatically to read “0”


2.) Errors in Weighing: Sources(i) Any factor that will change the apparent mass of the sample

Dirty or moist sample container - also may contaminate sample

- important to dry sample before weighing

Sample not at room temperature- avoid convection air currents (push/lift

pan) Adsorption of water, etc. from air by sample

Vibrations or wind currents around balance Non-level balance

Office dust


3.) Errors in Weighing: Sources(i) Any factor that will change the apparent mass of the sample

Buoyancy errors – failure to correct for weight difference due to displacement of air by the sample.

Correction for buoyancy to give true mass of sample

m = true mass of sample

m’ = mass read from balance

d = density of sampleda = density of air (0.0012

g/ml at 1 atm & 25oC)dw = density of calibration

weights (~ 8.0 g/ml)

)dd

1(

)dd

1('m

ma

w

a

Different displacement of ice and balsa wood in water

icebalsa

Volume Measurements

1.) Errors in volumes: Source (i) Always measure volume at bottom of a concave meniscus

- always fill all volumetric flasks or transfer pipettes to calibration line

(ii) always read at the same eye level as the liquid

(iii) Don’t force out last drop from pipette! (iv) Remove air bubbles

Tools of the Trade

15.46 mL 15.31 mL 1% error

Eye level View from above

Experimental Error & Data Handling Introduction

1.) There is error or uncertainty associated with every measurement.(i) except simple counting

2.) To evaluate the validity of a measurement, it is necessary to evaluate its error or uncertainty

Same Picture Different Levels of Resolution

You can read the name of the boat on the left picture, which is lost in the right picture.

Can you read the tire manufacturer?

Experimental Error & Data Handling

Both numbers have 4 significant figures

Zeros are simple place holders

Both zeros are significant figures

zero is a significant figure

Significant Figures

1.) Definition: The minimum number of digits needed to write a given value (in scientific notation) without loss of accuracy.

(i) Examples:

142.7 = 1.427 x 102

0.006302 = 6.302 x10-3

2.) Zeros are counted as significant figures only if:(i) occur between other digits in the number

9502.7 or 0.9907

(ii) occur at the end of number and to the right of the decimal point

177.930

Experimental Error & Data Handling Significant Figures

3.) The last significant figure in any number is the first digit with any uncertainty

(i) the minimum uncertainty is ± 1 unit in the last significant figure(ii) if the uncertainty in the last significant figure is ≥ 10 units, then one less

significant figure should be used.(iii) Example:

9.34 ± 0.02 3 significant figures

But

6.52 ± 0.12 should be 6.5 ± 0.1 2 significant figures

4.) Whenever taking a reading from an instrument, apparatus, graph, etc. always estimate the result to the nearest tenth of a division

(i) avoids losing any significant figures in the reading process7.45 cm

Significant Figures

5.) Addition and Subtraction(i) use the following procedure:

Express all numbers using the same exponent Align all numbers with respect to the decimal point

Add or subtract using all given digits Round off the answer so that it has the same number of digits to

the right of the decimal as the number with the fewest decimal places


1 decimal point 12.5 x 104

2.48 x 104

+ 1.235 x 104

16.215 x 104 = 16.2 x 104

12.5 x 104

2.48 x 104

+ 1.235 x 104

1.25 x 105

2.48 x 104

+ 1.235 x 104


5.) Addition and Subtraction(i) use the following procedure:

Round off the answer to the nearest digit in the least significant figure.

Consider all digits beyond the least significant figure when rounding.

If a number is exactly half-way between two digits, round to the nearest even digit.

- minimizes round-off errors Examples:

3 sig. fig.: 12.534 12.5

4 sig. fig.: 11.126 11.13

4 sig. fig.: 101.250 101.2

3 sig. fig. 93.350 93.4

Significant Figures

6.) Multiplication and Division(i) use the following procedure:

Express the answers in the same number of significant figures as the number of digits in the number used in the calculation which had the fewest significant figures.

Examples:


3.261 x 10-5

x 1.78 5.80 x 10-5

3 significant figures

34.602.4287 14.05

4 significant figures


7.) Logarithms and Antilogarithms(i) the logarithm of a number “a” is the value “b”, where:

(ii) example:

(iii) The antilogarithm of “b” is “a”

(iv) the logarithm of “a” is expressed in two parts

a = 10b or Log(a) = b

The logarithm of 100 is 2, since:100 = 102

a = 10b

Log(339) = 2.530

character mantissa


7.) Logarithms and Antilogarithms(v) when taking the logarithm of a number, the number of significant figures

in the resulting mantissa should be the same as the total number of significant figures in the original number “a”

(vi) Example:

Log(5.403 x 10-8) = -7.2674

(vii) when taking the antilogarithm of a number, the number of significant figures in the result should be the same as the total number of significant figures in the mantissa of the original logarithm “b”

(viii) Example:

Antilog(-3.42) = 3.8 x 10-4

4 sig. fig. 4 sig. fig.

2 sig. fig. 2 sig. fig.


8.) Graphs(i) use graph paper with enough rulings to accurately graph the results

(ii) plan the graph coordinates so that the data is spread over as much of the graph as possible

(iii) in reading graphs, estimate values to the nearest 1/10 of a division on the graph


8.) Graphs(ii) plan the graph coordinates so that the data is spread over as much of the

graph as possible

(iii) in reading graphs, estimate values to the nearest 1/10 of a division on the graph

Experimental Error & Data Handling Errors

1.) Systematic (or Determinate) Error(i) An error caused consistently in all results due to inappropriate methods or experimental techniques.(ii) Results in all measurements exhibiting a definite difference from the true

value. (iii) This type of error can, in principal, be discovered and corrected.

Buret incorrectly calibrated


2.) Random (or Indeterminate) Error(i) An error caused by random variations in the measurement of a physical

quantity.(ii) Results in a scatter of results centered on the true value for repeated

measurements on a single sample.(iii) This type of error is always present and can never be totally eliminated

Random Error Systematic Error

True value


3.) Accuracy and Precision(i) Accuracy: refers to how close an answer is to the “true” value

Generally, don’t know “true” value Accuracy is related to systematic error

(ii) Precision: refers to how the results of a single measurement compares from one trial to the next

Reproducibility Precision is related to random error

Low accuracy, low precision Low accuracy, high precision

High accuracy, low precision High accuracy, high precision


4.) Absolute and Relative Uncertainty(i) Both measures of the precision associated with a given measurement.(ii) Absolute uncertainty: margin of uncertainty associated with a measurement(iii) Example:

If a buret is calibrated to read within ± 0.02 mL, the absolute uncertainty

for measuring 12.35 mL is:

Absolute Uncertainty = 12.35 ± 0.02 mL

(iv) Relative uncertainty: compares the size of the absolute uncertainty with the size of its associated measurement

(v) Example:For a buret reading of 12.35 ± 0.02 mL, the relative

uncertainty is:

ValueMeasured

yUncertaintAbsoluteyUncertaintRelative

0.2%0.16%(100)mL12.35

mL0.02y(%)UncertaintRelative

(Make sure units cancel)

1 sig. fig.


5.) Propagation of Uncertainty(i) The absolute or relative uncertainty of a calculated result can be estimated

using the absolute or relative uncertainties of the values used to obtain that result.

(ii) Addition and Subtraction The absolute uncertainty of a number calculated by addition or

subtraction is obtained by using the absolute uncertainties of numbers used in the calculations as follows:

Example:

22value

2valueAnswer .Uncert.Abs.Uncert.Abs.Uncert.Abs

1

Value Abs. Uncert. 1.76 (± 0.03)+ 1.89 (± 0.02)- 0.59 (± 0.02) 3.06

04.002.002.003.0.Uncert.Abs 222Answer

Answer:

Errors

5.) Propagation of Uncertainty(iii) Once the absolute uncertainty of the answer has been determined, its relative uncertainty can also be calculated, as described previously.

Example (using the previous example):

Note: To avoid round-off error, keep one digit beyond the last significant figure in all calculations.

- drop only when the final answer is obtained


%1%3.1)100(06.3

04.0.(%)Uncert.lRe

Round-off errors

1 sig. fig.


5.) Propagation of Uncertainty(i) Multiplication and Division

The relative uncertainties are used for all numbers in the calculation

Example:

22value

2valueAnswer .Uncert.lRe.Uncert.lRe.Uncert.lRe

1

64.5

02.059.0

02.089.103.076.1

)100(

59.0

02.0,)100(

89.1

02.0),100(

76.1

03.0.Uncert.lRe

%4.3,%1.1%,7.1.Uncert.lRe

%4%0.44.31.17.1.Uncert.lRe 222Answer

3 sig. fig.

1 sig. fig.


5.) Propagation of Uncertainty(ii) Once the relative uncertainty of the answer has been obtained, the absolute uncertainty can also be calculated:

(iii) Example (using the previous example):

)100(ValueCalculated

yUncertaintAbsolutey(%)UncertaintRelative

Rearrange:

value)d(calculatey(%)UncertaintRelative

yUncertaintAbsolute)100(

2.023.0100

%0.4)64.5(

yUncertaintAbsolute 1 sig. fig.


5.) Propagation of Uncertainty(iv) For calculations involving Both additions/subtractions and

multiplication/divisions: Treat calculation as a series of individual steps Calculate the answer and its uncertainty for each step Use the answers and its uncertainty for the next calculation, etc. Continue until the final result is obtained

(v) Example:

First operation: differences in brackets

?619.0

02.089.1

02.059.003.076.1

226 02.003.003.0

036.017.102.059.003.076.1

3 sig. fig.

3 sig. fig.

1 sig. fig., but carry two sig. fig. through calculation


Errors

5.) Propagation of Uncertainty (v) Example:

Second operation: Division

212

13

1

16

%.1%.3%3%.3

%3%61.0%.189.1

%.317.1

02.089.1

03.017.1

Convert to relative

uncertainty

3 sig. fig.

1 sig. fig.


Errors

5.) Propagation of Uncertainty (vi) Uncertainty of a result should be consistent with the number of significant

figures used to express the result.

(vii) Example:

1.019 (±0.002)

28.42 (±0.05)

But:12.532 (±0.064) too many significant figures

12.53 (±0.06) reduce to 1 sig. fig. in uncertainty

same reduction in results

Result & uncertainty match in decimal place

The first digit in the answer with any uncertainty associated with it should be the last significant figure in the number.


Errors

5.) Common Mistake (vi) Number of Significant Figures is Not the number shown on your calculator.

Not 10 sig. fig.

596966414.223.9

97.23


Errors

ExampleFind the absolute and percent relative uncertainty and express the answer with a reasonable number of significant figures:

[4.97 ± 0.05 – 1.86 ± 0.01]/21.1 ± 0.2 =

Documents

Tools of the Trade Laboratory Notebook Objectives of a Good Lab Notebook (a)State what was done (b)State what was observed (c)Be easily understandable