chapter 1 errors in chemical analysis

7/30/2019 Chapter 1 Errors in Chemical Analysis

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Errors in Chemical Analysis

Lecture 1


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Data quality Measurements invariably involve errors and

uncertainties. Uncertainties can never be completely eliminated,measurement data can give us only an estimate ofthe truevalue.

Reliability can be assessed in several ways: Experiments designed to reveal the presence oferrors

Compared with the known compositions

Consult to the chemical literature Equipment Calibration Statistical tests


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Representative Data Chemists usually carry two to five portions

(replicates) of a sample through an entireanalytical procedure. Replicates are samples of about the same size that

are carried through an analysis in exactly the sameway.

One usually considers the bestestimate to bethe central value for the set: Usually, the mean or the median is used as the

central value for a set of replicate measurements. The variation in data allows us to estimate the

uncertainty associated with the central result


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The Mean and Median The most widely used measure of central value

is the mean, . The mean, also called thearithmetic mean, or the average,

where xi represents the individual values ofx makingup the set ofN replicate measurements.

The median is the middle result when replicatedata are arranged according to increasing or

decreasing value.


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EXAMPLE 5-1

Calculate the mean and median for thedata shown in Figure 5-1.

Because the set contains an evennumber of measurements, the median

is the average of the central pair:


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Precision Describes the reproducibility of measurements

Or, the closeness of results that have beenobtained in exactly the same way.

Three terms are widely used to describe the

precision of a set of replicate data: standard deviation;

variance;

coefficient of variation.

Deviation from the mean:


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Accuracy Indicates the closeness of the measurement to

the true or accepted value Expressed in terms of either absolute or relative

error.

Absolute error: where xt is the true or accepted value of the quantity

We retain the sign in stating the absolute error.

Relative error:


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The difference between accuracy and precision


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Types of Errors in Experimental Data

The precision of a measurement is readily

determined by comparing data fromcarefully replicated experiments.

To determine the accuracy, we have toknow the true value, which is usually whatwe are seeking in the analysis.


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Analyst 1: relatively high precision & high accuracy Analyst 2: poor precision but good accuracy

Analyst 3: excellent precision & significant error in thenumerical average for the data

Analyst 4: poor precision & poor accuracy


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Types of Errors Random(or indeterminate) error:

Affect measurement precision Causes data to be scattered more or less

symmetrically around a mean value. Analysts 1 and 3 is significantly less than that for analysts 2

and 4.

Systematic (or determinate) error: Affect the accuracy of results

Causes the mean of a data set to differ from theaccepted value. Analysts 1 and 2 have little systematic error;

Analysts 3 and 4 show systematic errors of about -0.7% and-1.2%.


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Gross error:

Often the product of human errors.

usually occur only occasionally, are often large, andmay cause a result to be either high or low.

lead to outliers, results that appear to differ markedlyfrom all other data in a set of replicate measurements.


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Instrument Errors All measuring devices are potential

sources of systematic errors. Calibration eliminates most instrumental

systematic errors.

Electronic instruments are subject toinstrumental systematic errors. Ex: low battery voltage, noises

In many cases, errors of these types aredetectable and correctable.


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Method Errors The nonideal chemical or physical behavior of

the reagents and reactions on which an analysisis based

Ex: the slowness of some reactions, the

incompleteness of others, the instability of somespecies

Errors inherent in a method are often difficult to

detectand are thus the most serious of the threetypes of systematic error.


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Personal Errors Many measurements require personal

judgments. J udgments of this type are oftensubject to systematic, undirectional errors.

Analytical procedures should always be adjustedso that any known physical limitations of theanalyst cause negligibly small errors.

A universal source of personal error is prejudice,or bias. Number bias is another source of

personal error that varies considerably fromperson to person.


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Effect of Systematic Errors on

Analytical Results Systematic errors may be either constant or

proportional. Constant errors

Independent of the size of the sample being analyzed.

The absolute error is constant with sample size, butthe relative error varies when sample size is changed.

The excess of reagent required to bring about a color

change during a titration is an example. The effect of a constant error becomes more serious

as the size of the quantity measured decreases.


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Proportional errors

Decrease or increase in proportion to the sizeof the sample.

The absolute error varies with sample size,

but the relative error stays constant withchanging sample size.

A common cause of proportional errors is thepresence of interfering contaminants in thesample.


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Systematic Instrument and

Personal Errors Detection Instrument errors

Some systematic instrument errors can be found andcorrected by calibration.

Periodic calibration of equipment is always desirablebecause the response of most instruments change

with time as a result of wear, corrosion, ormistreatment.

Personal errors

Most personal errors can be minimized by care andself-discipline.

It is a good habit to check instrument readings,notebook entries, and calculations systematically.


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Systematic Method Errors Detection

Take one or more of the following

steps to recognise and adjust for asystematic error:

Analysis of Standard Samples Independent Analysis

Blank Determinations Variation in Sample Size


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Analysis of Standard Samples The best way of estimating the bias of an

analytical method is by the analysis ofstandard reference materials. Standard Reference Materials (SRMS):

Materials that contain one or more analytes atknown concentration levels.

Can sometimes be prepared by synthesis.

Can be purchased from a number of governmentaland industrial sources. Ex: National Institute ofStandards and Technology (NIST); SigmaChemical Co.


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chapter 1 errors in chemical analysis

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