Errors and evaluation of analytical data, Study notes of Chemistry

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Errors and evaluation of

analytical data

Presented by

K.N.S.SWAMI., M.Sc., SET.

Guest Faculty in Chemistry

Department Of Chemistry

P. R. Government College (Autonomous),Kakinada.

CONTENTS: ➢ ERRORS ➢ ACCURACY AND PRECISION ➢ PROPAGATION OF ERRORS ➢ SIGNIFICANT FIGURES ➢ COMPUTATION RULES ➢ CONFIDENCE LIMITS & CONFIDENCE INTERVAL

Generally Chemical analyses are affected by two types of errors: Classification Of Errors

1. Systematic (or determinate) error, causes the mean of a data set to differ from the accepted value.
2. Random (or indeterminate) error, causes data to be scattered more or less symmetrically around a mean value.
3. Systematic or determinate or constant errors: These errors can be avoidedand their magnitude can be determined, thereby correcting the measurements. or ➢ have a definite value, ➢an assignable cause, and are of the same magnitude for replicate measurements made in the same way. ➢ They lead to bias in measurement results.

There are Four types of systematic errors:

• Personal errors and Operational errors
• Instrumental errors and reagent errors
• Method errors
• Additive and proportional errors I.Personal errors and Operational Errors: These errors are not connected with the method or procedure but the individual analyst is responsible for them. This type of errors may arise due to the inability of the individual making observations. Some important personal errors are: A. Inability in judging color change sharply in visual titrations. B. Error in reading a burette. C.Mechanical loss of material in various steps of an analysis. D.Failure to wash and ignite a precipitate properly. E. Insufficient cooling of crucible before weighing. F.Using impure reagents. G.Ignition of precipitate at incorrect temperatures. H.Errors in calculations.

III. Errors of method: These originate from incorrect sampling and from incompleteness of a reaction. ➢ In gravimetric analysis errors may arise owing to appreciable solubility of precipitates, CO- precipitation, and post-precipitation, decomposition, or volatilization of weighing forms on ignition, and precipitation of substances other than the intended ones. ➢ In titrimetric analysis errors may occur owing to failure of reactions to proceed to completion, occurrence of induced and side reactions, reaction of substances other than the constituent being determined, and a difference between the observed end point and the stoichiometric equivalence point of a reaction.

IV. Additive and proportional errors:

➢ Absolut vale of additive error is independent of the amount of the constituent present in the determination e.g., loss in weight of a crucible adds error to the weight of precipitate is ignited in it. ➢ On the other hand, the magnitude of proportional error depends upon the quantity of the constituent.

• e.g., impurity present in a standard substance gives a wrong value for the normality of a standard solution.

Random or Indeterminate Errors:

These errors are accidental and analyst has no control over them. ➢ These are random in nature and lead to both high and low result with equal probability. ➢ These cannot be eliminated or corrected and are the ultimate limitation on the measurement. ➢ These can be treated by statistics repeated measurements of the same variable can have the effect of reducing their importance.

Determination of Accuracy: Absolute Error

• The absolute error of a measurement is the difference between the measured value and the true value. If the measurement result is low, the sign is negative; if the measurement result is high, the sign is positive.

Absolute Error = Experimental Value - True Value

Relative Error

• The relative error of a measurement is the absolute error divided by the true value.
• Relative error may be expressed in percent, parts per thousand, or parts per million, depending on the magnitude of the result. % Error = Experimental Value- Theoretical Value Theoretical

× 100

A substance was known to contain 49.10 + or - 0.02 per cent of a constituent A. The results obtained by two analysts using the same substance and the same analytical method were as follows.

The arithmetic mean is 49.42% and the results range from 49.40% to 49.44%. We can summarise the results of the analyses as follows. ➢ The values obtained by Analyst 1 are accurate (very close to the correct result), but the precision is inferior to the results given by Analyst 2. The values obtained by Analyst 2 are very precise but are not accurate. ➢ The results of Analyst 1 face on both sides of the mean value and could be attributed to random errors. It is apparent that there is a constant (systematic) error present in the results of Analyst 2. Precision was previously described as the reproducibility of a measurement. However, the modern analyst makes a distinction between the terms 'reproducible’ and 'repeatable’. On further consideration of the above example: ➢ If Analyst 2 had made the determinations on the same day in rapid succession, then this would be defined as 'repeatable' analysis. However, if the determinations had been made on separate days when laboratory conditions may Vary, this set of results would be defined as 'reproducible’. Thus, there is a distinction between a within-run precision (repeatability) and a between-run precision (reproducibility).

Methods of expressing Precision:

Multiplication and Division:

Now suppose, on the other hand, that multiplication and division are involved’, i.e, let R= AB/C ABC. Again the actual measurements are A+ α ,B+ β and C+ ᵞ. Then Let us neglect , α and β , since it may be supposed that the errors are very small compared with the measured values. Then subtracting R=AB/C gives Placing the right-hand terms over a common terminator, we get ρ = R+ ρ = (A+ α ) (B+ β )

C+γ

= AB+ α B+ β A+ αβ C+γ C+γ ρ = AB+ α B+ β A

• AB C α BC+ β AC- γ AB C (C+ γ )

It is now convenient to consider the relative error, ρ /R by dividing by R=AB/C, which leads, after appropriate cancellation to Since ᵞ is very small compared with C, this reduces to Thus it is found that determinate errors are propagated follow.

1. Where addition or subtraction is involved, the absolute determinants errors are transmitted directly into the result.
2. Where multiplication or division is involved, the relative determinate errors are transmitted directly into the result. R ρ α BC+ β AC-^ γ AB = AB ( C+ γ ) ρ R = α (^) β (^) γ A B C

• (^) -