The document discusses various types of errors that can occur in quantitative chemical analysis, including random errors, systematic errors, determinate errors, indeterminate errors, and errors due to faulty instrumentation, impure reagents, or improper methodology. It also describes ways to minimize errors, such as calibrating apparatus, running blanks and controls, using multiple analytical techniques, and performing replicate measurements. Accuracy is defined as how close a measurement is to the true value, while precision refers to the reproducibility of measurements.

1. Errors
By

2. Definition
• Deviation from the absolute value or from the
true average of a large number of results.

3. Determinate / constant error
• Unsuspected
• May be avoided / determined
• Corrected
• Example
• Errors in calibration
• Operation of measuring instrument
• Impurities in the reagent.

4. Biased personal error
• Reading of meniscus.
• In weighing
• In matching colours
• In calculation

5. Determinate error can be combated by
• Use of calibrated apparatus.
• Use of blanks and controls.
• Several analaytical procedures.
• By eliminating impurities.
• By carrying out the experiment
under various condition.

6. Operational or personal error
• Individual Analyst is
responsible.
• Errors are physical in nature.
• It may occur when sound
analytical technique is not
followed.

7. Example of personal error
• Mechanical loss of material in various steps of an
analysis.
• Underwashing or overwashing of precipitate.
• Ignition of precipitates at incorrect temperature.
• Insufficient cooling of crucibles before weighing.
• Allowing hygroscopic materials to absorb moisture
before or during weighing.
• Use of reagents containing impurities.
• Person unable to judge changes sharply in visual
titrations which may result in slight overstepping of the
endpoint.

8. Instrument error
• Faulty construction of balances.

9. Reagent error
• The attack of reagents upon glassware result
in introduction of foreign materials.
• Volatilization of platinum at very high
temperatures.

10. Errors due to methodology
• Originate from incorrect sampling and
incompleteness of a reaction.
• In gravimetric analysis arise due to solubility
of precipitate, co-precipitation and post
precipitation.
• Volatilisation and decomposition on ignition.
• Precipitation of substance other than
intended one.

11. Errors due to methodology
• In titrimetric analysis , error may due to
occurrence of induced and side reaction.
• Reaction of substances other than the
constituent being determined.
• A difference in the observed and the
stoichiometric end point of a reaction.

12. Additive and proportional error
• Proportional error arise by the impurities
present in a standard substance.
• It leads to an incorrect value in the
normality of the standard solution.
• Loss in weight of crucible in which
precipitate is ignited and errors of
weights - additive error.

13. Indeterminate / Accidental error
• Successive measurements made by the same
observer under identical conditions produce
slight variations – indeterminate error
• It ‘s elimination by the analyst is impossible.
• Errors occur by accident or chance.
• It cannot be allowed for correction because of
the natural fluctuations that occur in all
measurements.

14. pseudo accidental or variable
determinate errors.
• Errors that arise from random fluctuation in
temperature or other external factors belong to
the determinate error are often called as pseudo
accidental or variable determinate errors.
• These errors may be reduced by controlling
conditions through the use of constant
temperature baths and ovens.
• The employment of buffers, maintenance of
constant humidity and pressure, reading fraction
of units on graduates, balances and apparatus
may reduce pseudo accidental errors.

15. MINIMIZATION OF ERRORS

16. Calibration of apparatus
• All apparatus like weights, flasks, burettes and
pipettes should be calibrated.
• The appropriate corrections applied to the
original measurements.
• In some case errors cannot be eliminated.
• Apply a correction for that effect.
• An impurity in a weighed precipitate may be
determined and its weight deducted

17. Running a blank determination
• It is carried out as a separate determination,
the sample being omitted, under exactly, the
same experimental conditions as employed in
the actual analysis of the sample.
• The object is to find out the effect of the
impurities introduced through the reagents
and vessels.

18. Running a control determination
• Determination carried out as nearly as
possible identical experimental conditions
upon a quantity of a standard substance
which contains the same weight of the
constituent.

19. Use of independent methods of
analysis
• Determination of strength of HCl both by
titration with solution of a strong base and by
precipitation and weighed as AgCl.
• If the results obtained by the two radically
different methods are concordant . It is highly
probable that the values are correct within
small limits of error.

20. Running parallel determination
• It serve as a check on the result of a single
determination and indicate only the precision
of the analysis.
• The values obtained should not less than
three parts per thousand.
• If larger variation is there then it must be
repeated until satisfactory concordance is
obtained.
• Duplicate / triplicate determination is suffice.

21. Standard addition
• A known amount of the constituent being is
added to the sample, which is then analysed
for the total amount of constituent present.
• The difference between the analytical results
for samples with and without added
constituent gives the recovery of the amount
of added constituent.
• If the recovery is satisfactory our confidence in
the accuracy of the procedure is enhanced.

22. • Even under constant experimental conditions
(same operator, same tools, and same
laboratory, short time intervals between the
measurements), repeated measurements of
series of identical samples always lead to
results which differ among themselves and
from the true value of the sample. Therefore,
quantitative measurements cannot be
reproduced with absolute reliability.

23. Random Errors.
• Random errors are the components of
measurement errors that vary in an
unpredictable manner in replicated
measurements.
• measuring techniques (e.g. noise),
• sample properties (e.g. In homogeneities),
• and chemical effects (e.g. equilibrium).
• Even under carefully controlled conditions
random errors cannot, in principle, be avoided,
they can only be minimized and evaluated with
statistical methods.

24. Systematic Errors.
• the closeness of agreement between the
expectation of a test result or measurement
result and a true value.
• According to their character and magnitude it
is classified as random and systematic.

25. ACCURACY

26. Definition
• The concordance between the data and the
true value.
• It is an agreement between the data and true
value.
• If true value is not known the mean calculated
from results obtained from several different
analytical methods which are very precise and
in close agreement with one another may be
considered the true value in practical sense.

27. • The difference between the mean and the
true value is known as absolute error.
• The relative error is found by dividing the
absolute error by the true value.
• Relative error is usually reported on a
percentage basis by multiplying the relative
error by 100.
• If reported in parts by multiplying the relative
error by 1000

29. Absolute method
• The substance must be of known purity.
• The test of the accuracy of the method under
consideration is carried out by taking varying
amounts of the constituent and proceedings
according to specified instruction.
• The amount of the constituent must be varied,
because the determinate errors in the
procedure may be a function of the amount
used.

30. Method I
• It is a measure of accuracy in the absence of
foreign substance
• The difference between the mean of an
adequate number of results and the amount
of the constituent actually present.
• It is usually expressed as parts per thousand.

31. Method II
• The constituent in the presence of other
substance.
• It require testing the influence of a large
number of elements each in varying the
amounts.
• Separation is required before determination.
• The accuracy of the method is largely
controlled by separation.

32. Comparative method
• In analysis it is impossible to prepare solid
synthetic samples of desired composition.
• Necessary to sort a standard sample is in
question.
• It is determined by one or more accurate
method of analysis.
• It involves secondary standard not satisfactory
from theoretical standpoint.

33. • It is useful in applied analysis.
• If fundamentally different methods of analysis
for a given constituent [ gravimetric,
titrimetric and spectrometric]. The agreement
between at least two methods of essentially
different character can usually be accepted as
indicating the absence of an appreciable
determinate error .

34. PRECISION

35. Precision
• The concordance of a series of measurements
of the same quantity.
• The mean deviation or the relative mean
deviation is a measure of precision.
• It is a measure of reproducibility of data
within a series of result.
• Results within a series which agree closely
with one another are said to be precise.

36. • Precise results are not necessarily accurate for
a determined error may be responsible for the
inaccuracy of each result in a series of
measurement.
• It is usually reported as the average deviation,
standard deviation or range.
• Precision is a measure of the agreement
among the values in a group of data.

37. • Accuracy is the agreement between the data
the true value.
• In quantitative analysis the precision of
measurements rarely exceeds 1 to 2 parts per
thousand.
• Accuracy expresses the correctness of a
measurement
• Precision the reproducibility of a
measurement.

38. • Precision always accompany accuracy, but a
high degree of precision does not imply
accuracy.
• Example
• A substance contain 49.06 + 0.02 of
constituent.
• Analyst I = 49.01
• Analyst II = 49.42

39. • The analyst I is accurate and precise but
analyst II is precise but less accurate than
Analyst I .
• It is established during the development stage
• It wont include
• Day – to – day fluctuation, lab to lab variation,
small modification in technique varying skills
of analysis, undetected, operational or
instrumental factors.

48. Quality Assurance vs. Quality
Control
Quality Assurance
An overall
management plan to
guarantee the
integrity of data
(The “system”)
Quality Control
A series of
analytical
measurements used
to assess the
quality of the
analytical data
(The “tools”)

49. True Value vs. Measured Value
True Value
The known,
accepted value of
a quantifiable
property
Measured Value
The result of an
individual’s
measurement of
a quantifiable
property

50. Accuracy vs. Precision
Accuracy
How well a
measurement agrees
with an accepted
value
Precision
How well a series of
measurements agree
with each other

51. Systematic vs.
Random Errors
Systematic Error
Avoidable error due
to controllable
variables in a
measurement.
Random Errors
Unavoidable errors
that are always
present in any
measurement.
Impossible to
eliminate

52. Internal Standards
• A compound chemically similar to the
analyte
• Not expected to be present in the
sample
• Cannot interfere in the analysis
• Added to the calibration standards
and to the samples in identical
amounts.

53. Internal Standards
• Refines the calibration process
• Analytical signals for calibration
standards are compared to those for
internal standards
• Eliminates differences in random and
systematic errors between samples
and standards