The document explains the concept of error in analytical chemistry, highlighting the importance of reliability and accuracy due to potential serious consequences from errors in laboratory results. It categorizes errors into determinate (systematic) and indeterminate (random) errors, discussing their sources, effects, and examples, as well as methods to minimize these errors. Additionally, it covers procedures for improving accuracy and precision in analyses, such as calibration, blank determinations, and the use of standard additions.

2. • Error is the difference between the true result (or accepted
true result) and the measured result.
• Error = Measured Mean Value – True Value
True Value
•And the difference between the experimental value and true
value is termed as Absolute Error.
• Absolute error may be negative or positive.
• If the error in an analysis is large, serious consequences may
result.
• As reliability, reproducibility and accuracy are the basis of
analytical chemistry.
• A patient may undergo expensive & even dangerous medical
treatment based on an incorrect laboratory result because of an
analytical error.
INTRODUCTION OF ERRORS

3. Errors in the results in an analysis can be resulted from various
sources. Some major sources of errors in pharmaceutical
analysis are described here under:
1. Human Sources: The Qualification and experience of an
analyst performing the analysis has major impact on error
in results. If an experiment is performed by inexperienced
person the chances of error are more as compared to same
experiment performed by the experienced analyst.
2. Instrumental, Apparatus and Glassware: If the Instrument,
Glassware as well as apparatus used in analysis is of low
quality and uncalibrated the chances of error are increased
at significant extent.
SOURCES OF ERRORS

4. 3. Experimental Conditions: If the analysis is carried out in the
conditions which are unfavorable for particular experiment
or analysis the desirable result will not obtained.
4. Constituents used in Analysis: If various constituents like
standard, Solvents, Reagents etc used in analysis are not of
desired quality and purity the results will be obtained with
errors.
5. Procedure: If analytical Procedure used in analysis is not
validated and if validated but not followed carefully the
errors in the results will obtained.

5. Errors that may be broadly divided into two heads,
namely : (i) Determinate (systematic)Errors
(ii)Indeterminate (random) Errors
1. Determinate (Systematic) Errors –These are errors that
possess a definite value with a reasonable cause and these
avoidable errors may be measured and accounted for
rectification. The most important errors belonging to this
particular class are :
(a) Personal Errors : They are exclusively caused due to
‘personal equation’ of an analyst and do not due to either
on the prescribed procedure or methodology involved.
TYPES OF ERRORS

6. (b) Instrumental Errors : These are invariably caused due to
faulty and uncalibrated instruments, such as : pH meters, uv-
spectrophotometers, potentiometers etc.
(c) Reagent Errors : The errors that are solely introduced by
virtue of the individual reagents, for instance : impurities
inherently present in reagents ; high temperature volatalization
of platinum (Pt) ; unwanted introduction of ‘foreign
substances’ caused by the action of reagents on either
porcelain or glass apparatus.
(d) Constant Errors : They are observed to be rather
independent of the magnitude of the measured amount ; and
turn out to be relatively less significant as the magnitude
enhances.

7. (e) Proportional Errors : The absolute value of this kind of
error changes with the size of the sample in such a fashion that
the relative error remains constant. It is usually incorporated
by a material that directly interferes in an analytical procedure.
(f) Errors due to Methodology : Both improper (incorrect)
sampling and incompleteness of a reaction often lead to
serious errors. A few typical examples invariably encountered
in titrimetric and gravimetric analysis
(g) Additive Errors : It has been observed that the additive
errors are independent of the quantum of the substances
actually present in the assay.
Examples : (i) Errors caused due to weights, and (ii) Lossin
weight of a crucible in which a precipitate is incinerated.

8. 2. Indeterminate (Random) Errors- As the name suggests,
indeterminate errors cannot be pin-pointed to any specific
well-defined reasons.. These errors are mostly random in
nature and ultimately give rise to high as well as low results
with equal probability. They can neither be corrected nor
eliminated, and therefore, form the ‘ultimate limitation’ on the
specific measurements.

9. Salient Features of Indeterminate Errors-
(1)Repeated measurement of the same variable several times
and subsequent refinement to the extent where it is simply
a coincidence if the corresponding replicates eventually
agree to the last digit,
(2)Both unpredictable and imperceptible factors are
unavoidably incorporated in the results what generally
appear to be ‘random fluctuations’ in the measured
quantity.
(3)Recognition of specific definite variables which are beyond
anyone’s control lying very close to the performance limit
of an instrument, such as : temperature variations, noise as
well as drift from an electronic circuit, and vibrations
caused to a building by heavy vehicular-traffic.

10. MINIMIZATION OF ERRORS

11. All instruments (weights, flasks, burettes, pipettes, etc.) should be
calibrated, and the appropriate corrections applied to the original
measurements.
 In some cases where an error cannot be eliminated, it is possible to
apply a correction for the effect that it produces; thus an impurity in a
weighed precipitate may be determined and its weight deducted.
Calibration of apparatus and application of corrections

12. This consists in carrying out a separate determination, the sample being
omitted, under exactly the same experimental conditions as are 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, or to determine the excess of standard solution
necessary to establish the end-point under the conditions met with in the
titration of the unknown sample.
A large blank correction is undesirable, because the exact value then
becomes uncertain and the precision of the analysis is reduced.
Running a blank determination

13. This consists in carrying out a determination under as nearly as
possible identical experimental conditions upon a quantity of a standard
substance which contains the same weight of the constituent as is
contained in the unknown sample. The weight of the constituent in the
unknown can then be calculated from the relation:
Results Found For Standard Weight of Constituent in Standard
=
Results Found For Unknown X
Where,
x is the weight of the constituent in the unknown.
Standard samples include primary standards (sodium oxalate,
potassium hydrogen phthalate, arsenic(II1) oxide, and benzoic acid) and
ores, ceramic materials, irons, steels, steel-making alloys, and non-
ferrous alloys.
Running a control determination

14. Example1:
• Iron may first be determined gravimetrically by precipitation as
iron(II1) hydroxide after removing the interfering elements, followed by
ignition of the precipitate to iron(II1) oxide.
• It may then be determined titrimetrically by reduction to the iron(I1)
state, and titration with a standard solution of an oxidising agent, such as
potassium dichromate or cerium(1V) sulphate.
Example 2:
• Determination of the strength of a hydrochloric acid solution both by
titration with a standard solution of a strong base and by precipitation
and weighing as silver chloride.
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.
Use of independent methods of analysis

15. These serve as a check on the result of a single determination and
indicate only the precision of the analysis.
The values obtained for constituents which are present in not too small
an amount should not Vary among themselves by more than three parts
per thousand. If larger variations are shown, the determinations must be
repeated until satisfactory concordance is obtained. Duplicate, and at
most triplicate,
 Determinations should suffice. It must be emphasized that good
agreement between duplicate and triplicate determinations does not
justify the conclusion that the result is correct; a constant error may be
present.
The agreement merely shows that the accidental errors, or variations of
the determinate errors, are the same, or nearly the same, in the parallel
determinations.
Running parallel determinations

16. A known amount of the constituent being determined is added to the
sample, which is then analyzed for the total amount of constituent
present.
The difference between the analytical results for samples with and
without the 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.
 The method is usually applied to physico-chemical procedures such as
polarography and spectrophotometry.
Standard addition

17. This procedure is of particular value in spectroscopic and
chromatographic determinations.
It involves adding a fixed amount of a reference material (the internal
standard) to a series of known concentrations of the material to be
measured.
The ratios of the physical value (absorption or peak size) of the internal
standard and the series of known concentrations are plotted against the
concentration values. This should give a straight line.
Any unknown concentration can then be determined by adding the
same quantity of internal standard and finding where the ratio obtained
falls on the concentration scale.
Internal standards

18. Amplification methods
It is used when a very small amount of material is to be
measured which is beyond the limit of the apparatus.

19. A known amount of the element being determined, containing a
radioactive isotope, is mixed with the sample and the element is isolated
in a pure form (usually as a compound), which is weighed or otherwise
determined.
The radioactivity of the isolated material is measured and compared
with that of the added element: the weight of the element in the sample
can then be calculated.
Isotopic dilution

20. ACCURACY
• Near to the true value/standard value is known as Accuracy.
• It is degree of agreement between True value/standard value and
Measured value/observed value.
• True value is rarely known so Standard value is used.
A B
C
O O O
10
9
8
7
O
O
O
O O
O
A=29
B=26
C=25
Standard Value=30

21. Question:-
There are two analysts X&Y, who determine the percentage of the PCM
in the same brand of tablet. The Standard value of PCM in that tablet
is 100% & obeservations are given below.
Analyst X: 99.80, 99.90, 100.00, 99.30
Analyst Y: 98.75, 98.75, 98.80, 98.80
Who has done more Accurate Analysis?
Solution:-
Standard value=100%
99.80+99.90+100.00+99.30 399
Analyst X = 4 = 4 = 99.75
Error =100-99.75 = 0.25%
98.75, 98.75, 98.80, 98.80 395.1
Analyst X = 4 = 4 = 98.775
Error =100- 98.775 = 1.225%
Analyst X has done the more Accurate Analysis.

22. PRECISION
• Repeatability of the values is known as Precision, if done for the same
quantity.
•Precision is defined as degree of agreement between Replicate
measurement of same quantity.
•It is determined/expressed in terms of standard deviation.
A B
C
O O
O
10
9
8
7
O
O
O
O O
O
A=30
B=24
C=24

23. Question:-
Two analysts done the analysis &standard value is 100% &
obeservations are given below.
Analyst X: 97, 96, 99, 96
Analyst Y: 92, 91, 93, 92
Who has done more Accurate Analysis?
Solution:-
S=√Ʃ(x-x⁻)²
N-1
Analyst A: S=√6/4-1=√2 =1.414
Analyst B : S=√2/4-1=√0.667 =0.816
Analyst B has done the more Precise Analysis.

24. Definition: Significant Figures of a number are those digits,
which carries meaning contributing to its measurement
resolution.
Rules:
1.It is based on Decimal System.
0,1,2,3,4,5,6,7,8,9 is used.
2.All Non Zero digits are Considered as Significant.
i.e.,1,2,3,4,5,6,7,8,9
3.All leadings Zeros are non-significant
Eg.,0.077---4
4.If any zero is coming in between the two non-zero values
then those zeros will be, considered as significant.
Eg.,2008---4 3.002---4
SIGNIFICANT FIGURES

25. 5.Trailing Zero rule
It present in Decimal- Significant
eg.,2.70---3 2.700---4
It present without Decimal- NonSignificant
eg.,270---2 2700---2
6. If any value is present as10ⁿ or 10‫־‬ⁿ than considered as
non-significant.
Eg.,1.3x10³‫־‬---2 1.3x10³---2
7. Significant figures of the measurement of any instrument
should not be greater than the instrument limit.
Eg.,1.0001g - 0.50005g - 0.5001g
8. Constant values like ᴫ(pi) contains n no. of significant
figures
Eg.,800---1 29.090---5 2.07---3