Errors in Analysis
Content
• Error
• Types of error
• Minimizing the errors
• Accuracy, precision and significant figures
Learning
Objectives
At the end of this lecture, the student will be able to
• Define error
• Classify error
• Discuss about determinate and indeterminate error
• Explain how to minimize the error at each step
• Discuss about the different types of methods for minimizing
the errors
• Define Accuracy, precision, Significant figures
Errors
Definition: Error
is the difference between the true result (and accepted true result) and the
measured result
Expression of Errors
Errors are expressed either in absolute terms or in relative
terms
Absolute Errors: E abs = Calculated value
–True Value
Relative Error: Used
in the determination of accuracy of a measurement and is expressed in terms of
percentage
Relative Error E rel: Absolute
error/True value X100
It is also expressed in parts per thousand (ppt)
Types of
Errors:
Determinate or systematic error
Indeterminate or random error
Determinate
errors
• Determinate errors are caused by faults in the analytical
procedure or the instruments used in the analysis
• The name determinate error implies that the cause of this
type of error may be found out and then either avoided or corrected
• Determinate errors are systematic errors; that is, they are
not random
• Sometimes the determinate error is proportional to the
true result, giving rise to proportional errors
• Other determinate errors may be variable in both sign and
magnitude, such as the change in the volume of a solution as the temperature
changes
• Although this variation can be positive or negative, it can
be identified and accounted for
• Determinate errors can be additive or they can be
multiplicative
• It depends on the error and how it enters into the calculation
of the final result
• This determinate error could be the result of an
incorrectly calibrated balance
For example:
• If the balance is set so that the zero point is actually
0.5 mg too high, all masses determined with this balance will be 0.5 mg too
high
• If this balance was used to weigh any standard solution
used in the laboratory, the standard concentration will be erroneously high,
and all of the results obtained using this standard will be erroneously low
• The error is reported as the absolute error, the absolute
value of the difference between the true and measured values
How are determinate errors
identified and corrected?
• Two methods are commonly used to identify the existence of
systematic errors
Standard methods and
To run several analyses
• Standard method:
is to analyze the sample by a completely different analytical procedure that is
known to involve no systematic errors
• They have been evaluated extensively by many laboratories
and shown to be accurate and precise
• If the results from the two analytical methods agree, it
is reasonable to assume that both analytical procedures are free of determinate
errors
• The second method is to run several analyses of a reference
material of known, accepted concentration of analyte
• The difference between the known (true) concentration and
that measured by analysis should reveal the error
• If the results of analysis of a known reference standard
are consistently high (or consistently low), then a determinate error is
involved in the method
How to correct the
determinate error?
• The cause of the error must be identified and either
eliminated or controlled if the analytical procedure is to give accurate
results
• Many clinical and analytical laboratories participate in
proficiency testing programs, where “unknown” standard samples are sent to the
laboratory on a regular basis
• The results of these samples are sent to the government or
professional agency running the program
• The unknowns are of course known to the agency that sent
the test samples; the laboratory receives a report on the accuracy and
precision of its performance
Reasons for
determinate errors in analytical procedures:
• uncalibrated balances
• Improperly calibrated volumetric flasks
• Pipettes, malfunctioning instrumentation,
• Impure chemicals
• Incorrect analytical procedures or techniques
• Analyst error
The following are the
types of determinate errors may be noted:
a) Operational and personal errors
b) Instrumental and reagent errors
c) Errors of method
d) Additive and proportional errors
Determinate
Errors: a) Operational and Personal Errors
• Analyst error: The person performing the analysis causes
these errors
• They may be the result of inexperience, insufficient
training, or being “in a hurry”
• An analyst may use the instrument incorrectly, perhaps by placing
the sample in the instrument incorrectly each time
• Setting the instrument to the wrong conditions for
analysis
• Consistently
misreading a meniscus in a volumetric flask as
high (or low)
Improper use of
pipettes, such as
These are due to factors for which the individual analyst
is responsible and are not connected with the method or procedure
They form part of the ‘personal equation’ of an observer
The errors are mostly physical in nature and occur when sound
analytical technique is not followed
Examples:
• Mechanical loss of materials in various steps of analysis
• Under washing or over washing of precipitates
• Ignition of precipitates at incorrect temperatures
• Insufficient cooling of crucibles before weighing
• Allowing hygroscopic materials to absorb moisture before
and after weighing
• Allowing the volatile materials to volatile after weighing
• Maintaining incorrect temperature and time for reaction before
completion
•Burette reading properly not done
• Some other analyst-related errors are Carelessness, which is
not as common as is generally believed transcription errors, that is, copying
the wrong information into a lab notebook or onto a label Calculation errors
Elimination of this
error:
• Proper training, experience, and attention to detail on
the part of the analyst can correct these types of errors
Determinate
Errors: b) Instrumental and Reagent Errors
•These arises due to the faculty construction of balances,
use of uncalibrated weights, improperly graduated glass wares and other
instruments
1. Instrumental
errors:
• Numerous errors involving instrumentation are possible,
including:
Faulty construction of balances
Use of uncalibrated or improperly calibrated weights
incorrect instrument alignment
Incorrect wavelength settings
Incorrect reading of values, and incorrect settings of the
readout (i.e., zero signal should read zero)
• Any variation in proper instrument settings can lead to
errors
• In instrumental analysis, electrical line voltage
fluctuations are a particular problem
• This is especially true for automated instruments running
unattended overnight
• Instruments are often calibrated during the day, when
electrical power is in high demand. At night, when power demand is lower, line
voltage may increase substantially, completely changing the relationship between
concentration of analyte and measured signal
• Regulated power supplies are highly recommended for analytical instruments. The procedure for unattended analysis should include sufficient calibration checks during the analytical run to identify such problems
Elimination of such
errors:
• These problems can be eliminated by a systematic procedure
to check the instrument settings and operation before use
• Such procedures are called standard operating procedures
(SOPs) in many labs
• There should be a written SOP for each instrument and each
analytical method used in the laboratory
2. Reagent errors:
• Contaminated or decomposed reagents can cause determinate
errors
• Impurities in the reagents may interfere with the
determination of the analyte, especially at the ppm level or below
• Prepared reagents may also be improperly labeled
• The suspect reagent may be
tested for purity using a known procedure or the analysis should be
redone using a different set of
reagents and the
results should be compared
Determinate
Errors: c) Errors of Method
These errors are due to incorrect sampling and form
incompleteness of a reaction
For Example: In titrimetric analysis:
Due to failure of reaction to proceed to completion
Occurrence of side reactions
Reactions of substances other than the constituents being
determined
A difference between the observed end point and stoichiometric
end point of the reaction
Determinate
Errors: d) Additive and Proportional Errors
• The absolute value of an additive error is independent of amount
of constituent present in the determination
For example:
Loss in weight of a crucible in which a precipitate is ignited
and errors in weights. The presence of this error is revealed by taking samples
of different weights
Powdered gloves may contain a variety of trace elements and
should not be used by analysts performing trace element determinations
• The absolute value of a proportional error depends upon
the amount of the constituents
For example:
Estimation of ‘chlorate’—an oxidant by iodometric determination
--Presence of ‘Bromate’—another oxidizing agent would give rise to positively
higher results, and hence, it must be duly corrected
Indeterminate
Errors
Indeterminate errors are not constant or biased
They are random in nature
Are the cause of slight variations in results of replicate samples
made by the same analyst under the same conditions
For example:
A balance that is capable of measuring only to 0.001 g
cannot distinguish between two samples with masses of
1.0151 and 1.0149 g
In one case the measured mass is low, in the other case it
is high
These random errors cause variation in results, some of which
may be too high and some too low
The average of the replicate determinations is accurate,
but each individual determination may vary slightly from the true value
Indeterminate errors arise from sources that cannot be corrected,
avoided, or even identified, in some cases
Commonly Identified
Indeterminate Errors
• Concentration errors
• Labeling errors
• Calculation errors
• Manual calculation using wrong formula Computational
calculation
• Using wrong formula in excel Using different location (wrong
cell) in the excel sheet
• Improper use of symbols
• Rounding off errors
Minimization
of Errors
Analyst has no control on random errors but systemic errors
can be reduced by following methods:
Calibration of
apparatus: By calibrating all the instruments, errors can be minimized and
appropriate corrections are applied to the original measurements
Control
determination: Standard substance is used in experiment in identical
experimental condition to minimize the errors
Blank determination:
By omitting sample, a determination is carried out in identical condition to minimize
the errors occurs due to impurities present in reagent
Independent method of
analysis: It is carried out to maintain accuracy of the result
For Example: Iron (III) is first determined gravimetrically
by precipitation method as iron (III) hydroxide and then determined
titrimetrically by reduction to the iron (II) state
Parallel
determination: Instead of single determination, duplicate or triplicate
determination is carried out to minimize the possibilities of accidental errors
Standard addition:
This method is generally applied to physico-chemical procedures such as
polarography and spectrophotometry
Internal standards:
It is used in spectroscopic and chromatographic determination
Amplification methods:
It is used when a very small amount of material is to be measured which is
beyond the limit of the apparatus
Isotopic dilution:
It is used for the compound containing radio-active isotope
Understand the
Importance of Each Step to Minimize Errors
GENERAL INSTRUCTIONS:
For minimizing errors for analytical reagents:
No bottle is to be opened for a longer time than is
absolutely necessary
No reagent is to be returned to the bottle after it has
been removed
Liquid reagents should be poured from the bottle
A pipette should never be inserted into the reagent bottle
Particular care should be taken to avoid contamination of
the stopper of the reagent bottle
When a liquid is poured from a bottle, the stopper should
never be placed on the shelf or on the working bench it may be placed upon a
clean watch glass
Many chemists
cultivate the habit
of holding the
stopper between the thumb and fingers of one hand
The stopper should be returned to the bottle immediately
after the reagent has been removed, and all reagent bottles should be kept
scrupulously clean, particularly round the neck or mouth of the bottle
• Allow the flask to stand for a while before making the
final adjustment to the mark to ensure that the solution is at room temperature
• It should be noted, however, that for some solutions as,
for example, iodine and silver nitrate, glass containers only may be used, and
in both these cases the bottle should be made of dark (brown) glass
• Solutions of EDTA are best stored in polythene containers
• Immediately after the solution has been transferred to the
flask, it should be labelled with:
(1) The name of the solution
(2) Its concentration (if any)
(3) The data of preparation and
(4)The initials of
the person who
prepared the solution, together
with any other relevant data
GENERAL INSTRUCTIONS:
For minimizing errors for weighing:
The chief sources of error are the following:
• Change in the condition of the containing vessel or of the
substance between successive weighing by absorption or loss of moisture, by
electrification of the surface caused by rubbing, by its temperature being
different from that of the balance case
• Effect of the buoyancy of the air upon the object and the weights
• Hygroscopic, efflorescent, and volatile substances must be
weighed in completely closed vessels
• Substances which have been heated in an air oven or
ignited in a crucible are generally allowed to cool in a desiccator containing
a suitable drying agent
• Substances which have been heated in an air oven or
ignited in a crucible are generally allowed to cool in a desiccator containing
a suitable drying agent
• The time of cooling in a desiccator cannot be exactly
specified, since it will depend upon the temperature and upon the size of the
crucible as well as upon the material of which it is composed
• Platinum vessels require a shorter time than those of
porcelain, glass, or silica
• It has been customary to leave platinum crucibles in the desiccator
for 20-25 minutes, and crucibles of other materials for 30-35 minutes before
being weighed
• It is advisable to cover crucibles and other open vessels
GENERAL INSTRUCTIONS:
For Minimizing Errors for graduated flasks:
Vessels intended to contain definite volumes of liquid
• The neck is made narrow so that a small change in volume
will have a large effect upon the height of the meniscus
• The error in adjustment of the meniscus is accordingly
small
• To read the position of the meniscus, the eye must be at
the same level as the meniscus, in order to avoid errors due to parallax
GENERAL INSTRUCTIONS:
For Minimizing Errors Reading a burette / pipette:
The analyst reads the burette from a position above a line
perpendicular to the burette and makes a reading of 12.58 mL or 12.67 mL
The analyst reads the burette from a position along a line perpendicular to the burette and makes a reading of 12.6 mL
GENERAL INSTRUCTIONS:
For Minimizing Errors SAMPLE PREPARATION PRECAUTIONS:
• Sample preparation should be performed in a:
Laboratory fume
hood
For safety use Goggles
Lab coats or aprons
Gloves resistant to
the chemicals in use should be worn at all times in the laboratory
Errors in
Assay
• Incorrect weighing and transfer of analyte and standards
• Insufficient extraction of the analyte from the matrix e.g.
tablets
• Incorrect use of pipettes, burettes, volumetric flasks for
volume measurement
• Measurement carried out using improperly calibrated
instrumentation.
• Failure use an analytical blank
• Selection of assay conditions that cause degradation of
the analyte
• Failure to allow for or to remove interference by
excipients in the measurement of an analyte
Errors in
Titrimetric Analysis
• Failure of reactions to proceed to completion Involvement
of either induced or side reactions
• Reactions due to substances other than the one being
assayed
• A noticeable difference occurring between the
stoichiometric equivalence point of a reaction and the observed end-point
Accuracy,
Precision
• Accuracy
How close mean of measured values is to true value
• Precision
Repeatability of measurements
Example:
Determine the accuracy and precision of the mass of a piece of a metal
performed by three different students, where mass of a piece of metal is
0.520gm. Data obtained by each student are recorded as follow.
Student A: 0.521, 0.521, 0.509 Average: 0.515
Student B: 0.516, 0.515, 0.514 Average: 0.515
Student C: 0.521, 0.520, 0.520 Average: 0.520
Significant
Figures
• Digit: Any one of the ten numerals, including zero
• Significant figure:
A digit which denotes the amount of the quantity in the place in which it
stands
For example: 2.7808 g and 1.0032 g → zero is significant,
whereas in 0.0050 g → zero is not significant but only to locate the decimal
point, the value can also be written as 5mg
Summary:
• Error: The difference between the true result (or accepted
true result) and the measured result
• Classification of errors: Determinate error → which can be
determined, indeterminate error → which cannot be determined
•Classification of determinate error:
a) Operational and personal errors
b) Instrumental and reagent errors
c) Errors of method
d) Additive and proportional errors
• Minimization of error: Calibration of apparatus, Controlled
determination, Blank determination, Independent methods of analysis, Parallel
determination, amplification method, standard addition method, internal standard
method, isotopic dilution
• Correct way of using analytical reagents, bottles,
samples, weighing, burette, pipette and graduated flasks can minimize the
errors
•Accuracy: How close is mean of measured values is to true
value
• Precision: Repeatability of measurements
• Significant figure: A digit which denotes the amount of the
quantity in the place in which it stands
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