This document discusses errors in chemical analysis. It defines types of errors such as absolute error, relative error, accuracy, and precision. It also differentiates between systematic/determinate errors and random/indeterminate errors. Systematic errors affect accuracy and can be constant or proportional. Random errors cause scattered data and tend to cancel out with more measurements. Gross errors are large, careless mistakes by the experimenter. Sources and corrections of different error types are also outlined.

1. CHM 2201
ERRORS IN CHEMICAL ANALYSIS
By Godfrey Muhwezi
Monday,
September
19, 2022 1

2. To cover in this section
• Definitions
• Absolute and relative error
• Types of errors and their causes
• Estimation of error
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3. Definitions
• True Result; The 'correct' value for a measurement which remains
unknown except when a standard sample is being analysed. It can be
estimated from the results with varying degrees of precision depending on
the experimental method
• Accuracy; The nearness of a measurement or result to the true value.
Expressed in terms of error.
• Error refers to the difference between a measured value and the “true” or
“known” value.
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4. Definition continued
• Precision; The variability of a measurement. As in the case of error,
above, it may be expressed as an absolute or relative quantity. Standard
deviations are the most valuable precision indicators.
• Spread: The numerical difference between the highest and lowest results
in a set. It is a measure of precision.
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5. Absolute error
• Absolute error is defined as the actual difference between the true result and the experimental value
in the same units.
• The absolute error E in the measurement of a quantity xi is given by the equation
where xt is the true, or accepted, value of the quantity
Note that we retain the sign in stating the error
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6. Relative error
• Often, the relative error Er is a more useful quantity than the absolute error.
The percent relative error is given by the expression (Expressed as a
percentage)
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7. • Relative error can also be represented in ppt(parts per thousand) or ppb
parts per billion
• Relative error (Er)= [ Xi- Xt)/ Xt] 1000 ppt (expressed as a ppt)
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8. Examples
• 1. Okot measured the weight of pineapple approximated as 682.325g, but the
original weight is 684.075g. Determine the absolute and relative error in the
weighing
• 2. Suppose that the collision frequency for Argon atoms striking other Argon
atoms in the upper atmosphere was calculated as 1005 and that the accepted
value was 1000. What is the relative error?
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9. Types of errors.
1. Systematic or determinate errors
• The errors that affect the accuracy of a result. This type of error causes the
mean of a set of data to differ from the accepted value. A systematic error
causes the results in a series of replicate measurements to be all high or all
low.
• Systematic errors may be constant or proportional. Constant errors are
independent of the size of the sample being analyzed. Proportional errors
decrease or increase in proportion to the sample size.
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10. Examples of systematic errors
• Heat loss in an experiment to measure enthalpy change
• Losing a product (such a gas) in a reaction
• Overshooting the end point in a titration
• Reading meniscus the wrong way- say reading from the top when measuring volume
• Forgetting to zero a mass balance
• Add more
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11. Sources of systematic or determinate errors
• Instrument type:
• All measuring instruments are potential sources of systematic errors eg Pipettes, burettes,
may hold or deliver volumes slightly different from that one indicated by their graduations.
These differences arise from;
a. Using glassware at a temperature that differs significantly from the calibration temperature
b. Distortions from the container walls due to heating while drying,
c. Errors from the original calibration
d. From contaminations from the inner walls of the containers
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12. Source of systematic errors continued
• Method errors: These arise from non ideal chemical or physical behavior
of analytical systems. Method errors can be caused by
a) Slowness of some reactions
b) Incompleteness of others e.g. decomposition of the pyridine ring
c) Instability of some species
d) Lack of specificity of most reagents
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13. Sources of systematic errors continued
• Personal errors: These result from the carelessness, inattention, or
personal limitations of the experimenter. E.g
a. In estimating the position of a pointer between two scale divisions
b. The colour of a solution at the end point in a titration
c. The level of a liquid with respect to a graduation in a pipette or burette.
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14. Correction of systematic errors
• Instrument errors: Use of periodic calibration
• Method errors: These are estimated by analysing standard reference
materials.
• Personal errors: Can be minimized by care and self-discipline. Errors due to
limitations of the experimenter can usually be avoided by carefully choosing
the analytical method or using an automated procedure
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15. Blank Determinations
• Blank determinations are useful for detecting certain types of constant
errors. In blank determination all steps of the analysis are performed in the
absence of a sample. A blank solution contains the solvent and all the
reagents in an analysis but none of the sample. The results from the blank
are then applied as a correction to the sample measurements. Blank
determinations reveal errors due to interfering contaminants from the
reagents and vessels employed in analysis.
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16. Random or indeterminate errors
These are errors brought or arising from our natural limitations on our ability
to make physical measurements.
• They affect the distribution of values around the central value and are
characterised by the random variation of both the magnitude and direction.
• Since indeterminate errors are randomly scattered around a central value,
positive and negative errors tend to cancel, provided that enough
measurements are made. In such situations the mean or median is largely
unaffected by the precision of the analysis. Monday, September 19,
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17. • It causes data to be scattered more or less symmetrically around a mean
value. Can be positive or negative around the mean value.
• They are non-identifiable because most are too small to be identified.
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18. Gross errors
These errors are personal and arise from the carelessness or ineptitude of the experimenter or analyst hence they
are often the product of human errors
• They usually affect a single result in a set of replicate data causing it to differ significantly from the remaining
results for that particular set.
• They usually occur only occasionally, are often large, and may cause a result to be either high or low.
• Gross errors lead to outliers, results that appear to differ markedly from all other data in a set of replicate
measurements.
• For example
 Reversing a sign
 Spilling a solution
 Reading a scale backward
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19. Sources of Gross errors
a. Human over sight e.g when monitoring 1.50, you will write 1.05.
b. Mistakes while reading and recording; one may read 23 as 28.
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20. • Correction
 They can be eliminated through self-discipline
 Using an average measurement for a set of measurements
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