Nature and Scope of Error, Chemistry tutorial


Analytical chemistry is the branch of chemistry that seeks ever enhanced signifies of measuring the chemical composition of natural and artificial materials. The methods of this science are employed to recognize the substances that might be present in a material (that is, qualitative analysis) and to find out the precise amounts of the recognized substance (that is, quantitative analysis).

The modern analytical chemistry is overwhelmingly a quantitative science. It might be helpful for an analyst to proclaim to have detected some boron in the distilled water sample; however it is much more helpful to be capable to state how much boron is present. The errors that take place in qualitative studies in any analytical laboratory are of greatest significance.

Definitions of Errors:

Error is stated as a difference between the computed, estimated or measured value and the accepted true, specified or theoretically precise value. The quantitative results are not of any value unless they are accompanied via some estimate of the errors inherent in them. This principle is mainly applicable to any field of study in which the numerical experimental outcomes are obtained.

This is common to carry out replicate determinations in the course of a single experiment in order to reveal the presence of random errors. For illustration, an analyst carries out a titrimetric experiment three times and acquires values of 31.29, 31.16 and 33.29ml. It must be noted that because of variations inherent in the measurements all the three values are different. This is evident that the third titre is substantially dissimilar from the other two.

This signifies the two titres are reported as 31.23ml whereas the third value is discarded.

The second frequent problem comprises the comparison of two or more sets of result. Assume that the vanadium content of steel sample was computed by two dissimilar processes. The first process has an average value of around 1.04% having an estimated error of 0.07% and the average value for the second process is 0.95% having an error of 0.04%. Some of questions occur from such results. Are the errors in the two processes significant difference? Are the two average values considerably difference? Which of the mean values is closer to the truth?

Types of Errors:

Three kinds of errors have been recognized. These are termed as gross, random and systematic errors.

Gross Errors:

Gross errors are stated as errors which are so serious that there is no real alternative to discard the experiment and making a fresh beginning. The complete instrumental breakdown and accidentally dropping of a crucible throughout the course of experiment demonstrate gross errors. Such errors takes place only occasionally even in the best synchronized laboratories.

Random Errors:

These are the indeterminate errors and can't be ignored due to the uncertainty in each and every experiment. These kinds of errors are as well termed as accidental errors and are because of inherently unpredictable fluctuations in the readings of measurement of apparatus or in the experimenter's interpretation of instrumental reading. Random errors influences exactness and cause replicate yields to fall on either side of a mean value. Such errors can be estimated by employing replicate measurements and are minimized by good method like averaging of multiple measurements however not removed. Random errors are caused due to both humans and equipment.


a) The kind of variation related by the same analyst reading the identical absorbance scale lots of times.

b) Variation related by three or four different analyst reading the identical measuring scale or reading the lower measurement of the volumetric flask.

Systematic errors:

The Systematic errors are as well termed as determinate errors. Such errors are non random and take place whenever something is wrong by the measurement. In the similar given experiment there might be some sources of systemic error, a few are positive and others negative. The net systemic error is termed as the bias of the experiment, an overall deviation of result from the true value even whenever random errors are too small. Systematic errors cause all outcomes to be either too high or too low and can't be detected simply by employing replicate measurements, however can be corrected by employing standard processes and materials. Such errors are caused due to humans and equipment. Some generally encountered determinate errors throughout the course of laboratory experiments.

Instrumental Errors:

These are errors outlined due to the utilization of faulty equipments, and also uncalibrated or poorly calibrated weights and glass wares throughout the course of laboratory experiments.

Operative Errors:

Principally these are the personal (or operator) errors featured to either inexperience on the use of equipment or lack of care via the analyst in the physical manipulation comprised. It might be mathematical error in the computation or prejudice in estimating measurement. Illustrations of operative errors are incomplete drying of samples and the transfer of solutions.

Methodic Errors:

This is a very severe problem for an analyst as such errors are inherent in the technique or procedure. These comprise errors like co-precipitation with impurities, incomplete reaction, impurities in the reagents used and so on. The methodical error is as well correctable via running a reagent blank and standard addition.

Radom errors and systematic errors can take place independently of one other and might occur at various phases of the experiment.

Accuracy is the extent of agreement between a measured value and the true value. Precision is the degree of agreement between the replicate measurements of the similar quantity and doesn't necessarily imply correctness. Precision illustrates random error and bias explains systematic error whereas both precision and accuracy influence accuracy.

Tackling Systematic Errors:

Some of the procedures are available in handling systematic errors and are computed by a broad range of statistical methods.


The first precautions is taken at the inception of any laboratory experiment is to recognize the most probable sources of systematic errors. At this phase issues such as instrumental functions that require calibrating, the steps of the analytical process where errors are inherent, and the checks which can be made throughout the analysis, like contamination of reagents, should be recognized.

Experimental Design:

A thoughtful experimental planning is necessary in locating and minimizing the main sources of systematic errors. Weighing via difference can eliminate some systematic error since they occurred to the similar extent in both weighing and subtraction procedure removes them.

The other illustration is in the concentration measurement of sample of a single material by using spectrometer. Two processes are available for this analysis; in the first process, a sample is put in 1 cm path-length spectrometer cell at a wavelength of around 400 nm. Some of the systematic errors can take place; the wave length might be 405 nm rather than 400 nm, therefore rendering the reference value for ? unsuitable, the path length of the cell might not be precisely 1cm, or the molar extinction coefficient may not be accurate. On the other hand, calibration graph approach might be adopted in which case the value of ? is not needed. The errors because of wavelength shifts, absorbance errors and path length inaccuracies are predicted to cancel out, as they take place equally in the calibration and test experiment under the similar conditions. Main sources of systematic errors are removed by this process.

Standard Reference Material:

The third line of action against systematic errors is in the use of standard reference materials and process. Each and every piece of apparatus is calibrated through a suitable process before the experiment is started. Volumetric equipment can be calibrated by the use of gravimetric methods. Spectrometer wavelength scales is calibrated by the help of standard light sources which consists of narrow emission lines at well-established wavelength. Likewise spectrometer absorbance scales can be calibrated by standard solid or liquid filters.

Comparison with other methods:

The occurrence of systematic errors in any specific process is checked via comparing the results with such obtained from various methods. If they two unrelated processes used to carry out one analysis consistently yield outcomes showing only arbitrary differences, then it can be inferred that no significant systematic errors are present given each step of the two processes are independent of one the other and comparisons made over the entire concentration range for that the process is to be employed.

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