SYSTEMATIC ERROR: HOW TO CALCULATE IT, IN CHEMISTRY, IN PHYSICS, EXAMPLES - CHEMISTRY - 2025

The systematic error is one that is part of the experimental or observational errors (measurement errors), and that affects the accuracy of the results. It is also known as a determined error, since most of the time it can be detected and eliminated without repeating the experiments.

An important characteristic of systematic error is that its relative value is constant; that is, it does not vary with the size of the sample or the thickness of the data. For example, assuming that its relative value is 0.2%, if measurements are repeated under the same conditions, the error will always remain 0.2% until it is corrected.

In the laboratory, a bad technique or a wrong step in any method ends up becoming a systematic error that affects the accuracy of the results. Source: Jarmoluk via Pixabay.

Generally, systematic error is subject to inappropriate handling of the instruments, or to technical failure by the analyst or scientist. It is easily detected when experimental values ​​are compared against a standard or certified value.

Examples of this type of experimental error occur when analytical balances, thermometers, and spectrophotometers are not calibrated; or in cases where a good reading of the rules, the verniers, the graduated cylinders or burettes is not carried out.

How to calculate the systematic error?

Systematic error affects accuracy, causing the experimental values ​​to be higher or lower than the actual results. A real result or value is understood to be one that has been exhaustively verified by many analysts and laboratories, establishing itself as a standard of comparison.

Thus, comparing the experimental value with the real one, a difference is obtained. The larger this difference, the greater the absolute value of the systematic error.

For example, suppose that 105 fish are counted in a tank, but it is known in advance or from other sources that the true number is 108. The systematic error is therefore 3 (108-105). We are faced with a systematic error if by repeating the fish count we obtain 105 fish over and over again.

However, more important than calculating the absolute value of this error is to determine its relative value:

Relative error = (108-105) ÷ 108

= 0.0277

That when expressed as a percentage, we have 2.77%. That is, the error of the counts has a weight of 2.77% on the true number of fish. If the tank now has 1,000 fish, and it proceeds to count them dragging the same systematic error, then there would be 28 less fish than expected, and not 3 as happens with the smaller tank.

Constancy and proportionality

The systematic error is usually constant, additive and proportional. In the above example, the 2.77% error will remain constant as long as the measurements are repeated under the same conditions, regardless of the size of the fish tank (already touching an aquarium).

Also note the proportionality of the systematic error: the larger the sample size or the thickness of the data (or the volume of the tank and the number of its fish), the larger the systematic error. If the tank now has 3,500 fish, the error will be 97 fish (3,500 x 0.0277); the absolute error increases, but its relative value is invariable, constant.

If the number is doubled, this time with a 7,000 fish tank, then the error will be 194 fish. The systematic error is therefore constant and also proportional.

This does not mean that it is necessary to repeat the count of the fish: it will be enough to know that the determined number corresponds to 97.23% of the total fish (100-2.77%). From there, the true number of fish can be calculated by multiplying by the factor 100 / 97.23

For example, if 5,200 fish were counted, then the actual number would be 5,348 fish (5,200 x 100 / 97.23).

Systematic error in chemistry

In chemistry, systematic errors are usually caused by bad weighings due to an uncalibrated balance, or by a bad reading of volumes in glass materials. Although they may not seem like it, they affect the accuracy of the results, because the more there are, the more their negative effects add up.

For example, if the balance is not well calibrated, and in a certain analysis it is necessary to carry out several weighings, then the final result will be further and further away from what is expected; it will be more inaccurate. The same happens if the analysis constantly measures volumes with a buret whose reading is incorrect.

Apart from the balance and glass materials, chemists can also make mistakes in handling thermometers and pH meters, in the speed of stirring, in the time required for a reaction to take place, in the calibration of the spectrophotometers, in assuming a high purity in a sample or reagent, etc.

Other systematic errors in chemistry can be when the order in which the reagents are added is altered, the mixture of a reaction is heated to a temperature higher than that recommended by the method, or the product of a synthesis is not recrystallized correctly.

Systematic error in physics

In physics laboratories, systematic errors are even more technical: any equipment or tool without proper calibration, a wrong voltage applied, the wrong arrangement of mirrors or parts in an experiment, adding too much moment to an object that should fall due to the effect of gravity, among other experiments.

Note that there are systematic errors that originate from an instrumental imperfection, and others that are more of the operational type, the product of an error on the part of the analyst, scientist or individual in question who performs an action.

Examples of systematic error

Other examples of systematic errors will be mentioned below, which do not necessarily have to occur within a laboratory or in the scientific field:

-Place the buns in the lower part of the oven, toasting them more than is desirable

-Poor posture when sitting

-Seal the mocha pot only due to lack of strength

-Do not clean the steamers of coffee machines just after texturing or heating the milk

-Use cups of different sizes when you follow or want to repeat a certain recipe

-Want to dose solar radiation on shady days

-Execute chin-ups on the bars with your shoulders raised towards your ears

-Play multiple songs on a guitar without first tuning its strings

-Fry fritters with insufficient volume of oil in a cauldron

-Perform subsequent volumetric titrations without standardizing the titrant solution again

References

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