As mentioned in the last post, the unawareness of uncertainties in our measurement renders our experimental data insignificant.While measuring any quantity, there can be various errors incorporated in the measurement and the knowledge of these errors is essential to get accurate and precise results.Thus, today we start our discussion of Analytical Chemistry with a topic called ‘Errors’!!
What is an error?
An error is the difference between the real/true value and the measured value. If the measured value is ,
more than the true value(T) —————➤ Positive error ——————➤+ve fluctuation.
less than the true value(T) —————➤ Negative error——————➤ -ve fluctuation.
What are the causes of errors in any measurement?
Errors can be caused due to various reasons like lack of care in making measurements or incorrectly handling the instrument or using a faulty instrument or limitations in making correct observations etc.Based on this , errors can be broadly classified as –
- These errors can be present in any measurement made , irrespective of utmost care taken while conducting the experiment.They are uncontrollable errors.They are Indeterminate i.e whose reason cannot be determined.They originate in the limited ability of the analyst to control or make corrections to the external conditions or inability to detect factors that could cause errors during the experiment.
- The results are not constant even though system is extended to its maximum sensitivity.The results fluctuate in a random manner about a mean value (μ).These errors are Random in size and in sign – they could be positive or negative.
- These errors are small in magnitude.They cannot be eliminated but can be minimised.
- The source/cause of fluctuation cannot be pinpointed and it could be due to myriad reasons.
- Individual uncertainties causing these errors are very small on both sides of the true value ‘T’ and thus this error can be both +ve and -ve in magnitude.
- e.g. – Temperature variations in atmosphere while conducting the experiment,vibrations in a building caused by moving traffic, humidity in the balance room which cause fluctuations in the balance etc.
- Mathematically a numerical relationship exists between magnitude of the indeterminate error and frequency of its occurence.For large number of observations made,the relationship can be pictorially represented by a Gaussian/Normal distribution curve as follows –
The above curve is called the NORMAL DISTRIBUTION/GAUSSIAN/BELL SHAPED CURVE.This curve is symmetric around the mean point ‘T’ (true value) e.g. T = 5.The above curve tells us that –
- The positive errors(right side of the true value T) and the negative errors (left side of T) are equally likely to occur.
- The frequency of small errors E1 is large i.e small indeterminate errors occur more frequently.Point A(on both sides) denotes the deviation from true value in the figure above.E1 is small because it is closer to the true value T. e.g. E1 = 5± 0.05.Thus, point A on the left means 5-0.5(negative side) and that on the right means 5+0.5(positive side).
- The frequency of large errors E2 is very small i.e random errors that are very large in magnitude are rare.Point B(on both sides of T) represents such errors.E2 is large because it is far away from the true value T.e.g. E2 = 5 ± 3.5.
- Random errors are present in all experiments and so one should be prepared for them. Unlike determinate errors, random errors are not predictable, which makes them difficult to detect. But since these errors are statistical in nature,it is easier to remove them by statistical methods like averaging.
- These are errors whose cause which can be determined or located.
- They have a definite value and could be larger in magnitude.
- With proper precaution , they can be eliminated.
- They are unidirectional i.e they have the same sign and magnitude for replicate measurements and thus they are also called “SYSTEMATIC ERRORS”.
- Determinate errors could be –
- Instrumental or reagents errors – e.g. faulty balance or weights , the cloth tape that one uses is stretched out from years of use,evaporation of a volatile reagent from reagent bottle ,the measuring instrument is miscalibrated etc.
- Methodical errors – Sometimes the method used to conduct the experiment might be incorrect or not appropriate.There might be chances of errors occuring during intermediate stages of the experiment.e.g.– decomposition of precipitate on ignition.
- Personal and operative errors – These errors are caused due to lack of correct knowledge of experiment procedure or inexperienced experimentalist.e.g. blowing out the last drop from the pipette during titration.
Gross errors are caused by experimenter’s carelessness or equipment failure.These can be minimised if proper care is taken.
Now that we know what errors are and how they can affect our measurements, we should have mathematical parameters which help us to measure these errors. In the next post we shall discuss various terms and formulas which will help us to represent our errors. Till then,
Be a perpetual student of life and keep learning…
References and Further Reading –
2) Analytical Chemistry, 6th Edition by Gary D. Christian.