Errors – Introduction and Types
In every scientific experiment, we aim to get results as close as possible to the true value. But sometimes, our measurements differ slightly from the actual value. This difference is called an error. Understanding errors helps us improve the accuracy and reliability of our experiments.
What is an Error?
Absolute Error is the difference between the measured (experimental) value and the true value. It can be either positive or negative.
Relative Error shows how big the error is compared to the true value. It is calculated as:
Relative Error = (Measured Value – True Value) / True Value
- Relative error is usually written as a percentage (multiply by 100) or as parts per thousand (multiply by 1000).
- Accuracy is often expressed in terms of the relative error.
Accuracy
Accuracy means how close your result is to the true or accepted value. In real experiments, the exact true value is not always known. Scientists usually accept a “standard” or “average” value obtained from many laboratories using different methods.
In short, higher accuracy means your result is close to the correct value.
Precision
Precision means how closely repeated measurements match each other. It tells how consistent your results are when you perform the same experiment several times.
For example, if you weigh the same substance three times and get values that are almost the same, your work is precise. However, precision doesn’t always mean accuracy — your method could be consistently wrong due to an error in the instrument or technique.
Introduction to Errors
Every measurement has three important aspects:
- Choosing the correct unit and standard for comparison.
- Measuring the magnitude (numerical value) properly.
- Understanding the precision and accuracy of the result.
To ensure reliable results, analysts use different statistical methods to check the significance and reliability of data. Simply put, an error is the difference between the standard value and the experimental value.
Types of Errors
Errors in experiments are mainly of two types:
- Determinate Errors – can be avoided or corrected.
- Indeterminate Errors – occur by chance and cannot be completely controlled.
Determinate Errors:
Determinate errors can be identified and minimized. They have a definite cause and can often be corrected. These are of three main kinds:
(A) Operational and Personal Errors
These errors occur due to mistakes made by the analyst, such as wrong readings or incorrect handling. They depend on personal judgment and can be reduced by experience and careful observation.
Examples:
- Reading the meniscus level in a burette incorrectly.
- Wrong estimation of a pointer position on a balance.
(B) Instrumental and Reagent Errors
These errors occur because of faulty or uncalibrated instruments or poor-quality chemicals.
Examples:
- Using an unadjusted balance or uncalibrated burette/pipette.
- Using reagents that react with containers or have impurities.
- Fluctuations in electrical instruments due to voltage changes.
(C) Method Errors
These errors are caused by incorrect sampling or incomplete reactions. They are difficult to identify or fix.
Examples:
- In gravimetric analysis: due to insoluble precipitates or post-precipitation.
- In volumetric analysis: due to incomplete chemical reactions.
Constant and Proportional Errors:
(1) Constant Errors
These errors remain the same for all measurements. They may be small and hard to notice but can still affect results.
Example: A titration always having a 0.1 mL reading error. If 10 mL titrant is used, the error is 1%; if 50 mL is used, it’s only 0.2%. So, as volume increases, the effect of constant error becomes smaller.
(2) Proportional Errors
These depend on the composition or impurities in the sample.
Example: In iodometric estimation of copper, if the sample contains iron (Fe³⁺) impurities, they also liberate iodine like copper does. This gives a falsely higher iodine yield and incorrect results.
Indeterminate Errors
Indeterminate errors are also called random or accidental errors. They occur without a known cause — for example, slight variations in reading due to random environmental factors. They cannot be completely avoided, but repeating the experiment and taking averages helps minimize their impact.
Minimization of Errors
Although errors can’t be completely removed, they can be reduced by following these steps:
- Calibration of Instruments: Regularly check and adjust instruments to maintain accuracy.
- Analyzing a Standard Sample: Compare results with a known standard (such as one from NBS – National Bureau of Standards).
- Running a Blank Determination: Perform the procedure without the sample to detect and correct for impurities or background interference.
- Independent Analysis: Verify results using a different analytical method.
Example:
- By Alkalimetry: Titrate hydrochloric acid (HCl) with sodium hydroxide (NaOH) using a suitable indicator.
- By Gravimetry: Precipitate HCl as silver chloride (AgCl) using silver nitrate (AgNO₃), then compare the results.
Detailed Notes:
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