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Mistakes
Mistakes are NOT considered to be experimental errors.
It is assumed that if an experimenter has made a mistake then he/she will discard the results of the experiment or calculation and start again, that is, results from an experiment that included mistakes would NOT be reported.
Mistakes occur if the experimenter is careless, or, if the experimenter is incompetent.
When the results of an experiment are reported, it is assumed that the experimenter was both careful and competent.
Examples of common mistakes:
- in simple arithmetic:
(a) 5.69 + -0.09 = 5.60 NOT 5.78
(b) 32.5 - -1.5 = 34.0 NOT 31.0
(c) 0.25 × 100 = 25 NOT 2.5
(d) 100 ÷ 0.2 = 500 NOT 2000
- in calculations due to incorrect order of operations:
(a) 3 + 2 × 5 = 13 NOT 30
(b) 1 + 5 ÷ 10 = 1.5 NOT 0.6
- in calculations due to incorrect conversion factor:
(a) 250 mL = 0.250 L NOT 2.50 L
(b) 250 g = 250,000 mg NOT 0.250 mg
- in calculations due to incorrect scientific notation:
(a) using 2.50 × 10-2 instead of 2.50 × 102 to represent 250
(b) using 0.250 × 10-1 instead of 2.50 × 10-1 to represent 0.250
- in reading scales on apparatus
(a) a measuring cylinder has 9 divisions between the mark for 1 mL and the mark for 10 mL, then each division is 1 mL (not 0.1 mL)
(b) a thermometer has 9 divisions between the mark for 1°C and the mark for 2°C, then each division is 0.1°C (not 1°C)
- in recording measurements from a burette
When a 50.00 mL burette is full, it contains 50.00 mL of solution, and the bottom of the mensicus lies on the mark that says 50.00 mL. When you open the stopcock (tap) and let the solution run out until the bottom of the meniscus sits on top of the mark representing 31.80 mL then the volume of solution left in the burette is 31.80 mL, but you have used 50.00 - 31.80 = 18.20 mL
- due to carelessness
(a) dropping some solid reactant after it has been weighed
(b) dropping some solid product before it has been weighed
(c) spilling some solution after its volume is recorded
(d) adding solid solute to a volumetric flask, adding water to the flask but overshooting the mark and then using a pasteur pipette to remove some of the "water" from the volumetric flask
(e) rinsing a transfer pipette with water instead of the solution which will be used to fill it
(f) rinsing a burette with water instead of the solution which will be used to fill it
(g) rinsing a conical flask for an acid-base titration with the acid or base instead of with water
(h) recording the volume of solution in a 250.0 mL volumetric flask as 25.0 mL
Remember, if you make a mistake during an experiment or calculation, you should discard what you have done so far and start again.
You should not report the results of an experiment that includes mistakes.
Mistakes are NOT the same as experimental errors. Experimental errors are either random or systematic errors as described below.
Random Errors
Random errors result from random events which cannot be eliminated during the experiment.
Random errors usually result from the experimenter's inability to take exactly the same measurement in exactly the same way any number of times and get the exactly the same number.
Examples of the sources of random errors are:
- fluctuation of the power supply during the use of electronic equipment such as an electronic balance
- using a contaminated reagent in a particular experiment
- experimenter being distracted while taking a measurement
- locating the bottom of the meniscus for volume measurements using pipettes, burettes, measuring cylinders, etc
Since random errors cannnot be eliminated from the experiment, they are minimised by repeating the experiment a number of times until the uncertainty has been reduced to an acceptable level.
The arithmetic mean (or average) value of the measurements is then calculated, and is the number that is used as the final result, or, in further calculations.
arithmetic mean (average) = sum of all the results divided by the number of results
Example:
A student weighs the amount of magnesium oxide produced during an experiment 3 times and records the results in the table shown on the right.
Calculate the arithmetic mean (average) of the student's results.
arithmetic mean = sum of all results ÷ number of results
sum of all results = 1.462 + 1.458 + 1.459 = 4.379 g
number of results = 3
arithmetic mean (average) = 4.379 ÷ 3 = 1.460 g
|
| Trial | Mass / g |
|---|
| 1 | 1.462 |
| 2 | 1.458 |
| 3 | 1.459 |
|
If one of the results in a set of results is enormously different to the other results, this result is rejected before the arithmetic mean (average) is calculated.
(Technically, this result is known as a grossly-deviant result).
Example:
A student measures the volume of acid in a burette five times and records the values as shown in the table on the right.
Calculate the arithmetic mean (average) of the student's results.
Results from Trials 1, 2, 4 and 5 are about 21.6 mL, but the volume recorded for Trail 3, 23.75 mL, is very different (it is grossly-deviant)!
We reject the volume measurement for Trial 3, and use the other 4 trial results to calculate the arithmetic mean (average).
arithmetic mean = sum of all results ÷ number of results
sum of all results = 21.64 + 21.62 + 21.59 + 21.63 = 86.48 mL
number of results = 4
arithmetic mean (average) = 86.48 ÷ 4 = 21.62 mL
|
| Trial | Volume / mL |
|---|
| 1 | 21.64 |
| 2 | 21.62 |
| 3 | 23.75 |
| 4 | 21.59 |
| 5 | 21.63 |
|
Systematic Errors
Systematic errors are errors inherent in the experiment and which can be determined and therefore compensated for.
Systematic errors are reproducible inaccuracies that are inherent in the procedure, operator, instrumentation, and, treatment of results.
The source and magnitude of systematic errors can, in principle, be determined.
Examples of sources of systematic errors are:
- changes in response of balance due to changes in conditions such as temperature, pressure, humidity and age.
- changes in volumes of calibrated apparatus with changing conditions such as temperature
- changes in densities of solutions with changing conditions such as temperature
- absorption of water or carbon dioxide from the air by samples before and during weighing
- evaporation of liquids before and during weighing
- errors in calibration of glassware
- faulty instrumentation
- systematic error in procedure such as acid-base indicator error, mishandling of apparatus, misreading instructions, loss of sample which was not due to carelessness (eg, sublimation of a solid while you weigh it)
- calculation errors from uncertainty in measurement (not due to carelessness or incompetence)
- prejudice which makes the experimenter change a result because he/she thinks he/she knows the "right" answer
Because the source and magnitude of the systematic errors is known, they can be compensated for individually, or, as a set by calibrating the equipment used.
From the list above, we see that a number of measurements can be affected by changes in laboratory conditions (temperature, pressure, humidity).
We can eliminate this source of systematic error by providing a laboratory with a constant temperature, constant pressure, and constant humidity.
When chemists work with ideal gases, Standard Temperature and Pressure (STP) are used as a reference, which means that the temperature is kept at a constant 0°C and a constant pressure of 100 kPa.(1)
When you look at the labels on glassware used for volumetric analysis such as volumetric flasks, you will see the label includes a capital letter (A or B), a temperature, usually 20°C, as well as the volume.
The label is telling you that the volumetric flask will only measure 250 mL of solution at 20°C, at any other temperature the volume will not be 250 mL.
Volumetric analysis should therefore be carried out in a laboratory with a constant temperature of 20°C.
Many substances absorb moisture from the atmosphere, sodium hydroxide pellets are an excellent example. To eliminate this as a source of systematic error, the substance (the sodium hydroxide pellets for instance) is placed in a sealed vessel known as a dessicator. In the bottom of the dessicator is placed a substance, known as the dessicant, that is used to absorb moisture from the air. Silica gel is often used as the dessicant (also known as the drying agent). The dessicant absorbs the moisture in the dessicator so that our substance does not absorb water from the air.
Other dessicants (drying agents) used to keep the air in a dessicator free of moisture are granules of fused calcium chloride, anhydrous calcium sulfate and activated alumina.
To prevent liquids from evaporating before weighing, they could be kept in a sealed vessel saturated with the liquid's vapor.
Systematic errors from faulty instrumentation can be eliminated by calibrating the instrument before using it. This often involves using the instrument to measure substances with accurately known values and then constructing a calibration curve as a reference for the experiment. The experimenter uses the instrument to measure the unknown sample, and then uses the calibration curve to obtain an accurate value.
