A = ln(Io/I) = εcl
Where
A is the absorbance (optical density)
ε (=α/2.303) is the molar absorption coefficient (extinction coefficient)
It isn’t necessary to use a sophisticated spectrophotometer in order to determine the concentration of the absorbing species in solution. All that is required is a simple instrument which uses a diffraction grating to limit the range of wavelengths passed. Calibration data are obtained by measuring the absorbance’s of solutions of known concentration at a particular path-length (or path-lengths). Any absorption by the solvent, and reflection and scattering by the cell, is compensated for by the use of an identical cell containing the pure solvent as a ‘blank.’
Method: The apparatus used in this experiment are listed below.
- Colorimeter
- 2 × Plastic Cuvettes (Sample Cells)
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2 ×10 cm3 Graduated Pipette
- 10 × Test Tubes
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Potassium Permanganate (5.0×10-3 Mol dm-3)
Method: A series of dilutions are made from the potassium permanganate (5.0×10-3 Mol dm-3) until a dilution that is paler in colour than that of the unknown. This is done as follows: (Note: all apparatus is appropriately cleaned before use)
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5.0 cm3 of potassium permanganate is measured out into a test tube using a 10 cm3 graduated pipette.
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Using a different 10 cm3 graduated pipette 5.0 cm3 of distilled water is added to the same test tube and shook well the ensure mixing.
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This solution is then half the original concentration, so 5.0cm3 of this solution is measured out into another test tube using a 10 cm3 graduated pipette.
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To this solution a further 5.0 cm3 of distilled water is added and well shaken thus halving the concentration again.
- This procedure is repeated until a dilution that is paler than the provided unknown is obtained.
- The concentration of each solution is then calculated before using the provided colorimeter to measure the absorbance. The method for this is outlined below:
- A sample cell is filled to about three quarters with deionised water to be used as a blank representing a solution that has zero absorbance.
- Another sample cell is filled to a similar level with the various concentrations, measuring the absorbance of each at 530 nm.
Results:
To look at the results we can see that the experiment has produced the results that we should have expected. By this I mean that as each concentration halves so does the absorbance. To confirm this, a graph of concentration against path length was plotted using Microsoft Excel:
As you can see all points lie along the line of best fit indicating a good linearity and consistency in the results. Using this graph it is possible to calculate a value for the molar absorption coefficient for potassium permanganate, this is done as follows:
At constant path length
Since the path length is constant at 1 cm it may be ignored to give ε = m, and since b = the intercept = 0 as calculated by Microsoft Excel (-0.00032) it also may be ignored.
Since calculating the gradient by hand can incur some human error a least squares fitting routine (Microsoft Excel) was used to calculate a molar absorption coefficient of 3965.288 L mol-1 cm-1 (3 d.p.).Using this it is now possible to calculate the concentration of the unknown solution by the rearrangement of the beer-lambert law as shown below:
This can be checked using the graph above by drawing a line from the absorption point of the unknown to the line of best fit and then to the concentration. This is shown on the following page, also on the page following that you can see the same graph concentrated on the area of interest.
As you can see the graph indicates a concentration of approximately 2.41×10-5 mol dm-3 which clearly agrees with the value calculated earlier.
It should also be mentioned that the absorption coefficient calculated earlier is only applicable to the selected wavelength (530 nm) as it is dependant on the frequency of the incident radiation.
An alternate method of determining the concentration of the unknown sample would be to plot a graph of absorbance against the log concentration to produce a logarithm calibration curve:
The method applied to the determination of the unknowns concentration is similar to that applied to the previous graph only this time it is necessary to calculate the inverse log of the value obtained from the Y-axis. On the following page you will find a graph that has been focussed on the area of interest to apply this method.
The –log concentration found from this graph is approximately 4.611, remember the negative inverse log of this needs to be calculated as the logarithms power was reversed to make the graph more understandable.
The value for the concentration of the unknown is slightly different to that calculated earlier with a difference of 2.1×10-6 mol dm-3 but this is a small error (8.57%) and so I am confident to state the concentration of the unknown as
2.24×10-5 ±2.1×10-6 mol dm-3
There is little error to be taken from the graphs as most of the points lie along the lines, but I should mention that the error incurred in reading the absorbance is ±0.0015 as the display only read to 0.001
Conclusion: The reading taken from the spectrometer halved with the halving of each concentration. This is as was expected and so immediately we can be satisfied with the results obtained from an experiment that appears to have worked well. All result lie within a good error limit and aid a confident calculation of both the molar absorption coefficient and the concentration of the unknown sample (2.24×10-5 ±2.1×10-6 mol dm-3).
Evaluation: Although the experiment has ran accordingly well I would have been more confident if the solutions prepared would have been individually made-up using volumetric flasks and a burette to measure out the undiluted potassium permanganate. The use of hand pipettes introduces a problem in that they cannot be quite as well controlled as the burette could. Small leaks in the seal between the pipette and the syringe can result in a loss of the product resulting in a lower dilution than required. It would also have been useful to investigate the effect of path length with constant concentration on the molar absorption coefficient. The various path lengths that are available include 0.5cm 1cm 2cm and 4cm. If these could have been used it would have been used at the same wavelength is would have allowed for the calculation of a second molar absorption coefficient which could have given an average that may be closer to the actual than the one that has been presented. The spectrophotometer used was adequate for this experiment but more advanced equipment as shown below can provide better wavelength readability, better wavelength accuracy and greater absorbance reliability.
Diagram 1
References: Diagram one courtesy of http://www.motic.com/ap/eng/products/20d.html
