Coloured aqueous solutions: What does the intensity of colour depend upon?
KEY IDEAS
Look through a coloured solution in a colourless container. It may appear red, for example, if species (such as molecules or ions) absorb “blue wavelengths” from the white light that enters the solution from the other side. Or it may appear blue or green because of absorption of “red wavelengths” and “yellow wavelengths”.
[And the light absorption can be attributed to “excitation” of electrons in the species to higher “allowed” energy levels.]
What happens if we dilute a coloured aqueous solution by adding water? Of course, the colour becomes fainter. (But, if you have watched the video, you will know that this depends on where you are looking from.)
We say that the colour has become less intense, or less deep.
[And the light absorption can be attributed to “excitation” of electrons in the species to higher “allowed” energy levels.]
What happens if we dilute a coloured aqueous solution by adding water? Of course, the colour becomes fainter. (But, if you have watched the video, you will know that this depends on where you are looking from.)
We say that the colour has become less intense, or less deep.
This does not mean that the colour changes. No, the tint remains the same. It is just that a smaller fraction of the incoming light (at the same wavelengths) is absorbed.
The intensity of colour of a red solution depends upon how many of the blue-absorbing species’ molecules or ions interact with the incoming light before it comes to our eyes: the more molecules or ions that the light interacts with, the more blue light is absorbed, and the more intense is the red colour.
And the number of molecules with which passing light interacts is dependent on the concentration of the solution (symbol c), and how far the light travels through the solution before reaching our eyes (the path length, l)
Quantitatively, chemists’ use a measure of how much light of a given wavelength is absorbed by a solution called the absorbance, A, defined by
The intensity of colour of a red solution depends upon how many of the blue-absorbing species’ molecules or ions interact with the incoming light before it comes to our eyes: the more molecules or ions that the light interacts with, the more blue light is absorbed, and the more intense is the red colour.
And the number of molecules with which passing light interacts is dependent on the concentration of the solution (symbol c), and how far the light travels through the solution before reaching our eyes (the path length, l)
Quantitatively, chemists’ use a measure of how much light of a given wavelength is absorbed by a solution called the absorbance, A, defined by
where Io is the intensity of incident light (that entering the solution), and I is the intensity of transmitted light (that emerging from the solution and coming to our eyes, or a sensor).
I prefer to think in terms of a reverse measure called transmittance, T, defined as
I prefer to think in terms of a reverse measure called transmittance, T, defined as
because I can imagine more easily the fraction of incident light that is transmitted (I/Io) – rather than how many times more intense is the incident light rather compared with the transmitted light.
The extent to which the absorbance of a solution depends upon the concentration of absorbing species and the path length is given by Beer’s law (sometimes referred to as the Beer-Lambert law):
The extent to which the absorbance of a solution depends upon the concentration of absorbing species and the path length is given by Beer’s law (sometimes referred to as the Beer-Lambert law):
where the value of ε (Greek epsilon) is a characteristic of the absorbing species. (At the same concentration of solution, and through the same path length, some species absorb more intensely than others.)
Alternatively, and absolutely equivalently:
Alternatively, and absolutely equivalently:
The logarithmic nature of the absorbance relationship can be visualised as follows. Suppose that 20% of light of a particular “blue wavelength” is absorbed when it passes through a 1.0 cm path length of a solution of given concentration. That is, 80% is transmitted, and I/Io = 0.20.
How much of the incident light would be absorbed if it passed through a 4 cm path length (same concentration of solution, same wavelength of incident light)? The answer is not 4 ×20%. That would lead to crazy answers if 40% were absorbed in a 1 cm pathlength. 160% absorbed over a 4 cm path length? Nonsense!
Here goes …
How much of the incident light would be absorbed if it passed through a 4 cm path length (same concentration of solution, same wavelength of incident light)? The answer is not 4 ×20%. That would lead to crazy answers if 40% were absorbed in a 1 cm pathlength. 160% absorbed over a 4 cm path length? Nonsense!
Here goes …
- Over the first 1 cm of path, 0.20 of the incident light is absorbed, and 0.80 transmitted.
- The 0.80 transmitted can be regarded as incident on the front of the second 1 cm path length section. Over the second 1 cm of path, 0.20 of 0.80 (0.16) of the (originally) incident light is absorbed, and 0.80 of 0.80 (0.64) is transmitted.
- Over the third 1 cm of path, 0.20 of 0.64 (0.128) of the (originally) incident light is absorbed, and 0.80 of 0.64 (0.512) is transmitted.
- Over the fourth 1 cm of path, 0.20 of 0.512 (0.102) of the (originally) incident light is absorbed, and 0.80 of 0.512 (0.41) is transmitted.
So, allowing for rounding off of numbers, 0.41 of the (originally) incident light is transmitted, and the fraction absorbed is 0.20 + 0.16 + 0.13 + 0.10 = 0.59. It all computes.
As well as to follow this intuitive argument, you might want to apply Beer’s law to this situation.
An application of Beer’s law to analysis of solution concentrations
Beer's law can be used to estimate the concentration of an absorbing species in solution. First, a set of “standard” (known concentration) solutions is made up, and their absorbance over a defined path length, at a given wavelength, is measured. A plot of A vs molar concentration can be plotted as a straight line. The absorbance of the solution of unknown concentration allows its concentration to be estimated.
Beer's law can be used to estimate the concentration of an absorbing species in solution. First, a set of “standard” (known concentration) solutions is made up, and their absorbance over a defined path length, at a given wavelength, is measured. A plot of A vs molar concentration can be plotted as a straight line. The absorbance of the solution of unknown concentration allows its concentration to be estimated.
For example:
Solutions of a particular reagent are made up, and their absorbances measured at a defined wavelength (usually close to the maximum of its absorption peak) as it passes through a cell 5 cm long. The measurements are tabulated:
Solutions of a particular reagent are made up, and their absorbances measured at a defined wavelength (usually close to the maximum of its absorption peak) as it passes through a cell 5 cm long. The measurements are tabulated:
The solution of unknown concentration had an absorbance of 0.78, measured in the same cell and at the same wavelength. What is the concentration of the absorbing species?
The data of concentration (horizontal axis) and absorbance (vertical axis) form a straight-line plot, shown here.
You can manually draw a line of best fit, or use a graphing program to calculate the formula for the line of best fit. By either means, interpolation of a value 0.78 for the absorbance leads to a decision that the concentration of the unknown solution is 0.021 mol L-1 (2.1 x 10-2 mol L-1).
SELF CHECK
Teachers' notes
For a description of the activity discussed in the video, go to module T02 Beer's law: An activity.
For a description of the activity discussed in the video, go to module T02 Beer's law: An activity.
