L6 - Colorimetry

Colour Chemistry

Many solutions can be coloured.

You may already be familiar with some coloured aqueous solutions, for example:

• copper sulfate dissolved in water produces a blue solution (CuSO_4(aq))
• potassium permanganate dissolved in water produces a purple solution (KMnO_4(aq))
• iron(III) thiocyanate dissolved in water produces a red solution (FeSCN²⁺_(aq))
• bromine water is a red-brown solution (Br_2(aq))
• iodine dissolved in water is a yellow-brown solution
• the complex formed between starch and iodine is a deep blue colour
• acid-base indicator solutions come in a wide range of colours

The colour we see is the colour of the light that is transmitted through the solution.

"White light" is part of the electromagnetic spectrum and is made up of all the colours of the rainbow; red, orange, yellow, green, blue, indigo and violet (ROYGBIV).

If we shine white light through an aqueous solution of copper sulfate, the solution appears to be blue because it is transmitting the blue wavelengths of white light and absorbing other wavelengths such as red so that very little of these other wavelengths are transmitted through the solution to your eye.

The colour of the solution is due to the wavelengths of light that are not absorbed as "white light" passes through the solution.

Now, if we dilute the original copper sulfate solution by adding more water, the blue colour becomes less intense, it is a lighter blue colour because the solution is not absorbing as much of the other wavelengths as before:

If we were given an aqueous solution of copper sulfate of unknown concentration, solution (A), we might be able to take a guess at its concentration by looking at its colour:

• The "blueness" of solution (A) seems to lie about half-way between that of the concentrated (0.50 mol L^-1) solution and the dilute (0.10 mol L^-1) solutions above, so we might guess that the concentration of solution (A) lies about halfway between these two solutions: (0.50 + 0.10) ÷ 2 = 0.30 mol L^-1.
• Guessing the concentration of the solution in this way gives us a kind of "ball park" value for the concentration, but it is unlikely to result in us knowing the concentration of the solution accurately or precisely.
• But there might be a better way.
• We have already noted that there is a relationship between the intensity of the colour of solutions and their concentration.
• And we have seen that a concentrated blue solution will absorb more of the "non-blue" wavelengths of light than a more dilute solution, and we have a machine, a colorimeter (colourimeter), that can measure the amount of absorbance for us!

Colourimeters

• Colorimetry (colourimetry) is the name of the method we use to determine the concentration of a substance by measuring the relative absorption of light with respect to known concentrations of the substance.
• A colorimeter (colourimeter) is literally a meter to measure colour. It is an instrument that measures the absorption of light of a specific wavelength (λ) by a solution.⁽⁴⁾
• Therefore, we need to choose a wavelength of light to shine through our solution.
• The solution must be able to absorb measurable amounts of this wavelength.
• Different concentrations of the solution must absorb different amounts of this wavelength, and this difference must be significant (that is, much larger than the error inherent in the measurment).
• If a solution is blue, like CuSO_4(aq), we would not use a wavelength corresponding to blue light because very little of this is absorbed (most is being transmitted).
• Similarly, lots of the green and indigo wavelengths are not absorbed but are transmitted.
• Therefore we would choose to shine light from the "red-orange-yellow" part of the spectrum at this solution because these are the wavelengths that are being absorbed.
• We can use a "colour wheel" to decide which is most likely to be the best colour of light to shine on our solution:

If our solution is blue, we choose a light colour that is complementary to blue, that is, we choose the colour that is opposite this colour in the colour wheel, in this case we choose an orange light to shine on our blue solution.

• Now, it may be possible to select an appropriate wavelength for the light our colorimeter uses, but it is quite likely that our colorimeter will use coloured filters in order to "filter out" (absorb) the wavelengths of light that we do not want from "white light".
• In this case, if we want to determine the amount of orange light absorbed by our blue solutions, we would select an orange filter for our colorimeter.
• A simplified schematic diagram of using an orange filter in a colorimeter to measure the concentration of a blue copper sulfate solution is shown below:

• Light from the "white light source" passes through a slit then a filter to select the most appropriate wavelength of light. In this case, the orange filter absorbs all other wavelengths and allows the orange wavelengths to be transmitted through the filter.
• Some of this "orange light" is then absorbed by the "blue solution" which is contained in a glass receptacle.⁽⁵⁾
• The intensity of the "orange light" has decreased after it passes through the "blue solution" because the "blue solution" has absorbed a significant amount of "orange".
• The amount of light absorbed is measured and recorded as the "absorbance".
• The more concentrated the solution the greater the "absorbance" will be.

Beer Lambert Law

The Beer-Lambert law relates the attenuation of light to the properties of the material through which the light is traveling. We will take a brief look at the Beer-Lambert Law and explains the use of the terms absorbance and molar absorptivity relating to UV-visible absorption spectrometry.

The Absorbance of a Solution

For each wavelength of light passing through the spectrometer, the intensity of the light passing through the reference cell is measured. This is usually referred to as Io - that's I for Intensity.

The intensity of the light passing through the sample cell is also measured for that wavelength - given the symbol, I. If I is less than Io, then the sample has absorbed some of the light (neglecting reflection of light off the cuvette surface). A simple bit of math is then done in the computer to convert this into something called the absorbance of the sample - given the symbol, A. The absorbance of a transition depends on two external assumptions.

1. The absorbance is directly proportional to the concentration (c) of the solution of the sample used in the experiment.
2. The absorbance is directly proportional to the length of the light path (l), which is equal to the width of the cuvette.

Assumption one relates the absorbance to concentration and can be expressed as

1. A∝c

The absorbance (A) is defined via the incident intensity I_o and transmitted intensity I by

1. A= log₁₀(I_o/I)

Assumption two can be expressed as

1. A∝l

Combining Equations 1 and 3

1. A∝cl

This proportionality can be converted into an equality by including a proportionality constant (ϵ).

1. A=ϵcl

This formula is the common form of the Beer-Lambert Law, although it can be also written in terms of intensities:

1. A= log₁₀(I_o/I) =ϵcl

The constant ϵ is called molar absorptivity or molar extinction coefficient and is a measure of the probability of the electronic transition. On most of the diagrams you will come across, the absorbance ranges from 0 to 1, but it can go higher than that. An absorbance of 0 at some wavelength means that no light of that particular wavelength has been absorbed. The intensities of the sample and reference beam are both the same, so the ratio I_o/I is 1 and the Log₁₀ of 1 is zero.

You will find that various different symbols are given for some of the terms in the equation - particularly for the concentration and the solution length.

The Greek letter epsilon in these equations is called the molar absorptivity - or sometimes the molar absorption coefficient. The larger the molar absorptivity, the more probable the electronic transition. In uv spectroscopy, the concentration of the sample solution is measured in mol L-1 and the length of the light path in cm. Thus, given that absorbance is unitless, the units of molar absorptivity are L mol-1 cm-1. However, since the units of molar absorptivity is always the above, it is customarily reported without units.

The Importance of Concentration

The proportion of the light absorbed will depend on how many molecules it interacts with. Suppose you have got a strongly colored organic dye. If it is in a reasonably concentrated solution, it will have a very high absorbance because there are lots of molecules to interact with the light. However, in an incredibly dilute solution, it may be very difficult to see that it is colored at all. The absorbance is going to be very low. Suppose then that you wanted to compare this dye with a different compound. Unless you took care to make allowance for the concentration, you couldn't make any sensible comparisons about which one absorbed the most light.

The importance of the Container Shape

Suppose this time that you had a very dilute solution of the dye in a cube-shaped container so that the light traveled 1 cm through it. The absorbance is not likely to be very high. On the other hand, suppose you passed the light through a tube 100 cm long containing the same solution. More light would be absorbed because it interacts with more molecules. Again, if you want to draw sensible comparisons between solutions, you have to allow for the length of the solution the light is passing through. Both concentration and solution length are allowed for in the Beer-Lambert Law.

Determining the Concentration of a Solution using Colourimetry

• A colorimeter (colourimeter) measures the absorption of light of a specific wavelength (λ) by a solution.
• The colorimeter records this as the absorbance.
• In order to determine the concentration of a solution, we will need to obtain the absorbances for a range of different concentrations of the same solution using the same wavelength of light (same filter).
• We use the absorbance of each of these solutions of known concentration to draw a calibration curve.
• We can then measure the absorbance of our solution of unknown concentration and use the calibration curve to determine its concentration.
• If, for example, we have an aqueous solution of copper sulfate, CuSO_4(aq), and we want to determine its concentration colorimetrically, we would first prepare a stock solution of aqueous copper sulfate.
• We then use this stock solution to prepare a number of dilute copper sulfate solutions, calculating the concentration of each solution.
• Note that we should visually check the colour of our unknown solution against the colour of each of the prepared solutions in order to ensure that the colour of our solution lies between the colour of the most concentrated and most dilute solution we have prepared.
• Next we use the colorimeter (colourimeter) to measure the absorbance of each of these solutions of known concentration.
• The results of this experiment might look like those in the table below:

Next we plot these results on a graph and draw a "line of best fit" through the data points:

Now we measure the absorbance of our aqueous solution of copper sulfate of unknown concentration.

Example: Absorbance of unknown solution = 0.950

We plot the point (x) for this unknown solution on our calibration curve:

Reading off the graph we see that an absorbance of 0.950 corresponds to a concentration of 0.34 mol L^-1

Alternatively, if we know the mathematical equation for the straight line of the calibration curve, we can use that to determine the concentration of our unknown solution.

On the calibration graph we were given the expression:

Abs = 2.78 × [CuSO_4(aq)]

which is the mathematical equation for the calibration curve.

Substitute the value for the absorbance of our unknown solution into the equation:

0.950 = 2.78 × [CuSO_4(aq)]

Divide both sides of the equation by 2.78:

(0.950 ÷ 2.78) = (2.78 ÷ 2.78) × [CuSO_4(aq)]

Solve the equation to find the concentration of our unknown solution:

0.3417 mol L^-1 = [CuSO_4(aq)]

However, we are only justified in using 2 significant figures to express the concentration of our unknown solution, that is:

[CuSO_4(aq)] = 0.34 mol L^-1

In summary, to determine the concentration of a coloured solution using colorimetry:

1. Determine the wavelength (colour) of light to use for the colorimetric analysis.
2. Prepare a set of standard solutions of known concentration.
3. Measure the absorbance of each standard solution using the colorimeter.
4. Plot the absorbance vs concentration for each standard solution on a graph.
5. Draw the line of best fit through the data points. This is the calibration curve.
6. Measure the absorbance of the solution of unknown concentration using the colorimeter.
7. Use the calibration curve to determine the concentration of this solution.

worked example

The Problem: Chris the Chemist needs to determine the concentration of a deep blue copper sulfate solution.

First Chris transfers 25.00 mL of the solution by pipette into a 100.00 mL volumetric flask and makes the solution up to the mark with distilled water.

Next, Chris prepares copper sulfate solutions of known concentration and measures their absorbance in order to establish a calibration curve as shown below:

Then Chris measures the absorbance of the diluted solution and finds that it is 0.506

Determine the concentration of the original copper sulfate solution.

Step 1: Plot the absorbance for the diluted solution on the calibration curve to determine its concentration.

[CuSO_4(aq)(diluted)] = 0.18 mol L^-1

Step 2: Determine the concentration of the undiluted original solution:

c_iV_i = c_fV_f

c_i = [CuSO_4(aq)(original)] = ? mol L^-1

V_i = volume of CuSO_4(aq)(original) = 25.00 mL = 25.00 mL ÷ 1000 mL/L = 0.02500 L

c_f = [CuSO_4(aq)(diluted)] = 0.18 mol L^-1 (from calibration curve)

V_f = volume of CuSO_4(aq)(diluted) = 100.00 mL = 100.00 mL ÷ 1000 mL/L = 0.10000 L

c_i × 0.02500 L = 0.18 mol L^-1 × 0.10000 L

c_i × 0.02500 L = 0.018 mol

c_i × 0.02500 L ÷ 0.02500 L = 0.018 mol ÷ 0.02500 L

c_i = 0.72 mol L^-1 (only justified in 2 significant figures)

Further Applications of Colorimetry

1. Using Colorimetry to measure the concentration of a transition metal ion

• If an aqueous transition metal ion is intensely coloured, its concentration can be measured directly e.g. manganese concentration can be measured if it is oxidised to the deep purple manganate(VII) ion, MnO₄^–.
• However, many ions are not as intense as the MnO₄^– ion, BUT if a suitable ligand or complexing agent is added, then a more intensely coloured complex may be formed, from which accurate measurements of concentration can be made e.g.
  • The blue hexaaquacopper(II) ion forms a deeper violet–blue ammine complex with ammonia.
  • Yellow–brown iron(III) ions form a deep blood–red complex with the thiocyanate ion (SCN^–) by mixing it with ammonium/potassium cyanate.
• Once the method of producing a more intense colour is established, you then need to derive a calibration curve.
  • This is done by measuring the absorbance of solutions of known concentrations of the coloured complex and plotting the calibration curve/graph (see right of colorimeter diagram).
  • The known concentration range should include any likely absorbance measured from the solutions under test i.e. those whose concentration is being determined.
  • Generally at low concentrations the calibration curve is linear i.e. it obeys Beer's Law (Beer–Lambert Law). Without going into the mathematics of Beer's Law and absorption, it basically states that a solution's absorbance is directly proportional to the concentration of the coloured solute.
    • For various reasons the calibration may curve upwards (positive deviation from Beer's Law) or curve over (negative deviation from Beer's Law). However, a linear or otherwise calibration curve still shows increasing absorption with increasing concentration and curved calibration graphs are acceptable, if not advisable, if your methodology is accurate.

How can we use colorimetry to deduce the formula of a complex?

• The method depends on measuring the absorbencies of solutions containing different ratios of transition metal ion to complexing agent.
• Just for the sake of argument, imagine that one mole of transition metal (M³⁺) ion reacts with two moles of a monodentate ligand (X^–). The reaction equation for the ligand displacement reaction to form the complex would be:

There are two basic approaches as to how you vary the transition metal ion – ligand ratio and the results illustrated in the diagram below.

Method (1) The mole ratio method keeping Mⁿ⁺ constant and gradually increasing the number of moles of ligand X from zero to a large molar excess.

• From 0.0 to 2.0 moles of X^– added per 1.0 moles of M³⁺ there is a steady rise in absorbance as more and more of the complex is formed. From over 2.0 of X^– per mol M³⁺ there is a more gradual rise in absorbance.
  • The point of intersection of the two linear portions of the graph gives you the X^–/M³⁺ ratio in the complex i.e. 2.0
  • Note that ligand exchange reactions are equilibrium reactions so you don't go to the maximum absorbance at 2.0 but the change in the 'rate of change' of absorbance does give the ratio.
  • If you do this for the reaction between iron(III) ions and thiocyanate ions which gives a blood–red complex, you obtain the change in graph gradient at 1.0 mol of CNS^– to 1.0 mol of Fe³⁺ for the reaction ...

For dilute solutions of copper(II) ions and ammonia the graph gradient change occurs at 4.0 moles of NH₃per mol of Cu²⁺ for the reaction ...

• Method (2) The continuous variations method in which you start with zero moles of Mⁿ⁺ and an excess of the ligand X. In each successive mixture you then increase the amount of Mⁿ⁺ and decrease the amount of X^– and keep the total moles of Mⁿ⁺ and X^– constant.
  • For the sake of argument, if you assume both stock solutions are the same molarity, then the ratio of the volumes automatically gives you the X/M ratio in the mixture.
  • For the fictitious M³⁺ and F^– complex, the peak will occur between the 6X^– : 4M³⁺ mixture (ratio 1.5) and the 7X^– : 3M³⁺ mixture (ratio 2.33). Theoretically the peak should occur at a ratio of 2.0 for X^–/M³⁺ i.e. theoretically, in terms of a total volume of 10 units, it means a 6.66X^– : 3.33M³⁺ mixture by volume.
  • For the iron(III)–thiocyanate complex in reaction (ii) the peak will occur at 5CNS^– : 5Fe³⁺
    • i.e. a CNS^–/Fe³⁺ ratio of 1.0 for the complex [Fe(H₂O)₅CNS]²⁺
  • For the copper(II)–ammonia complex in reaction (iii) the peak will occur at 8NH₃ : 2Cu²⁺
    • i.e. an NH₃/Cu²⁺ ratio of 4.0 for the complex [Cu(NH₃)₄]²⁺ or [Cu(H₂O)₂(NH₃)₄]²⁺.
• In both cases, you work out the mole ratios present in the mixtures from the known concentrations and volumes of the stock solutions of Mⁿ⁺ and X^– used in each experiment.

Monitoring Rate of Reaction in reactions involving Manganate (VII) ions

The manganate(VII) ion, MnO₄^–, e.g. in potassium manganate(VII) solution, is a brilliant purple colour and its concentration in very dilute solution can be measured by using colorimetry i.e. by comparing the absorbance of the solution versus a calibration graph of known concentrations of the manganate(VII) ion.

• This can be applied to kinetic experiments e.g. measuring the rate of reaction of acidified potassium manganate(VII) when it oxidises ethanedioic acid/ethanedioate ion. The reaction is autocatalysed by the manganese(II) ions formed.
• Therefore, theoretically, via the intensity of the manganate(VII) ion colour, you can investigate the effects of changing the concentration of potassium manganate(VII), ethanedioic acid, dilute sulfuric acid and manganese(II) sulfate.
• A simplistic view would be to write an overall rate expression such as ...
• rate = k[MnO₄^–]^a[(COOH)₂]^b[H⁺]^c[Mn²⁺]^d, where a, b, c and d represent the orders of reaction.
• However, (i) good results are not easy to obtain, specifically due to the effect of autocatalysis and (ii) it is unlikely the rate expression is as simple as you will encounter in your pre–university course!

Summary Video and practise experiment