Spectrophotometry is the branch of analytical chemistry that uses light absorbtion to determine the concentration of a colored compound. Absorbance is usually recorded by a spectrophotometer.
When a compound is dissolved in a solvent, it absorbs light at different wavelengths (depending on its color). To find the absorbance, we use the Beer-Lambert law, \(A = \varepsilon cl\). If you want to learn more about spectrophotometry, make sure to read the theory page.
Every spectrophotometer is different. In the IJSO, you will be provided with instructions on how to use it. Make sure to read the instructions, to save the time you'd otherwise waste trying to figure out what to do. It will also, usually be set to the proper wavelength, or they will tell you how to change the wavelength and the wavelength you need to use.
If you know the molar absorption coefficient for the specific compound, you can just find concentration as \(c = \frac{A}{\varepsilon l}\). However, that's not a very good ideea, since \(\varepsilon\) depends on temperature, solvent etc.
A better idea would be to create a graph for the dependence \(A = f(c)\). This dependence will take the form \(A = \varepsilon lc + A_0\), where \(A_0\) is the absorbance of distilled water, the cuvette walls etc., which you would also ignore if you used the method above. After this, you can either find the slope (\(\varepsilon l\)) and the free term (\(A_0\)), in order to find the unknown concentration, or simply use the graph to visually estimate what concentration corresponds to your measured absorbance.
The concentration of the weak acid is determined by direct titration using a standardized strong base and phenolphthalein indicator.
Sometimes, to compounds combine in a ratio we don't exactly know. To find out the exact reaction stoichiometry, we mix the compounds in different ratios and measure the absorbance of the resulting solution.
When you mix the two compounds in different ratios, as long as the two reactants have very low absorptivities and the product has a high one, you can safely say that the absorbtion will be maximum when the reactants are mixed in the stoichiometric ratio.
One thing that is important to keep in mind is that the total number of moles (reactant 1 + reactant 2) should remain the same, while the total volume should also remain the same. In case the two concentrations are different, both conditions can't be satisfied just by mixing the solutions - you'll also need to dilute with distilled water until you reach the required volume.
The best way to understand is using an example. Nickel ions \(\ce{Ni^{2+}}\) form a red complex with dimethylglyoxime (DMG). Since nickel ions are green and the complex is red, we can measure absorbance at a green wavelength - the complex absorbs most of the light, nickel doesn't absorb at all.
If the concentrations are \(c_{\ce{Ni}} = c_{DMG} = 10^{-3}M\), we get the following table:
| Trial | VNi (mL) | VDMG (mL) | Vtotal (mL) | nNi/nDMG | Absorbance |
|---|---|---|---|---|---|
| 1 | 0.0 | 25.0 | 25.0 | 0:1 | 0.000 |
| 2 | 2.5 | 22.5 | 25.0 | 1:9 | 0.24 |
| 3 | 5.0 | 20.0 | 25.0 | 1:4 | 0.49 |
| 4 | 7.5 | 17.5 | 25.0 | 3:7 | 0.73 |
| 5 | 8.3 | 16.7 | 25.0 | 1:2 | 0.80 |
| 6 | 10.0 | 15.0 | 25.0 | 2:3 | 0.72 |
| 7 | 12.5 | 12.5 | 25.0 | 1:1 | 0.60 |
| 8 | 15.0 | 10.0 | 25.0 | 3:2 | 0.48 |
| 9 | 17.5 | 7.5 | 25.0 | 7:3 | 0.33 |
| 10 | 20.0 | 5.0 | 25.0 | 4:1 | 0.17 |
| 11 | 22.5 | 2.5 | 25.0 | 9:1 | 0.07 |
| 12 | 25.0 | 0.0 | 25.0 | 1:0 | 0.000 |
If we graph the absorbance as a function of the molar ratio, or just examine the table, we see that the absorbance is maximum when \(\ce{Ni^{2+}}:DMG = 1:2\), so the formula of the complex is \([\ce{Ni}(DMG)]^{2+}\)
Video courtesy of YouTooBio (YouTube). Video used for educational purposes under YouTube’s embedding policy.