Job's Method is an extremely versatile approach to the determination of reaction stoichiometries. Here we describe its application to the determination of the stoichiometry of amino acid complexes with the Cu2+ ion.
Job's Method may be applied to stoichiometric detemination in either of 2 ways. For clarity, we discuss it in terms of the general reaction, (1):
The Standard Method. A series of solutions is prepared in which the sum of the number of moles of A and the number of moles of B is kept constant, but in which the relative amounts of A and B are systematically varied. Thus
For example, the following series of solutions might be prepared from two stock solutions, one 0.1 M in A and the other 0.1 M in B:
| Solution Number | Volume 0.1 M A solution, mL | Volume 0.1 M B solution, mL | Volume additional solvent, mL | Ratio [B]/[A] | mmoles Product |
|---|---|---|---|---|---|
| 1 | 0 | 0.9 | 1.1 | infinite | 0 |
| 2 | 0.1 | 0.8 | 1.1 | 8 | 0.01 |
| 3 | 0.2 | 0.7 | 1.1 | 3.5 | 0.0175 |
| 4 | 0.3 | 0.6 | 1.1 | 2 | 0.015 |
| 5 | 0.4 | 0.5 | 1.1 | 1.25 | 0.0125 |
| 6 | 0.5 | 0.4 | 1.1 | 0.8 | 0.01 |
| 7 | 0.6 | 0.3 | 1.1 | 0.5 | 0.0075 |
| 8 | 0.7 | 0.2 | 1.1 | 0.28 | 0.005 |
| 9 | 0.8 | 0.1 | 1.1 | 0.125 | 0.0025 |
| 10 | 0.9 | 0 | 1.1 | 0 | 0 |
Once the solutions are prepared, the amount of product formed is measured in each solution, and a plot of the amount of product formed versus moles of B in the solution is constructed. The crux of Job's Method is that the maximum amount of product will form when A and B are present in the correct stoichiometric ratio. For the data in the table, this plot results. Normally the plot looks like an inverted "V", with the vertex skewed toward one side or the other. Straight lines are drawn through the points on both sides of the vertex, and the moles of B corresponding to their intersection point allows the stoichiometry to be determined. The value of x is then calculated from equation (2):
Because the intersection in the plot occurs at moles B = 0.072/(0.09 - 0.072) = 4, the coefficient of reactant B in equation (1) is 4.
The challenging aspect of the application of Job's Method is in finding a way to measure the amount of product formed in each solution. If the product precipitates, the product in each solution may be recovered by filtration and weighed. If the product absorbs light at a known wavelength, then each solution can be placed in a spectrometer and the absorbance at that wavelength determined. There are many other possibilities. The primary restraint, particularly when using a spectrometric method, is that ONLY THE AMOUNT OF PRODUCT is measured. If, for example, one of the reactants also has significant absorbance at the wavelength being used to monitor the amount of product, the shape of the Job's method plot will be affected, sometimes to an extent that prevents determination of the stoichiometry in a straightforward way. It is important to be alert for this problem.
The Limiting Reagent Method. In this modification of Job's Method, a series of solutions is prepared containing a fixed number of moles of reactant A and varying amounts of reactant B, such that the ratio, moles B/moles A runs the gamut from 0 to a value known to be larger than x. The amount of product in each solution is then measured. Once the amount of B exceeds the stoichiometrically required amount, A is the limiting reagent, and the amount of product formed will remain constant. Thus by noting the ratio [B]/[A] at which the amount of product formed levels off, the stoichiometry can be determined. A plot of amount of product versus [B]/[A] will reveal this point visually. Table 2 provides data for a series of solutions. Look here for a plot of the data.
| Solution Number | Volume 0.1 M A solution, mL | Volume 0.1 M B solution, mL | Volume additional solvent, mL | Ratio [B]/[A] | mmoles Product |
|---|---|---|---|---|---|
| 1 | 0.15 | 0 | 1.85 | 0 | 0 |
| 2 | 0.15 | 0.05 | 1.8 | 0.33 | 0.00125 |
| 3 | 0.15 | 0.1 | 1.75 | .667 | 0.0025 |
| 4 | 0.15 | 0.15 | 1.7 | 1 | 0.00375 |
| 5 | 0.15 | 0.2 | 1.65 | 1.33 | 0.005 |
| 6 | 0.15 | 0.25 | 1.6 | 1.67 | 0.00625 |
| 7 | 0.15 | 0.3 | 1.55 | 2 | 0.0075 |
| 8 | 0.15 | 0.45 | 1.4 | 3 | 0.01125 |
| 9 | 0.15 | 0.60 | 1.25 | 4 | 0.015 |
| 10 | 0.15 | 0.75 | 1.1 | 5 | 0.015 |
| 11 | 0.15 | 0.90 | 0.95 | 6 | 0.015 |
Application to Copper Amino Acid Complexes. Use this procedure if you have glycine, alanine, proline, threonine, and arginine. Prepare 10 mL of a 0.10 M solution of copper acetate monohydrate, Cu(C2H3O2)2.H2O, by weighing the appropriate amount of copper salt into a small Erlenmeyer flask and adding 10.0 mL of water from a graduate. Similarly, prepare 10 mL of a 0.10 M solution of your amino acid. Use 1- and 2-mL graduated pipets to prepare a series of solutions for a Job's Method study. You may model your study on Table 1 above. (NOTE: If you plan to use a Spectronic 20 Spectrometer to make absorbance measurements, 2 mL of solution is insufficient to adequately fill the test-tube cuvet. Thus instead of adding 1.1 mL of water to each solution, add 3.1 mL instead.) Once you start preparing solutions, be sure that the order of the test tubes is maintained! Scan the UV-visible spectrum of each solution in turn in the wavelength range between 800 and 400 nm, and obtain the absorbance of each solution at 550 nm. For the series of solutions, plot A at 550 nm versus the number of mmoles of amino acid. Extract the stoichiometry from the plot.
Use this procedure if you have methionine. Prepare 20 mL of 0.10 M copper acetate and 20 mL of 0.10 M methionine. Set up a series of 10 small test tubes in a test tube rack. Use 1- and 2-mL graduated pipets to prepare a series of solutions for a Job's Method study. Make mixtures according to Table 1 BUT use twice as much of each solution as indicated AND do not add the extra 1.1 mL of water to each mixture. The product forms as a solid. Be sure to maintain your series of test tubes in the proper order. Filter each solution through a Pasteur pipet filter, transferring the maximum possible amount of solid to the filter. You should use 1 filter per test tube, and keep the filters in the same order as the test tubes. Use a Pasteur pipet bulb to push the liquid through all of the filters. Measure the height of solid obtained in each filter. For the series of solutions, plot height of solid versus the number of moles of amino acid. Extract the stoichiometry from the plot.
Use this procedure if you have tryptophan. Prepare 10 mL of 0.10 M copper nitrate and 10 mL of 0.10 M tryptophan. The tryptophan will not dissolve, so add 1 mmole of NaOH (about 5 drops of 6 M NaOH). Set up a series of 10 small test tubes in a test tube rack. Use 1- and 2-mL graduated pipets to prepare a series of solutions for a Job's Method study. Make mixtures according to Table 1 BUT do not add the extra 1.1 mL of water to each mixture. The product forms as a solid. Be sure to maintain your series of test tubes in the proper order. Filter each solution through a Pasteur pipet filter, transferring the maximum possible amount of solid to the filter. You should use 1 filter per test tube, and keep the filters in the same order as the test tubes. Use a Pasteur pipet bulb to push the liquid through all of the filters. Measure the height of solid obtained in each filter. For the series of solutions, plot height of solid versus the number of moles of amino acid. Extract the stoichiometry from the plot.
Use this procedure if you have aspartic acid. Prepare 10 mL of 0.10 M copper nitrate and 10 mL of 0.10 M aspartic acid. The aspartic acid will not dissolve, so add 1 mmole NaOH (about 5 drops of 6 M NaOH). Use 1- and 2-mL graduated pipets to prepare a series of solutions for a Job's Method study. You may model your study on Table 1 above. Once you start preparing solutions, be sure that the order of the test tubes is maintained! Scan the UV-visible spectrum of each solution in turn in the wavelength range between 800 and 400 nm, and obtain the absorbance of each solution at 550 nm. For the series of solutions, plot A at 550 nm versus the number of mmoles of amino acid. Extract the stoichiometry from the plot.