3 Exp. 3: Reaction Stoichiometry and Formation of a Metal Ion Complex
PreLab
Use BB to quiz on the following before the lab
 The method of continuous variation was used to determine the stoichiometry for:
x A (aq) + y B (aq) > z P (aq)
In this experiment, the molarity concentrations of reactants A and B are both 1.50 x 103 M. The amount of product was measured for a variety of mixtures of A and B, where the total mixture volume was always kept constant at 10.0 mL. The following plot was generated:
 a) Using the equations of the trendlines, perform a simultaneous equations calculation to determine the volume of A used to obtain the maximum amount of product (= the value of x at the point of intersection of the lines).
 b) Determine the volume of B used to obtain the maximum amount of product (hint – what was the total volume of the mixture of A and B?).
 c) Using these two volumes, determine the simplest whole number volume ratio of reactants (volume A : volume B) used to obtain the maximum amount of product. Note that this ratio yields the reaction stoichiometry, i.e., volume A : volume B = x : y. One method you may use is to divide both volumes by the smaller volume. One volume (and mole ratio in an equimolar solution) will then be one. The second may be a whole number or may need to be multiplied by a factor to get a whole number. If the second ratio, for example, is 2.25, your volume (and mole) ratio is 1:2.25. Multiplying both by 4 yields a volume and mole ratio of 4:9.
 In the experiment to be performed in this lab, what is the unbalanced reaction that will be studied?
 What technique will be used in this experiment to determine the amount of product produced?
 What special feature of the product makes this a good technique to use?
 Why may happen if fingerprints or bubbles are present in your filled cuvette? Why should you handle the ‘ribbed’ side of the cuvette?
Objectives
The objectives of this laboratory are as follows:
 To determine the reaction stoichiometry for the formation of a metal ion complex between iron (II) cations and 1,10phenanthroline using continuous variation.
 To monitor the relative concentration of a colored metal ion complex in solution with absorption spectrometry.
Introduction
In 1928, French chemist Paul Job captured the imagination of the scientific community with a graphical representation of the UV absorption of Ti(NO3)/NH3 against the mole fraction, Xa, of Ti(NO3). This plot is now called a plot of continuous variation, or a Job’s Plot. Much like Job, you will use a continuous variation plot in order to discover the stoichiometric ration of a metal ligand complex. First, some background on stoichiometry.
The net result of a reaction can be summarized by a chemical equation. In order to write a chemical equation, a chemist must identify the reactants and products, as well as the ratios in which these species react and are produced, i.e., the stoichiometry of the reaction.
When two or more reactants are mixed together, it is possible to determine whether a reaction occurs by observing whether any property of the mixture changes. Further, by investigating how the change in an observed property varies when different ratios of reactants are mixed, the stoichiometry of the reaction can be determined.
Consider the study of a reaction where solutions of reactants A and B are mixed and product P is formed:
x A + y B –> z P
The reactant mixtures are carefully chosen so that sum of the moles of A and B are constant, and the amount of product that forms for each mixture is measured. This is known as the method of continuous variation. If either A or B is in excess, the excess will remain in solution rather than be used to form product. The maximum amount of P is formed when A and B are mixed in the correct stoichiometric amounts, when there is just enough of each to react with nothing left over.
Suppose for example that x = 3 and y = 2, and that total number of moles of A and B is kept fixed at 0.10 moles. The amount of product formed will be at a maximum when the ratio A: B is 3:2, that is when A = 0.06 moles and B = 0.04 moles:
Amount of P formed
Moles of A 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Moles of B 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00
Note that to the left of the maximum on the plot (A < 0.06 moles); there is not enough of A to react with all the B present. Thus, less than the maximum amount of product will be generated. To the right of the maximum (B < 0.04 moles), there is not enough of B to react with all the A present. So once again, less than the maximum amount of product will be generated. As long as the total amount of A + B is constant, the maximum amount of product forms when the A: B ratio is the stoichiometric ratio for that reaction.
The reaction to be studied in this lab involves the formation of a metal ion complex. Metal ions, especially transition metal ions, possess the ability to form complexes with both organic and inorganic molecules called ligands. These complexes are produced when lone pair electrons from the ligand are donated into empty orbitals of the metal ion (resulting in a coordinate covalent bond). Here, iron (II) cations will be mixed with the ligand 1,10phenanthroline to produce an iron (II)phenanthroline complex:

Equation 1: x Fe^{2+} + y phen –> Fex(phen)y ^{2+}
where phen = 1,10phenanthroline =
Using the method of continuous variation as outlined earlier, several reactant solutions are prepared in which the mole quantities of the metal ion and the ligand are varied but the sum of the mole quantities is kept constant. The amount of complex produced will be measured, the maximum indicating when the correct stoichiometric ratio of Fe^{2+}: phen is used.
In this experiment, both the Fe^{2+} and phenanthroline solutions will have the same molarity concentration. Mixtures prepared with the same total number of moles will therefore have the same total volume (recall that moles of solute can be calculated by multiplying the solution volume by its molarity). As an additional consequence, in each prepared mixture the volume ratio of reactants used will be identical to the mole ratio of reactants used:
nFe = MFe x VFe and nphen = Mphen x Vphen
if MFe = Mphen
then nFe:nphen º VFe:Vphen
Thus, it will be more convenient to analyze the amount of complex product formed as a function of reactant volumes, rather than as a function of reactant moles.
The challenge in this experiment is choosing an appropriate technique to measure the amount of complex formed. Since the complex is a redorange color (while both reactants are colorless), the technique of Absorption Spectroscopy will be used. When visible light is directed at a colored compound in solution, the compound will absorb some wavelengths of the light while transmitting other wavelengths. The higher the concentration of the colored compound, the more light it will absorb.
Consider, for example, a blue compound in solution. When visible light is directed at this solution, the compound will predominantly absorb wavelengths in the orange region of the color spectrum, while predominantly transmitting wavelengths in the blue region of the spectrum (note that orange and blue are complementary colors). The transmitted light gives rise to the solution color that we see. Since the iron (II)phenanthroline complex is a redorange color, it is expected to absorb bluegreen wavelengths, between 460 and 550 nm.
A UVVisible spectrophotometer is the device used to measure how much light of a specific wavelength is absorbed by a colored species in solution. A schematic diagram of a typical spectrophotometer is shown below.

Beer’s Law quantitatively describes the relationship between the light absorbed (A) and the concentration of the colored species in solution (c) as:
Equation 2: A = e l c
where e is the molar extinction coefficient (a constant that depends characteristics of the compound analyzed and the wavelength used for analysis) and l is the path length, or the distance traveled by light through the sample (a constant of 1.0 cm in this experiment). The important thing to note is that concentration and Absorbance are directly proportional.
Absorbance can thus be used as a direct measure of the amount of complex produced in each reactant mixture analyzed.
Procedure
Safety
Both reactant solutions are prepared in an acidic buffer. In addition, 1,10phenanthroline is a mild irritant. If any of these solutions comes into contact with your skin or eyes, rinse with copious amounts of water for 15 minutes, and inform your instructor.
Materials and Equipment
200 – 1000 µL pipette, two pipette tips, one cuvette for spectrophotometer, spectrophotometer, ten small test tubes, two 50mL beakers, wash bottle filled with distilled water, Parafilm© (or a small stopper), Kim Wipes©, 2.50 x 104 M Fe+2 solution and 2.5 x 104 M 1,10phenanthroline solution.
Experiment Instructions
There will be ~8 spectrophotometers available for student use. Your instructor will provide directions on how to use them correctly at the beginning of the lab session. Use the same cuvette for all measurements.
Preparing Mixtures of Reactant Solutions
Table 1: Iron (II): Phen volumes  
Tube  iron (II)  phen 
1  3.50 mL  1.50 mL 
2  3.00 mL  2.00 mL 
3  2.50 mL  2.50 mL 
4  2.00 mL  3.00 mL 
5  1.50 mL  3.50 mL 
6  1.25 mL  3.75 mL 
7  1.00 mL  4.00 mL 
8  0.75 mL  4.25 mL 
9  0.50 mL  4.50 mL 
10  0.25 mL  4.75 mL 
 Obtain approximately 25mL of 2.50 x 104 M Fe+2 and 40mL of 2.5 x 104 M phenanthroline in each of your small beakers. Use the appropriate micro pipettes to prepare the following solution mixtures in your small test tubes. You will use only two micropipette tips. Recall that µL represent 1 x 106 L and mL represent 1 x 103 L. Perform conversions in your notebook if necessary. You will fill and dispense the pipette multiple times per test tube for the larger volumes.
The rose to orange color of the iron (II)phenanthroline complex should fully develop within ten minutes of mixing.
Determining λmax of the Complex
 Rinse the cuvette with distilled water and dry it carefully with a Kim Wipe tissue. Fill your cuvette to the mark with phenanthroline only. This solution will be used as your calibration blank. Your colorimeter will prompt a zero calibration, which can also be accessed in the Experiment drop menu under the Calibrate tab. Choose Spect. 1, then Finish Calibration. You have now zeroed the spectrophotometer so that it will measure the solution absorbance and ‘zero’ the cuvette and solvent absorbance.
Measuring the Absorbance of the Solutions with Different Mole/Volume Ratios
 Measure the absorbance and λmax of each of the ten prepared solution mixtures. Record this data on your report form.
 Rinse the clean, empty cuvette with a small volume of the solution to be measured and rinse to waste*. Fill the cuvette at least ¾ full of the solution mixture in tube #1. Place it in the sample holder and measure the solution absorbance and peak wavelength. This can be done by placing the cursor at the highest absorbance peak and reading the x (wavelength, nm) and y (absorbance) readings at the bottom left of the graph. Use the Auto scale and zoom functions to calibrate your graph.
 Return the solution mixture into its original test tube. Rinse the same cuvette with a small volume of the next solution to be analyzed. Discard the rinse solution to your waste.
 Repeat this process with all other solution mixtures in tubes #210.
*You are accustomed to rinsing glassware with D.I. water. In this case, however, a small volume of water will dilute your sample. Each successive solution is closer than D.I water in both target species concentration and absorbance You will have greater success by rinsing your cuvette with the solution to be analyzed, especially as you move from low to high concentration or absorbance.
 When completely finished, dispose of your chemical waste as directed by your instructor.
Data Analysis
Using Microsoft Excel®, graph your absorbance data as a function of the volume of ligand (1, 10 Phenanthroline) used. Refer to student Appendix VII for help with an excel® scatterplot and series data. You will graph this data as two data sets with overlay. Treat ascending and descending values as two separate data sets, plotting them both on the same set of axes. You can do this by right clicking on your graph (or the filter icon) to select data. You can then input the x and y values that are ascending as a series and the x and y values that are descending by adding a second series. *The example graph from contrived data will slope and intercept the yaxis differently than your data. Add bestfit trendlines to both data sets and obtain the equations of these trendlines. Then solve for the point of intersection of these lines using your two equations in a simultaneous equations calculation.
From the point of intersection, you can determine the volume mixture of reactants used to obtain the maximum absorbance (hence, the maximum amount of complex formed). Finally, using this volume mixture, you can determine the simplest whole number volume ratio of Fe+2: Ph (identical to the mole ratio), which is the stoichiometric ratio for this reaction. One method you may use is to divide both volumes by the smaller volume. One volume (and mole ratio in an equimolar solution) will then be one. The second may be a whole number or may need to be multiplied by a factor to get a whole number. If the second ratio, for example, is 2.25, your volume (and mole) ratio is 1:2.25. Multiplying both by 4 yields a volume and mole ratio of 4:9. The following example data tables may help as you create your informal report.
Experimental Data
 Absorbance of Reactant Solution Mixtures
Molarity of Iron (II): Molarity of Phenanthroline: ___
Mixture  Volumes of Reactants Mixed (mL)  Absorbance (unitless)  lmax (nm)  
Iron (II)  Phenanthroline  
1  3.50  1.50  
2  3.00  2.00  
3  2.50  2.50  
4  2.00  3.00  
5  1.50  3.50  
6  1.25  3.75  
7  1.00  4.00  
8  0.75  4.25  
9  0.50  4.50  
10  0.25  4.75 
Data Analysis/Post Lab
 1) Using Microsoft Excel®, create a graph of Volume of Phenanthroline vs absorbance. Plot this data as two data sets with overlay Treat ascending and descending values as two separate data sets, plotting them both on the same set of axes (if needed, review the instructions in your student appendix). Add bestfit trendlines to both data sets and obtain the equations of these Attach this graph to your report using the Snip app. The graph should take up no more than ½ page and should be labeled appropriately.
Ascending datatrendlineequation: _ ________________________________
Descending data trendline equation: ________________________________
 2) Using the equations of the trendlines, perform a simultaneous equations calculation to determine the volume of phenanthroline used to achieve the maximum product absorbance (= the value of x at the point of intersection of the lines). Show your work.
 3) Determine the volume of iron (II) used to achieve the maximum product absorbance (hint, what was the total volume of the iron (II)–phenanthroline mixture?).
 4) Using these two reactant volumes (at the maximum absorbance) determine the simplest whole number volume ratio of Fe+2: phen, which is the stoichiometric ratio for this Use the following method: do not round until the last step:
 Convert mass or volume to moles (this is assumed as you are using equal molar ratios.
 Divide by the smaller number of moles.
 Multiply until you get a whole number.
 5) Write the balanced equation for the reaction studied in this Refer to Equation 1 for guidance. You will replace the x and y variables with your mole ratio data. You may refer to 1, 10 phenanthroline as phen.
 6) Since the two reactant solutions in this experiment have the same molarity, the volume ratio at maximum absorbance will be the same as the mole ratio at maximum absorbance. Perform appropriate calculations to prove that this is indeed the
 7) How does your data acquisition process support or contradict Beer’s law? Be specific and use the variables contained in Beer’s law.
 8) Find an outside application for continuous variation and/or Beer’s law.
Your Report:
 Complete the prelab and take the prelab quiz in your Blackboard shell before attending lab.
 Use a lab notebook to record observations and make calculations.
 Create an informal lab document to turn in at the beginning of the next lab. Your lab report should include clearly labeled and tabulated or graphed raw data, any formulas or equations, unknown number, or letter (if applicable), conclusive data such as chemical formula, etc. with clear example calculations or sample calculations*. Use tables or graphical data where applicable. Discuss results relevant to your findings. Think about the main point of the lab, or the results that you worked for and be sure to include it or them. Refer to How to Write an Informal Lab Report as you draft your report.
 Include numbered responses to any post lab questions. You do not need to rewrite the questions but will use complete sentences or a short paragraph as appropriate. Be specific. If you describe an error, for example, you must describe the direction the data would skew and why.
 Submit your document before your next lab appointment under the assignment tab on your laboratory Blackboard shell.
References:
Adapted from: Chem 11 Experiments, Santa Monica College http://www.smc.edu/AcademicPrograms/PhysicalSciences/Chemistry/LabManual/Pages/Chem11Experiments.aspx (accessed Jun 25, 2020).
Job, Paul (1928). “Formation and Stability of Inorganic Complexes in Solution”. Annales de Chimie. 10. 9: 113–203.
Molecular Absorption Spectroscopy; Determination of Iron with 1, 10 Phenanthroline, 2005. University of Kentucky, Lexington
Renny JS, Tomasevich LL, Tallmadge EH, Collum DB. Method of continuous variations: applications of job plots to the study of molecular associations in organometallic chemistry. Angew Chem Int Ed Engl. 2013;52(46):1199812013. doi:10.1002/anie.201304157