HANDOUT # 1
COMPLEX ION FORMATION-THE METHOD OF CONTINUOUS VARIATION USING SPECTROPHOTOMETRY
The purpose of this experiment is to determine the formula of a complex in solution using the method of continuous variation. Complex formation will be followed using a spectrophotometer.
Theory
The Problem of Direct Chemical Analysis of Species in Solution. Suppose a solution is prepared containing metal ions (MP+) and ligand ions or molecules (Lq-), and that these combine in some unknown way to form a complex
mM + nL ⇆ MmLn 1.1
(We have suppressed the charges on the ions since they do not affect our discussion.) Our problem is to determine the values of m and n in 1.1. We might try to do this by beginning with known amounts of M and L and then, after equilibrium is reached analyze chemically for the complex or for the remaining uncomplexed amounts. But clearly, if we analyze for M, L, or MmLn by chemical reaction with them (as is usual in chemical analysis) Equilibrium 1.1 will shift to make up for the loss, and this will make our results useless for figuring out m and n. There is a way around this difficulty which takes advantage of a mathematical property of the equilibrium constant and which involves measuring the concentration of the various species without consuming them.
A Qualitative Description of the Method of Continuous Variation. Suppose that Equilibrium 1.1 lies so far to the right that the reverse reaction is negligible. Mixing together in solution c moles of M and zero moles of L obviously can give no complex. But, if we gradually replace M by L, keeping the total number of moles equal to the constant c, the complex MmLn will be
moles
MmLn
p
c moles of M 0
0 moles of L c
Figure 1. Moles of MmLn formed as a function of ratio of added M to added L where total number added moles equals c. Solid line is for reaction going to completion. Dotted line is for equilibrium in which back reaction is significant.
formed in larger and larger amounts until the ratio of moles of M to moles of L is exactly equal to m/n. At this point ("p" of Figure 1) all the added M and L is in the complex and we have formed the maximum amount of complex possible under the restriction that a total of c moles of reactant be used. Continued replacement of M by L will result in too much L being present relative to M, so complex formation will use all the M but leave uncomplexed L in solution. This produces fewer complexes than before. Ultimately, when we get to zero moles of M and c moles of L, no complex is formed. The solid line in Figure 1 is a plot of what we have just described.
Now let us imagine that significant back reaction occurs in 1.1, so that the equilibrium is not all the way to the right. Then, even at point p, there is a significant amount of uncomplexed L and M present in solution. Nevertheless, it is possible to show that the maximum formation of MmLn still occurs at point p. The dotted curve in Figure 1 exemplifies the observed extent of formation of complex compared to the "ideal" of the complete reaction. In finding the maximum point p, we determine m/n and therefore the simplest formula for the complex. We can summarize this discussion in the form of a "law" of continuous variations: If M and L are mixed together in varying proportions subject to the restriction that [M] + [L] = constant, then the concentration of the complex MmLn will be a maximum when [M] and [L] satisfy the stoichiometric relation m[M] = n[L].
In this experiment, you will mix metal ion and ligand solutions together in varying ratios and follow the concentration of the colored complex produced by measurement of light absorption. The metal ion-ligand systems involved are Fe3+ with SCN- (thiocyanate) and Fe2+ with orthophenanthroline.
The equilibria between these metal ions and ligands and their respective complexes are pH dependent. To avoid complications due to changing pH, you will be working with buffered solutions.
EXPERIMENTAL PROCEDURE
You will use the Bausch and Lomb Spectronic 20 in this experiment. Refer to Appendix I for instructions on using this instrument. On the side shelf are five solutions. They are:
and 2% hydroquinone in 0.1 M HCl.
Rinse one of your burettes with 1 or 2 mL of solution M2 and then fill it. Likewise, fill another burette with solution L2. Obtain 11 clean, dry vessels and label them 1-11. Into the first, titrate 1 mL of M2 and 9 mL of L2 (1:9). Similarly, prepare solutions at ratios 2:8, 2.5:7.5, 3:7, 3.5:6.5, 4:6, 5:5, 6:4, 7:3, 8:2, 9:1, always maintaining a total volume of 10 mL. To each vessel add two drops of hydroquinone solution and stir the solution well. (The hydroquinone is a reducing agent which will prevent the ferrous ions from being air-oxidized to ferric ions.) Complex formation is not rapid in the ferrous-orthophenanthroline system, so these eleven solutions should be allowed to sit for an hour before being spectrophotometrically analyzed.
Be sure to adjust your spectrophotometer to 100% transmittance with a distilled water blank before taking this set of data. While you are waiting for the ferrous ion/orthophenanthroline system to equilibrate, prepare your solutions for the study of the ferric ion-thiocyanate system. Do this by preparing nine solutions in which the M1:L1 ratio varies from 1:9 to 9:1, as before, omitting the 2.5:7.5 and 3.5:6.5 cases. DO NOT ADD HYDROQUINONE TO THIS SET OF SOLUTIONS. (You want the more oxidized form of iron here.) When the solutions are prepared, (no waiting period is required for this system) measure their absorbencies at a wavelength of 447 nm. Also measure the absorbance of pure solution M1 and L1 at that wavelength.
After your one-hour waiting period has elapsed, adjust your spectrophotometer to 508 nm and reset your transmittance to 100% using a blank with distilled water. Measure the absorbance for each of your eleven ferrous-orthophenanthroline solutions and also for pure M2 (containing 2 drops of hydroquinone) and pure L2.
TREATMENT OF DATA
(A) The absorbencies you have recorded are the sum of absorbencies for all species in solution at that wavelength. MmLn absorbs at this wavelength. Did M or L alone absorb there too? If so, you should correct for this absorption in the following approximate way. Say pure solution M has an absorbance of AM. Call the absorbance of your 1:9 solution A1:9. Since this solution has in it only one tenth as much M as pure solution M, subtract away one tenth of the absorbance of solution M as being due to absorbance by M. That is, correct A1:9 = observed A1:9 - 0.1 AM (This correction is not terribly good because it ignores the fact that some of the added M is involved in complex formation.) Correct your data in this way for any absorbance by M or L.
(B) Plot your corrected absorbencies as ordinate (y-axis) against mL of solution M1 or M2. Use the maxima to determine m and n for your complexes. You should expect your maxima to occur rather near to positions on the abscissa corresponding to fairly small integers for n and m. Report your simplest formulas for the complexes.
(C) For the complex equilibrium
mM + nL ⇄ MmLn 1.2
Keq = [MmLn] 1.3
[M]m[L]n
You can figure out Keq for each system from your graphs. We have seen earlier that, if Reaction 1.2 went essentially to completion, and if you started with pure L and then went to 1:9, 2:8, 3:7, etc. for M:L, you would observe a linear increase in absorbance due to greater and greater amounts of MmLn being formed. At the stoichiometric ratio, the absorbance would be maximized because all M and L mixed together would have formed MmLn. Beyond this ratio, the absorbance would fall off linearly.
Keq = ¥
Absorbance
by M3L2
observed
Amax
1:9 2:8 3:7 4:6 5:5 6:4 7:3 8:2 9:1
M:L
Figure 2. Absorbance plot for complex having formula M3L2. Observed maximum occurs when M:L is equal to 3:2. Maximum absorbance would occur at same ratio if complex equilibrium went completely to complex formation (K = ¥ curve).
In Figure 2, we have indicated the absorbance at this "ideal" maximum as Amax. This is proportional to [MmLn]max, the concentration of complex if all M and L went into formation. The actual observed absorbance, Aobs is proportional to the actual concentration of MmLn. You can construct the idealized straight line "curves" from your observed curves by drawing tangents to your curves near the 1:9 and 9:1 ends where they are almost linear. The intersection of your straight lines should occur over your observed maximum. This fact will help you construct the lines. [If one or the other end of your curve is too irregular to give a good tangent, use one tangent plus the vertical through the maximum to obtain Amax and Aobserved.]
Now, from your solution data and your knowledge of m and n, you can calculate the maximum possible concentration of MmLn. Call this [MmLn]max. Then solve for [MmLn]obs using the relation
[MmLn]max = Amax 1.4
[MmLn]obs Aobs
Knowing [MmLn]obs and [MmLn]max, it is easy to calculate [M] and [L] actually present, and from this Keq of Equation 1.3.
Chemistry 15 - Laboratory Report Form
Experiment 1: Complex Ion Formation - The Method of Continuous Variation Using Spectrophotometry
Name Date
Partner ______
Data and Calculations
1. Fe3+ with SCN-
Solution / Abs / Corrected AbsL1 pure
1:9
2:8
3:7
4:6
5:5
6:4
7:3
8:2
9:1
M1 pure
Show calculation for A4:6 in the Fe3+/SCN- system:
2. Fe2+ with orthophenanthroline (OPT)
Solution / Abs / Corrected AbsL2 pure
1:9
2:8
2.5:7.5
3:7
3.5:6.5
4:6
5:5
6:4
7:3
8:2
9:1
M2 pure
Show calculation for A4:6 in Fe2+ - orthophenanthroline system:
3. Plot corrected absorbencies vs. mL M.
4. Balanced chemical equation for the formation of the
a) Fe3+ - SCN- complex:
b) Fe2+ - orthophenanthroline complex:
5. Calculate Keq for each system (equation 1.3). Show all your work.
a) Fe3+ - SCN- system:
M / L / MLInitial
Change
Equilibrium
b) Fe2+ - orthophenanthroline system:
M / L / MLInitial
Change
Equilibrium
3