Iron(III) Thiocyanate Revisited:

A Physical Chemistry Equilibrium Lab Incorporating Ionic Strength Effects

Note: this lab appears in the January 1998 issue of J. Chem. Educ. pp 90–92.

The purpose of this lab is to calculate the thermodynamic equilibrium constant for the equation Fe3+ + SCN- <=> Fe(SCN)2+ in 0.5 M acid from the experimentally observed equilibrium constant and activity coefficients generated by the Davies extension of the Debye-Huckel theory.

Introduction

A system's empirically observed equilibrium constant, Kobs, is related to the thermodynamic equilibrium constant, Ktherm, by the ratio of activity coefficients, Kg.
Kobs * Kg = Ktherm
In moderate to high ionic strength solutions, the values of the activity coefficients can deviate significantly from 1 and high ionic strength solutions are a fact of life: industrial reactions are often carried out at high concentration for the sake of maximum productivity, waste tanks tend to be concentrated pools of ionic solutions, and some reactions must be carried out at very high or low pH —such as the iron(III) thiocyanate reaction
Fe3+ + SCN - <=> Fe(SCN)2+
which must be run in 0.5 M acid to prevent significant iron hydrolysis (1)via
Fe3+ + 3H2O <=> Fe(OH)3 + 3H2O

In this lab, the ionic strength of the solution is calculated as well as the equilibrium constant, and these together are used to calculate the thermodynamic equilibrium constant via the Davies extension of the Debye-Huckel theory.

Prelab

Beer's Law states that absorbance is proportional to the concentration of the chromophore and the pathlength. Use Beer's law
A = ab[FeSCN2+]           (1)

and
Cs = [SCN- ] + [FeSCN2+]
Cf = [Fe3+] + [FeSCN2+]
(where A is the measured absorbance, a is the absorptivity, b is the cell length, Cs is the initial concentration of thiocyanate, and Cf is the initial concentration of iron) along with

to show

Rearrange this expression into the standard form for a quadratic equation, ax2 + bx + c = 0, i.e.,
(A/ab)2 - (Cf + Cs + 1/Kobs)(A/ab) + CfCs = 0
and use the method of reversion of series (5) to arrive at the expression

The concentrations of iron and thiocyanate are small, so the second term of the above expression can be dropped, resulting in an expression that can be rearranged to

Plotting CfCs/A vs. Cf + Cs yields a straight line with a slope/intercept ratio equal to Kobs. It should be noted that this method for finding Kobs is independent of the absorptivity, a, and the cell length, b, and does not rely on the assumption that all the thiocyanate is converted to iron(III) at high iron concentrations, a necessary assumption for some other nongraphical methods (6).

Experiment

You will be provided with 0.005 M Na2EDTA and 0.02 M KSCN solutions (labeled with their concentrations and respective uncertainty). Make up 2.0 M HClO4 from concentrated HClO4; 0.5 M HClO4 from the 2.0 M HClO4; 0.002 M KSCN from the provided 0.02 M KSCN; and approximately 0.1 M Fe(NO3)3*9H20 in 0.5 M HClO4. This last solution is standardized by titration with 0.005 M Na2EDTA, using variamine blue as indicator (7): 1 mL of 0.1 M Fe(NO3)3 in HClO4 solution is diluted with distilled water to 50 mL to bring the pH up to 2, one drop of indicator is added, and approximately 20 mL of Na2EDTA is added via buret until the yellow endpoint is reached.

The spectrometer is zeroed using the iron solution as the blank. A 0.0002 M thiocyanate solution in 0.5 M HClO4 is prepared by adding 10 mL of the 0.002 M KSCN to a 100-mL volumetric flask along with 25 mL of 2.0 M HClO4 and distilled water to the mark. This is mixed well and poured into a 250-mL beaker. Successive 1 mL portions of the iron solution are added by pipette, the solution is mixed, and the absorbance is measured. After each absorbance measurement the solution is returned to the 250-mL beaker and the next portion of iron is added. Ten absorbance measurements at different concentrations are generally good enough to obtain good results.

Results

The data are best analyzed by a computer spreadsheet program because there are several calculations and the concentration for each absorbance measurement must be corrected for dilution. Example spreadsheets are provided.

The variables for the linear plot are calculated as shown in Spreadsheet 1. A graph of CfCs/A vs. Cf + Cs is made, the best-fit line is found, and the slope/intercept ratio is used to calculate Kobs.

The next step is to relate Kobs to Ktherm. Using eqs 1 and 2 above, derive an expression for the equilibrium concentration of iron(III) thiocyanate using K`obs: [FeSCN2+] = KobsCfCs/[1+(Cf+Cs)Kobs]. The equilibrium concentration of FeSCN2+ is then used to calculate equilibrium concentrations of other ions in solution. These concentrations, along with the acid-ion concentrations and the potassium and nitrate spectator-ion concentrations, are used to calculate the ionic strength via

where zi is the charge on the ith ion and mi is the molality. To convert from molarity to molality, the ionic strength is multiplied by the density of the final solution, which is on the order of 1.02 g/mL, not a large correction. The results of these calculations are shown on Spreadsheet 2.

To correct for the effects of ionic strength, an expression for g, the activity coefficient, must be found for each species. In dilute solutions, the Debye-Huckel limiting law provides a method for calculating activity coefficients, but this approach generally fails for solutions with an ion concentration greater than 0.1 m. More recent theories have been developed that reportedly work well for solutions up to 3 m, but these generally require some knowledge of the structure of the ion in solution (9). Davies (10), on the other hand, found an empirical relationship that works well for high ionic strength solutions and is quite adequate for this experiment. According to the Davies formulation, in H2O at 25o C
where mo is the standard concentration of 1 m. Using this expression, Kg and Ktherm are calculated for each dilution, as shown on Spreadsheet 3. Calculate the thermodynamic equilibrium constant for the iron(III) thiocyanate formation reaction derived from tabulated values (11) of DGof at 298.15 K. Compare this with your experimental results.

Discussion

The iron thiocyanate reaction must be run in at least 0.5 M acid to prevent iron hydrolysis. At this high acid concentration, the ionic strength is essentially constant —which keeps Kobs essentially constant —which allows Kobs to be calculated from the slope of a straight line. The method also produces acceptable results when the ionic strength is varied by lowering the pH as far as 0.15; however, at acid concentrations above 0.7 M the equilibrium H+ + SCN- <=> HSCN can begin to effect the iron thiocyanate equilibrium by reducing the available SCN - . This additional equilibrium could possibly be accounted for by solving a system of simultaneous equilibria, but this correction would make for a much more complicated spreadsheet—beyond that which is normally required in an undergraduate laboratory exercise. For the above reasons, the practical acid range for this experiment is probably limited to 0.5-0.7 M acid, which does not provide much in the way of a test of the Davies equation: the estimation of activities at high ionic strength is a complicated matter—for which several approaches have been developed (see above)—and even though the Davies equation appears to work in this particular instance, other systems may require the use of a more detailed theory.

Comment on the fact that their thermodynamic equilibrium "constant" appears to vary with concentration. Comment on a popular iron(III) thiocyanate equilibrium classroom demonstration wherein Fe3+, NO3- , and SCN- salts are added to an FeSCN2+ solution and the observed color change is attributed to mass action (12). To help with this explanation, observe and explain the color changes of a FeSCN2+ solution brought about by the addition of inert salts such as KCl.

Spreadsheet 1: Calculation of Variables for Linear Plot

 Point A Cf Cs CsCf/A Cf + Cs 1 123 1.03E-03 1.99E-04 1.67E-09 1.23E-03 3 281 3.03E-03 1.95E-04 2.10E-09 3.23E-03 5 380 4.95E-03 1.92E-04 2.50E-09 5.14E-03 7 448 6.80E-03 1.88E-04 2.85E-09 6.99E-03

Spreadsheet 2: Calculation of Ionic Strength

 Point [FeSCN2+]= [Fe3+]= Cf - [FeSCN2+] [SCN-]= Cs - [FeSCN2+] I =0.5{(9*[Fe3+])+(4*[FeSCN2+])+([NO3-])+[K+]+[SCN-] +[H+]+[ClO4-]}density 1 2.54E-05 1.00E-03 1.74E-04 5.16E-01 3 5.86E-05 2.97E-03 1.36E-04 5.29E-01 5 7.93E-05 4.87E-03 1.13E-04 5.40E-01 7 9.24E-05 6.71E-03 9.60E-05 5.52E-01

 Point g Fe3+ g SCN- g FeSCN2+ g Kg Ktherm = Kobs * Kg 1 0.0624 0.735 0.291 6.34 926 3 0.0631 0.736 0.292 6.29 918 5 0.0631 0.736 0.292 6.29 918 7 0.0637 0.736 0.293 6.25 913

Literature Cited

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9.  Pitzer, K. S. Acc. Chem. Res 1977, 10, 371. Bahe L. W.; Parker, D. J. Am. Chem. Soc, 1975, 97, 5664.

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12.  Seager, S. L.; Slabaugh, M. R. Safety-Scale Laboratory Experiments for General, Organic and Biochemistry; West: St. Paul, MN, 1994; p 149.

13.  Dubois, R. J. Chem. Educ. 1937, 14, 324.