# Spectrophotometric Determination of Equilibrium Constant for a Reaction Assignment Words: 2628

DATE PERFORMED: JULY 20, 2007 SPECTROPHOTOMETRIC DETERMINATION OF EQUILIBRIUM CONSTANT FOR A REACTION ABSTRACT UV-VIS spectrophotometry is one of the most widely-used methods for determining and identifying many inorganic species. During this experiment, this spectrophotometry was used to determine the equilibrium constant, Keq, of the Fe3+(aq)+SCN-(aq)- FeSCN2+(aq) reaction. By determining the amount of light absorbed, the concentration of the colored FeSCN2+ solution was also quantitatively determined. From that data, the concentrations of the reagents at equilibrium may also be determined.

This experiment should thus provide a Keq value without computing for the concentration of each of the species in the reaction. This experiment will only deal with the aspect of chemical equilibrium, particularly the aforementioned equilibrium constant, and not with associated topics such as thermodynamics or kinetics. INTRODUCTION Reactions strive to attain equilibrium or stability. In kinetics, stability is attained when the rate of formation of the products is equivalent to the rate of reactant re-formation.

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Rate is determined by the rate expression, r=k[A]x, where A is the reactant, x the order of reaction with respect to the reactant and also to the coefficient of the reactant if it is an elementary reaction, and k, the rate constant. In equilibrium, there is an equilibrium constant determined by kf[A]x=kr[B]y, which is equivalent to the aforementioned parameter of equilibrium, rate of formation (forward) is equal to the rate of reformation (reverse). Therefore, Keq=(kf/kr)=([B]y/[A]x).

Concentration may be determined by taking the number of moles of the reagent or product and dividing it by the total volume of the solution (dimension: M, molarity). There is, however, another method of determining the equilibrium constant, Keq, of a reaction. Spectrophotometric analysis results in the quantitative determination of the concentration of the product, through the Beer-Lambert’s Law. The absorbance of light by a colored solution, such as FeSCN2+, is displayed when the solution is placed in the spectrophotometer.

By using standard solutions to determine the average molar absorptivity of the solution, and given the path length, the concentration of the product of the reaction, the red FeSCN2+ solution may be determined. From that data, and from the initial concentrations of the reactant species, the concentrations of the reactants at may also be determined. With the concentrations of the products and reactants solved for, the equilibrium constant, Keq, of the reaction may be determined using Keq=(kf/kr)=([B]y/[A]x).

In this experiment, the aim is to determine the equilibrium constant, Keq, of the Fe3+(aq)+SCN-(aq)- FeSCN2+(aq) reaction by using the Beer-Lambert’s Law and the Keq expression. RESULTS AND DISCUSSION [pic] Figure1. Calibration Curve The calibration of the sample was done so that the value of the molar absorptivity approximates as closely as possible, the overall composition of the samples and covers a reasonable range of the concentrations of the analyte. The linear relationship between the absorbance and the concentration signifies that Beer’s law holds in our standard.

Looking at the literature value of the molar absorptivity of [Fe(SCN)]2+ at 447 nm which is around 4500 cm-1M-1, we can observe that it is a bit far from our experimental molar absorptivity. This is because there are many factors such as solvent, solution composition, and temperature that all affect the value of the absorptivity. The absorption spectrum is also influenced by the pH of the solution, the concentration of electrolytes in the solution, and the presence of interfering substances. Thus, it is not wise to use literature values in quantitative analyses because the absorptivity varies with certain conditions.

In the calibration, we have considered [Fe(SCN)]2+ to be the absorbing medium since Fe3+ is a nonabsorbing species in the ultraviolet and visible regions. The thiocyanate ion acts as a chromophoric reagent. Its reaction with the Fe3+ ion gives the red [Fe(SCN)]2+ complex which absorbs the green from the incoming white radiation and transmits the red component of the complex unaltered. Beer’s Law states that absorbance is directly proportional to the concentration c of the absorbing species, and to the path length b of the absorbing medium by a proportionality constant called the absorptivity a.

In our experiment, we expressed the concentration of the absorbing species in terms of mol/L and the path length in centimetres. Thus, the proportionality constant becomes the molar absorptivity ?. We set the wavelength of the spectrophotometer to 447 nm so we could achieve maximum sensitivity. At this point, the change in absorbance per unit of concentration is greatest and there is greater adherence to Beer’s Law. Table I. Absorbance of Unknown Solutions |Solution |Absorbance |[Fe3+]init |[SCN-]init | |Unknown 1 |0. 158 |0. 001 |2. 0 x 10-4 | |Unknown 2 |0. 308 |0. 001 |4. 00 x 10-4 | |Unknown 3 |0. 457 |0. 001 |6. 00 x 10-4 | |Unknown 4 |0. 604 |0. 001 |8. 00 x 10-4 | |Unknown 5 |0. 743 |0. 001 |1. 00 x 10-3 | Table II. Determination of the Equilibrium Constant, Keq |Solution |[Fe3+] |[SCN-] |[[Fe(SCN)]2+] |Keq | |Unknown 1 |9. 57 x 10-4 |1. 57 x 10-4 |4. 34 x 10-5 |288. 85 | |Unknown 2 |9. 12 x 10-4 |3. 2 x 10-4 |8. 85 x 10-5 |311. 02 | |Unknown 3 |8. 87 x 10-4 |4. 67 x 10-4 |1. 33 x 10-4 |321. 02 | |Unknown 4 |8. 23 x 10-4 |6. 23 x 10-4 |1. 77 x 10-4 |345. 21 | |Unknown 5 |7. 80 x 10-4 |7. 81 x 10-4 |2. 19 x 10-4 |359. 04 | Average equilibrium constant Keq = 325. 04 Theoretical Keq = 890 %difference = 63. 5% Beer’s Law also has several limitations. We can encounter real limitations, chemical deviations, and instrumental deviations. Real limitations can be avoided by analyzing samples at concentrations less than 0. 1M. At high concentrations, ions are very close to one another. Because of electrostatic interactions between them, the molar absorptivity of the samples is altered. Chemical deviations occur when reactions are undergone by the absorbing species to give products which absorb differently from the analyte. We cannot improve our procedure to correct this error since we are not aware if such reactions are affecting the sample. Stray light caused by scattering and reflection off surfaces, lenses, and mirrors results in a lower reading of the absorbance.

As we have observed in our calibration curve, we have a value for the y-intercept, unlike in the ideal equation of Beer’s Law where the y-intercept is zero. The intercept means that the cells holding the analyte and blank solutions do not have equivalent optical characteristics or have different path lengths. It can also mean that the blank solution does not totally compensate for interferences. The use of only one cell and keeping it in one position for the blank and analyte measurements helps avoid the mismatched-cell problem.

We can directly relate the difference between the literature value of the equilibrium constant of [Fe(SCN)]2+ and the experimental value to the errors encountered in the calibration of the sample. We use the molar absorptivity from the data of the calibration to determine the concentration of [Fe(SCN)]2+ at equilibrium, which we, in turn, use to compute for the concentration of the reactants at equilibrium. This leads to the propagation of the error in the first part of the experiment into the computation of the equilibrium constant.

The high equilibrium value obtained from the experiment shows that the reaction is product-favored. The reaction is pushed forward to produce [Fe(SCN)]2+, which is initially not present in the solution. The different values of the equilibrium constant for each unknown may be accounted for by the limits of Beer’s Law during the calibration from which the molar absorptivity was obtained, making the equilibrium concentrations less accurate. Through this experiment, we have proved that it is possible and also easy to obtain the equilibrium constant from the spectrophotometric analysis of the samples.

CONCLUSION AND RECOMMENDATIONS In theory, the equilibrium constant, Keq, of a reaction may be easily determined when using the spectrophotometer. By using the Beer-Lambert’s law and the Keq expression, Keq is quantitatively and decisively determined. Complete failure occurred during this experiment, when the absorbance read-outs of the standard solutions came back as negative values. It is possible that reagent contamination caused this. There is no specific person to be blamed, although it proves to be a reminder that solution preparation must be done carefully at all times to yield the best possible results.

As for the experimental Keq found in this experiment, we may only theorize as to the source of the discrepancy, which is rather significant, given that the experimental values are twice the expected. In any case, the suggestion is clear. We must handle solution preparation with the greatest care. ANSWERS TO QUESTIONS 1. Nitric acid, HNO3, serves primarily as “filler”. It keeps the volume of the solution constant while the volumes of the reactants are modified. By serving as “filler” it effectively increases or decreases the initial concentration of the reactant.

In this case, as the volume of thiocyanate, SCN-, decreases, its concentration also decreases as HNO3’s presence keeps the solution’s volume constant. As a result of the decrease in concentration, it is possible that the absorbance of the solution vary, as the color intensity of the solution may vary with the decrease of thiocyanate concentration. Finally, the presence of H+ ions from the strong acid may also help push the reaction to completion, as the addition and presence of Hydrogen ions may favor formation of the product, [Fe(SCN)]2+. 2.

The condition given that the concentration of thiocyanate is equal to that of [Fe(SCN)]2+, is true only for the standard solutions where thiocyanate is the definite limiting reagent. For the unknown solutions, the given statement does not follow. It appears that there must be a greater number of moles of Fe3+ in comparison to the number of SCN- moles in order for the given statement to hold true. 3. Although solutions containing Fe3+ absorb at the visible region, this does not mean that it also absorbs strongly at the ultraviolet region. Therefore, it is not a completely absorbing species.

SCN- acts as a chromophoric reagent to produce [Fe(SCN)]2+, which strongly absorbs in the ultraviolet and visible regions. Since [Fe(SCN)]2+ is the absorbing species in the experiment, the absorbance readings will correspond to its absorption capacity. 4. Although both samples (distilled water and diluted Fe(NO3)3 in HNO3) have both zero absorbance readings, we should keep in mind that we wish to cover the overall composition of the samples and encompass a wider range of the concentrations of the absorbing species. Distilled water does not tell us anything related to the overall composition of our sample. . In the experiment, we may have encountered several instrumental deviations that lead to differences in the absorbance readings. Some of these are mismatched cells and stray light in the spectrophotometer. These deviations lead to errors in our experimental value of the molar absorptivity. When we use this molar absorptivity from the calibration curve later on for the computation of the equilibrium concentrations of [Fe(SCN)]2+, Fe3+, and SCN-, the error is propagated and is even more developed upon the computation of the equilibrium constant.

Another possible source of this difference is that the reaction of the Fe3+ with the thiocyanate is incomplete and less product is produced, which means there is less absorbing species in the sample leading to a lower absorbance reading. APPLICATIONS(S) Spectrophotometry and photometric methods have many important characteristics that make it one of the most useful tools for quantitative analysis. It has a very wide applicability because it can be used on both absorbing and nonabsorbing species. The detection limits for absorption spectroscopy can also be extended to 10-6 or even 10-7 M indicating its high ensitivity. It also offers moderate to high selectivity since specific wavelengths can be found at which the analyte alone absorbs so there in no need for a separation step. It is also a very accurate method since the range of errors in the procedure lie only with 1% – 5% and can even be decreased with special precautions. With modern instruments, spectrophotometric and photometric measurements can easily and rapidly be performed. Nonabsorbing species can be determined after chemical conversion into absorbing derivatives.

These species are caused to react with chromophoric reagents to give products that strongly absorb in the ultraviolet and visible regions. Usually, the reaction of the color-forming reagents with the analyte is forced near completion for the successful application of the reagents. There is a large number of inorganic, organic, and biochemical species that absorb ultraviolet or visible radiation and can be determined through direct quantitative methods. Ions of the transition metals are colored in solution and can thus be identified through spectrophotometric measurement.

Ultraviolet and visible absorption spectroscopy account for more than 90% of the analyses performed in clinical laboratories. REFERENCES  Skoog, D. A. , West, D. M. , et al. Fundamentals of Analytical Chemistry 8th edition. Brooks/Cole, Singapore. 2004.  Lothian, G. F. Absorption Spectrophotmetry. Hilge, London. 1958.  Kolthoff, I. M, Sandell E. B, et al. Quantitative Chemical Analysis: 4th Edition. Macmillan Co. , New York. 1969.  Atkins, P. W. , et al. Physical Chemistry 8th edition. Oxford University Press, United Kingdom. 2005.  H. I Bloemink et al.

H2S…Cl2 Characterized in a Pre-reactive Gas Mixture of Dihydrogen Sulfate and Chlorine Through Rotational Spectroscopy: The Nature of the Interaction. Department of Chemistry, University of Exeter. Journal of the Chemistry Society-Faraday Transactions. V91 N14. 07. 21. 1995. p. 2059-2066 APPENDIX A. WORKING EQUATIONS A = ? bc where A ??? absorbance ? ??? molar absorptivity b ??? path length c ??? concentration of absorbing species For the standard solutions: [SCN-] = mmol SCN- total volume solution [Fe(SCN)]2+ = [SCN-] m (slope) = ? b b = 1 cm ? = m/b For the unknown solutions: [SCN-]init = mmol SCN- total volume solution Fe3+]init = mmol Fe3+ total volume solution [Fe(SCN)]2+eq = A ??? 0. 0135 3327. 5 [SCN-]eq = [SCN-]init – [Fe(SCN)]2+eq [Fe3+]eq = [Fe3+]init – [Fe(SCN)]2+eq Keq = [Fe(SCN)]2+eq [SCN-]eq [Fe3+]eq % Difference = |Keq exp – Keq theo| x 100 Keq theo B. SAMPLE CALCULATIONS [Fe(SCN)]2+ = [SCN-] [SCN-] = (0. 20 mL)(0. 002 M) = 4. 0 x 10-5 M 10. 00 mL [SCN-] = (0. 40 mL)(0. 002 M) = 8. 0 x 10-5 M 10. 00 mL [SCN-] = (0. 60 mL)(0. 002 M) = 1. 2 x 10-4 M 10. 00 mL [SCN-] = (0. 80 mL)(0. 002 M) = 1. 6 x 10-4 M 10. 00 mL ? = 3,327. 5 cm-1M-1 = 3,327. 5 M-1 1 cm [Fe3+]init = (5. 00 mL)(0. 002 M) = 0. 00100 M 10. 0 mL [SCN-]init = (1. 0mL)(0. 002M) = 2. 00 x 10-4 M 10. 0 mL [SCN-]init = (2. 00mL)(0. 002M) = 4. 00 x 10-4 M 10. 0 mL [SCN-]init = (3. 00mL)(0. 002M) = 6. 00 x 10-4 M 10. 0 mL [SCN-]init = (4. 00mL)(0. 002M) = 8. 00 x 10-4 M 10. 0 mL [SCN-]init = (5. 00mL)(0. 002M) = 1. 00 x 10-3 M 10. 0 mL [Fe(SCN)]2+eq = 0. 158 ??? 0. 0135 = 4. 34 x 10-5 M 3327. 5 [Fe(SCN)]2+eq = 0. 308 ??? 0. 0135 = 8. 85 x 10-5 M 3327. 5 [Fe(SCN)]2+eq = 0. 457 ??? 0. 0135 = 1. 33 x 10-4 M 3327. 5 [Fe(SCN)]2+eq = 0. 604 ??? 0. 0135 = 1. 77 x 10-4 M 3327. 5 [Fe(SCN)]2+eq = 0. 743 ??? 0. 0135 = 2. 19 x 10-4 M 3327. 5 [SCN-]eq = [SCN-]init – [Fe(SCN)]2+eq = 2. 00 x 10-4 M ??? 4. 4 x 10-5 M = 1. 57 x 10-4 M [SCN-]eq = [SCN-]init – [Fe(SCN)]2+eq = 4. 00 x 10-4 M ??? 8. 85 x 10-5 M = 3. 12 x 10-4 M [SCN-]eq = [SCN-]init – [Fe(SCN)]2+eq = 6. 00 x 10-4 M ??? 1. 33 x 10-4 M = 4. 67 x 10-4 M [SCN-]eq = [SCN-]init – [Fe(SCN)]2+eq = 8. 00 x 10-4 M ??? 1. 77 x 10-4 M = 6. 23 x 10-4 M [SCN-]eq = [SCN-]init – [Fe(SCN)]2+eq = 1. 00 x 10-3 M ??? 2. 19 x 10-4 M = 7. 81 x 10-4 M [Fe3+]eq = [Fe3+]init – [Fe(SCN)]2+eq = 0. 00100 M ??? 4. 34 x 10-5 M = 9. 57 x 10-4 M [Fe3+]eq = [Fe3+]init – [Fe(SCN)]2+eq = 0. 00100 M ??? 8. 85 x 10-5 M = 9. 12 x 10-4 M [Fe3+]eq = [Fe3+]init – [Fe(SCN)]2+eq = 0. 00100 M ??? 1. 3 x 10-4 M = 8. 87 x 10-4 M [Fe3+]eq = [Fe3+]init – [Fe(SCN)]2+eq = 0. 00100 M ??? 1. 77 x 10-4 M = 8. 23 x 10-4 M [Fe3+]eq = [Fe3+]init – [Fe(SCN)]2+eq = 0. 00100 M ??? 2. 19 x 10-4 M = 7. 81 x 10-4 M Keq = [Fe(SCN)]2+eq [SCN-]eq [Fe3+]eq = 288. 85 Keq = [Fe(SCN)]2+eq [SCN-]eq [Fe3+]eq = 311. 02 Keq = [Fe(SCN)]2+eq [SCN-]eq [Fe3+]eq = 321. 08 Keq = [Fe(SCN)]2+eq [SCN-]eq [Fe3+]eq = 345. 21 Keq = [Fe(SCN)]2+eq [SCN-]eq [Fe3+]eq = 359. 04 Theoretical Keq value of [Fe(SCN)]2+ = 890 % Difference = |Keq exp – Keq theo| x 100 Keq theo = |325. 04 – 890| x 100 890 = 63. 5% ———————– Average Keq value = 325. 04

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