Experiment 34
Determination of the Equilibrium Constant
Lab Report Analysis
Date: February 05, 2026
Abstract This experiment investigates the equilibrium constant (Keq) for the formation of the iron(III) thiocyanate complex ion, [FeSCN]2+. By varying the initial concentrations of Fe3+ and SCN- ions and measuring the equilibrium concentration of the complex using spectrophotometry, the equilibrium constant was determined. The Beer-Lambert law was employed to relate absorbance to concentration.
Results demonstrate that the equilibrium constant remains relatively constant across different initial concentrations, validating the law of chemical equilibrium. The average Keq value obtained was approximately 150-200 M-1, confirming the reaction favors product formation.
1. Introduction Chemical equilibrium represents a dynamic state in which the rates of forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. The equilibrium constant (Keq) is a quantitative measure of the position of equilibrium and is defined by the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients.
In this experiment, we examine the equilibrium reaction:
Fe3+(aq) + SCN-(aq) ■ [FeSCN]2+(aq)
The equilibrium constant expression for this reaction is:
Keq = [FeSCN2+] / ([Fe3+][SCN-])
The [FeSCN]2+ complex exhibits a deep red color, making it ideal for spectrophotometric analysis. By measuring the absorbance of this complex at its λmax (typically around 450-480 nm), we can determine its equilibrium concentration using the Beer-Lambert law: A = εbc, where A is absorbance, ε is molar absorptivity, b is path length, and c is concentration.
1.1 Objectives • Determine the equilibrium constant for the Fe3+/SCN- reaction
• Verify that Keq remains constant regardless of initial concentrations
• Apply spectrophotometric techniques and Beer-Lambert law
• Construct and use a calibration curve for quantitative analysis
• Analyze experimental error and precision in equilibrium measurements
2. Materials and Methods
2.1 Materials Reagents: 0.200 M Fe(NO3)3 in 0.5 M HNO3, 0.00200 M KSCN, 0.5 M HNO3
Equipment: Spectrophotometer (UV-Vis), cuvettes (1 cm path length), volumetric flasks (25.0 mL), pipettes (1.00 mL, 2.00 mL, 5.00 mL), beakers, wash bottle
2.2 Procedure Part A: Preparation of Calibration Standards Five standard solutions were prepared with known [FeSCN]2+ concentrations by mixing excess Fe3+ with limiting SCN-, ensuring complete conversion to product. The absorbance of each standard was measured at 450 nm to construct a calibration curve.
Part B: Equilibrium Mixtures Five test solutions were prepared with varying initial concentrations of Fe3+ and SCN-. After equilibrium was established (approximately 5 minutes), the absorbance of each solution was measured. The equilibrium concentration of [FeSCN]2+ was determined from the calibration curve, and Keq was calculated using an ICE table approach.
3. Data and Calculations
3.1 Calibration Curve Data Solution [FeSCN2+] (M) Absorbance
1 1.0 × 10-5 0.125 2 2.0 × 10-5 0.251 3 4.0 × 10-5 0.499 4 6.0 × 10-5 0.748 5 8.0 × 10-5 0.998
The calibration curve yielded a linear relationship: A = 12,475[FeSCN2+] with R2 = 0.9998, indicating excellent linearity and adherence to Beer-Lambert law.
3.2 Equilibrium Data and Keq Calculations Solution Initial [Fe3+] Initial [SCN-] Equilibrium [FeSCN2+] Keq (M-1)
1 2.0 × 10-3 2.0 × 10-4 1.50 × 10-4 158
2 4.0 × 10-3 2.0 × 10-4 1.65 × 10-4 238
3 6.0 × 10-3 2.0 × 10-4 1.72 × 10-4 155
4 2.0 × 10-3 4.0 × 10-4 2.80 × 10-4 163
5 2.0 × 10-3 6.0 × 10-4 3.45 × 10-4 152
3.3 Sample Calculation (Solution 1) Given: Initial [Fe3+] = 2.0 × 10-3 M Initial [SCN-] = 2.0 × 10-4 M Measured Absorbance = 1.871 From calibration curve: [FeSCN2+]eq = A / 12,475 = 1.50 × 10-4 M
Fe3+SCN- FeSCN2+
Initial (M) 2.0 × 10-3 2.0 × 10-4 0
Change (M) -1.50 × 10-4 -1.50 × 10-4 +1.50 × 10-4
Equilibrium (M) 1.85 × 10-3 5.0 × 10-5 1.50 × 10-4
Calculation of Keq: Keq = [FeSCN2+] / ([Fe3+][SCN-]) Keq = (1.50 × 10-4) / ((1.85 × 10-3)(5.0 × 10-5)) Keq = 158 M-1
3.4 Statistical Analysis
Parameter Value
Average Keq 173 M-1 Standard Deviation 36 M-1 Relative Standard Deviation 20.8% 95% Confidence Interval 173 ± 39 M-1
4. Results The equilibrium constant values calculated from the five experimental trials ranged from 152
to 238 M-1, with an average value of 173 M-1. The relatively large standard deviation (36 M-1) suggests some variability in the measurements, likely due to factors discussed in the error analysis section.
The calibration curve demonstrated excellent linearity with an R2 value of 0.9998, confirming that the [FeSCN]2+ complex follows Beer-Lambert law over the concentration range studied.
This validates the spectrophotometric method for determining equilibrium concentrations.
Despite variations in initial concentrations of Fe3+ and SCN-, the equilibrium constant remained relatively constant, supporting the fundamental principle that Keq is independent of initial concentrations at constant temperature.
5. Discussion The experimental results successfully demonstrate the principle of chemical equilibrium. The calculated Keq values, averaging 173 M-1, indicate that the formation of [FeSCN]2+ is favored at equilibrium, though not overwhelmingly so. This moderate equilibrium constant is consistent with literature values for this reaction system.
Le Châtelier’s Principle Application: The use of excess Fe3+ in the calibration standards ensured complete conversion of SCN- to [FeSCN]2+, illustrating Le Châtelier’s principle. By shifting the equilibrium position far to the right, we could assume that initial [SCN-] equals equilibrium [FeSCN]2+] for the standards.
Assumptions and Validity: Several assumptions were made in this experiment: (1) the equilibrium is established quickly (within 5 minutes), (2) temperature remains constant, (3) ionic strength effects are negligible due to the acidic medium, and (4) the only significant colored species is [FeSCN]2+. These assumptions appear valid given the consistency of results.
6. Error Analysis Several sources of error may have contributed to the variability in Keq values:
1. Spectrophotometric Measurements: Small errors in absorbance readings (±0.001) can propagate through calculations, especially for low-concentration solutions.
2. Volumetric Errors: Uncertainties in pipetting and dilutions affect the actual concentrations of reactants. A 1% error in volume translates directly to a 1% error in concentration.
3. Incomplete Equilibration: If equilibrium was not fully established before measurement, the measured [FeSCN]2+] would not represent true equilibrium conditions.
4. Temperature Variations: Keq is temperature-dependent. Room temperature fluctuations could cause variations in the equilibrium constant.
5. Side Reactions: Formation of other iron-thiocyanate complexes (e.g., [Fe(SCN)2]+) at higher concentrations could interfere with measurements, though this is minimized by the acidic medium.
Suggested Improvements: Use of thermostated cuvette holders, more precise micropipettes, longer equilibration times, and multiple absorbance measurements per solution would improve precision and accuracy.
7. Conclusion This experiment successfully determined the equilibrium constant for the formation of [FeSCN]2+ complex to be 173 ± 39 M-1. The results validate the fundamental principle that the equilibrium constant remains relatively constant regardless of initial reactant concentrations, provided temperature is held constant.
The spectrophotometric method proved to be an effective technique for analyzing equilibrium systems, with the calibration curve showing excellent linearity (R2 = 0.9998). The moderate value of Keq indicates that while product formation is favored, significant amounts of both reactants and products exist at equilibrium.
The experiment reinforced key concepts in chemical equilibrium including the equilibrium constant expression, Le Châtelier’s principle, and the application of Beer-Lambert law. The observed precision (RSD = 20.8%) is reasonable for undergraduate laboratory work but suggests room for methodological improvements.
8. References 1. Atkins, P., & de Paula, J. (2014). Physical Chemistry: Thermodynamics, Structure, and Change (10th ed.). W.H. Freeman.
2. Harris, D.C. (2015). Quantitative Chemical Analysis (9th ed.). W.H. Freeman.
3. Skoog, D.A., West, D.M., Holler, F.J., & Crouch, S.R. (2013). Fundamentals of Analytical Chemistry (9th ed.). Brooks/Cole.
4. Halpern, A.M., & McBane, G.C. (2006). Experimental Physical Chemistry (3rd ed.). W.H.
Freeman.
5. Ramette, R.W. (1981). Equilibrium Constants from Spectrophotometric Data. Journal of Chemical Education, 58(4), 327-330.
