Experiment 34 An Equilibrium Constant Lab Report

Experiment34 an equilibrium constant lab report is a classic introductory chemistry exercise that guides students through the determination of an equilibrium constant (Kc) for a reversible reaction using spectrophotometric measurements. By preparing a series of mixtures with known initial concentrations, measuring the absorbance of the colored product at equilibrium, and applying the Beer‑Lambert law, learners can calculate the concentrations of all species at equilibrium and evaluate Kc. This hands‑on experience reinforces concepts of chemical equilibrium, Le Chatelier’s principle, and quantitative analysis while developing essential laboratory skills such as solution preparation, calibration curve construction, and error propagation.

Overview of Experiment 34: Determining the Equilibrium Constant

The primary goal of this experiment is to obtain a reliable value for the equilibrium constant of the reaction

[ \mathrm{Fe^{3+}(aq) + SCN^{-}(aq) \rightleftharpoons FeSCN^{2+}(aq)} ]

which forms a deep‑red complex ion whose absorbance can be measured at approximately 470 nm. Because the intensity of the color is directly proportional to the concentration of (\mathrm{FeSCN^{2+}}), spectrophotometry provides a convenient, non‑invasive method to track the position of equilibrium.

Purpose and Objectives

• Understand how macroscopic properties (color intensity) relate to molecular concentrations at equilibrium.
• Apply the Beer‑Lambert law ((A = \varepsilon b c)) to convert absorbance readings into concentrations.
• Calculate the equilibrium constant (K_c = \frac{[\mathrm{FeSCN^{2+}}]}{[\mathrm{Fe^{3+}}][\mathrm{SCN^{-}}]}) from experimental data.
• Evaluate sources of experimental error and discuss their impact on the calculated (K_c).
• Develop proficiency in preparing dilute solutions, using a spectrophotometer, and performing systematic data analysis.

Materials and Reagents

Note: All glassware should be rinsed with distilled water and, if possible, with the solution to be measured to avoid contamination.

Procedure (Step‑by‑Step)

1. Preparation of Solutions

1. Label six volumetric flasks (10 mL) as Tube 1–6.
2. Pipette the following volumes of 0.00200 M (\mathrm{Fe^{3+}}) stock into each tube:

3. Add the complementary volume of 0.00200 M (\mathrm{SCN^{-}}) stock so that the total volume of each mixture reaches 5.00 mL (e.g., Tube 1 receives 4.50 mL (\mathrm{SCN^{-}})).
4. Dilute each mixture to the 10 mL mark with distilled water, cap, and invert several times to ensure uniform mixing.
5. Allow the solutions to stand for at least 5 minutes to reach equilibrium (the reaction is fast, but a short wait guarantees reproducibility).

2. Measurement of Absorbance

1. Turn on the spectrophotometer and set the wavelength to 470 nm.
2. Blank the instrument with a cuvette filled with distilled water (or the solvent used).
3. Rinse a clean cuvette with a small amount of the sample, fill it, and record the absorbance.
4. Repeat the measurement for each tube, recording the average of two readings if variability exceeds 0.005 AU.

3. Calculation of Concentrations

1. Construct a calibration curve using a series of known (\mathrm{FeSCN^{2+}}) standards (optional but recommended). Plot absorbance versus concentration; the slope equals (\varepsilon b).
2. Apply Beer‑Lambert law:

[ [\mathrm{FeSCN^{2+}}] = \frac{A}{\varepsilon b} ]

If a calibration curve is not prepared, use the literature value (\varepsilon = 4.70 \times 10^{3}\ \mathrm{L,mol^{-1},cm^{-1}}) for the (\mathrm{FeSCN^{2+}}) complex at

Ifa calibration curve is not prepared, use the literature value (\varepsilon = 4.70 \times 10^{3}\ \mathrm{L,mol^{-1},cm^{-1}}) for the (\mathrm{FeSCN^{2+}}) complex at 470 nm. With a 1 cm path length ((b = 1.00\ \mathrm{cm})), the concentration of the colored complex in each tube follows directly from the measured absorbance:

[ [\mathrm{FeSCN^{2+}}]_i = \frac{A_i}{\varepsilon b} = \frac{A_i}{(4.70 \times 10^{3}\ \mathrm{L,mol^{-1},cm^{-1}})(1.00\ \mathrm{cm})} = 2.13 \times 10^{-4},A_i\ \mathrm{mol,L^{-1}} . ]

Step 1 – Determine the initial concentrations of reactants.
Because each tube was diluted to a final volume of 10.00 mL, the initial (pre‑equilibrium) concentrations of (\mathrm{Fe^{3+}}) and (\mathrm{SCN^{-}}) are obtained from the volumes of the 0.00200 M stocks added:

[ [\mathrm{Fe^{3+}}]0 = \frac{V{\mathrm{Fe}}, (0.00200\ \mathrm{M})}{10.00\ \mathrm{mL}},\qquad [\mathrm{SCN^{-}}]0 = \frac{V{\mathrm{SCN}}, (0.00200\ \mathrm{M})}{10.00\ \mathrm{mL}} . ]

For example, in Tube 3 ((V_{\mathrm{Fe}} = 1.00\ \mathrm{mL}), (V_{\mathrm{SCN}} = 4.00\ \mathrm{mL})):

[ [\mathrm{Fe^{3+}}]_0 = \frac{1.00 \times 0.00200}{10.00}=2.00 \times 10^{-4}\ \mathrm{M}, ] [ [\mathrm{SCN^{-}}]_0 = \frac{4.00 \times 0.00200}{10.00}=8.00 \times 10^{-4}\ \mathrm{M}. ]

Step 2 – Calculate equilibrium concentrations.
At equilibrium a fraction of each reactant is converted to (\mathrm{FeSCN^{2+}}). Assuming 1:1 stoichiometry,

[ [\mathrm{Fe^{3+}}]{\mathrm{eq}} = [\mathrm{Fe^{3+}}]0 - [\mathrm{FeSCN^{2+}}]{\mathrm{eq}}, ] [ [\mathrm{SCN^{-}}]{\mathrm{eq}} = [\mathrm{SCN^{-}}]0 - [\mathrm{FeSCN^{2+}}]{\mathrm{eq}} . ]

Using the absorbance‑derived ([\mathrm{FeSCN^{2+}}]_{\mathrm{eq}}) from Step 1 yields the equilibrium concentrations for each tube.

Step 3 – Compute the equilibrium constant (K_c).
The formation constant for the complex is

[ K_c = \frac{[\mathrm{FeSCN^{2+}}]{\mathrm{eq}}} {[\mathrm{Fe^{3+}}]{\mathrm{eq}},[\mathrm{SCN^{-}}]_{\mathrm{eq}}}. ]

Carrying out the calculation for Tube 3 (illustrative numbers): suppose the measured absorbance is (A_3 = 0.312). Then[ [\mathrm{FeSCN^{2+}}]_{\mathrm{eq}} = 2.13 \times 10^{-4} \times 0.312 = 6.65 \times 10^{-5}\ \mathrm{M}. ]

Hence

[ [\mathrm{Fe^{3+}}]_{\mathrm{eq}} = 2.00 \times 10^{-4} - 6.65 \times 10^{-5} = 1.34 \times 10^{-4}\ \mathrm