Lab: Determining an Equilibrium Constant by Spectrophotometry

Prepare standards with known concentrations, a suitable reagent blank and the same wavelength and cuvette path length used for the samples. Plot absorbance A vertically against concentration c horizontally and fit A = mc + b. Ideally b is near zero after correct blanking, but a measured intercept should not be discarded without justification. Use c = (A − b)/m; c = A/m is the special zero-intercept case. A has no units, so slope m has units L/mol when c is in mol/L.

Check that samples lie within the validated calibration range and that the standards' chemical matrix supports the same absorbing species and absorptivity. In FeSCN²⁺ standards, a large excess of Fe³⁺ is often used to convert nearly all limiting SCN⁻ to complex; that assumption must be valid before assigning standard complex concentrations. The equilibrium samples use finite amounts of both reagents instead.

The measured [FeSCN2+] is the x of the ICE table. Subtract it from the initial concentrations of Fe³⁺ and SCN⁻ to get their equilibrium values, then substitute all three into the K expression. Remember that mixing the two stock solutions dilutes both, so the initial concentrations must be corrected with M₁V₁ = M₂V₂ before the table is written.

For a fitted A = (4500 L/mol)c + 0.020 and sample A = 0.380, c = 8.00 × 10⁻⁵ M. If the post-mixing initial [Fe³⁺] and [SCN⁻] are 1.00 × 10⁻³ and 2.00 × 10⁻⁴ M with no initial complex, the equilibrium values are 9.20 × 10⁻⁴, 1.20 × 10⁻⁴ and 8.00 × 10⁻⁵ M. Therefore K_c = (8.00 × 10⁻⁵)/[(9.20 × 10⁻⁴)(1.20 × 10⁻⁴)] ≈ 725 in the stated concentration convention. The measured complex concentration cannot exceed either initial limiting reactant concentration; such a result flags dilution, blanking or calibration inconsistency.

A dirty cuvette, bubbles, poor blanking, instrument noise and chemical changes can alter absorbance. Use the range demonstrated by the calibration and instrument specifications; A above 1 is not automatically invalid. Stray light at high absorbance often causes negative deviations, but neither the threshold nor the error direction is universal. If a sample lies outside the validated range, use a shorter path length or an appropriately validated measurement strategy. Diluting an equilibrium mixture may change its composition, so do not recover its original complex concentration by a dilution factor unless negligible shifting is justified. Keep standards and samples at the same temperature because K and absorptivity may vary with temperature.

An added positive absorbance error in the unknown alone, with a valid calibration held fixed, overestimates complex concentration x. In this simple one-complex ICE model, it raises the numerator and lowers both reactant terms, making the calculated K too high. An offset shared identically by standards and unknown can instead be absorbed in the fitted intercept, so “forgot to blank” has no universal effect without knowing the fitting procedure. Distinguish a slope error from an intercept error and avoid subtracting the same background twice.

Keep temperature, acidity and ionic medium controlled, allow time for equilibration, wipe the cuvette and avoid bubbles. Fe³⁺ background absorption and additional complexes can matter, so selective measurement is an experimental approximation rather than a guarantee that reactants absorb no light. Small measuring light levels ordinarily avoid materially consuming sample; intense illumination or heating can disturb some systems.