Measuring K in the Lab

Only ${\text{FeSCN}}^{2+}$ is strongly coloured, so the colour intensity measures its concentration. A colorimeter or spectrophotometer shines light of the wavelength the complex absorbs most (blue light, about 450 to 470 nm) through a cuvette and reports absorbance, A. Beer's law states that $A=\epsilon bc$, where $\epsilon$ is the molar absorptivity (a constant for that substance and wavelength, in L/(mol·cm)), b is the path length (usually 1.00 cm) and c is the concentration. To find $\epsilon b$, you make standards in which $[{\text{FeSCN}}^{2+}]$ is known. The trick is Le Chatelier's principle: mix a small, known amount of ${\text{SCN}}^{-}$ with a large excess of ${\text{Fe}}^{3+}$, so the equilibrium is pushed so far right that essentially all the thiocyanate becomes ${\text{FeSCN}}^{2+}$. A graph of absorbance against concentration for the standards is a straight line through the origin, the calibration curve, whose slope is $\epsilon b$. Then you prepare test mixtures with similar amounts of both ions, measure their absorbance, read $[{\text{FeSCN}}^{2+}]$ at equilibrium from the calibration line, and use an ICE table to find the other two concentrations. If several mixtures with different starting amounts all give about the same K, you have evidence for the equilibrium law itself.

Stir excess solid calcium hydroxide in distilled water at a recorded temperature until the solution is saturated, then filter it so that no undissolved solid reaches the flask, since any solid would neutralize extra acid. Pipette 25.00 mL of the clear filtrate and titrate it with standardized HCl using phenolphthalein or bromothymol blue. At the endpoint, moles of HCl equal moles of ${\text{OH}}^{-}$, which gives $[{\text{OH}}^{-}]$. Each formula unit releases one ${\text{Ca}}^{2+}$ and two ${\text{OH}}^{-}$, so $[{\text{Ca}}^{2+}]=\frac{1}{2}[{\text{OH}}^{-}]$ and $K_{sp}=[{\text{Ca}}^{2+}][{\text{OH}}^{-}{]}^2$. Keep the solutions covered: carbon dioxide from the air reacts with hydroxide to form calcium carbonate, lowering $[{\text{OH}}^{-}]$. Accepted values are about $5\times 10^{-6}$ at 25 °C.

Calibrate a pH meter with buffers of known pH, then measure the pH of an acetic acid solution of known concentration, for example 0.100 mol/L. The pH gives $[{\text{H}}_3{\text{O}}^{+}]=10^{-\text{pH}}$, which equals $[{\text{CH}}_3{\text{COO}}^{-}]$ at equilibrium, and the acid that remains is the initial concentration minus that amount. Substituting into $K_a=\frac{[{\text{H}}_3{\text{O}}^{+}][{\text{CH}}_3{\text{COO}}^{-}]}{[{\text{CH}}_3\text{COOH}]}$ gives Ka. Notice the significant figures: a pH reported to two decimal places gives $[{\text{H}}_3{\text{O}}^{+}]$ to only two significant figures. A second method uses a titration curve: at the half-equivalence point, half the acid has become its conjugate base, so $[\text{HA}]=[{\text{A}}^{-}]$ and $\text{pH}=\text{p}{K}_a$.

• Fingerprints, scratches or bubbles on a cuvette scatter light, so A reads high, $[{\text{FeSCN}}^{2+}]$ is overestimated and K comes out too high. Handle cuvettes by the frosted sides.
• Incomplete conversion in the standards: if some ${\text{SCN}}^{-}$ stays unreacted, the true $[{\text{FeSCN}}^{2+}]$ is lower than assumed, so the slope ($\epsilon b$) is too small and every later concentration too large.
• Undissolved solid in the Ca(OH)₂ filtrate neutralizes extra acid, so $[{\text{OH}}^{-}]$ and Ksp are too high; absorbed ${\text{CO}}_2$ makes them too low.
• An uncalibrated pH meter shifts every reading; an error of only 0.05 pH units changes $[{\text{H}}_3{\text{O}}^{+}]$ by about 12%.
• Temperature drift changes K itself, so record the temperature and compare with accepted values at that temperature.
• Report percent error against an accepted value and look for systematic errors (all results high or all low) as well as random scatter between trials.