Determine the thermodynamic acid dissociation constant (pKa) and standard Gibbs free energy of ionization of Bromothymol Blue indicator by precision spectrophotometric absorbance measurements at 616 nm across buffered solutions from pH 6.20 to 7.70 at 25.0 °C. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
Ready to dispense 7.1 pH of liquid.
Adjust pH V, then weigh the dispensed aliquot.
Mass observations are determined by the high-precision thermodynamic equation of state for pure liquid water. Readings reflect thermal equilibrium and analytical balance force restoration.
["Spectrophotometric pKa determination assumes strict adherence to Beer-Lambert's law and ideal two-state chemical equilibrium.", 'Total indicator concentration must remain in the range 10⁻⁵ to 10⁻⁴ M to prevent self-buffering and dye dimerization.', 'Secondary ionic strength variations modulate activity coefficients; constant ionic strength (I = 0.100 M) is required to maintain constant apparent pKa.'] The spectrophotometric model evaluates Bromothymol Blue (BTB) at λ = 616 nm across six buffer solutions from pH 6.20 to 7.70 at 25.00 °C. The limiting absorbances are A_acid = 0.040 AU (in 0.10 M HCl) and A_base = 0.960 AU (in 0.10 M NaOH). At intermediate pH, the speciation ratio is [In⁻]/[HIn] = (A - A_acid)/(A_base - A) = 10^(pH - 7.100). The measured absorbances are [0.143, 0.225, 0.347, 0.500, 0.653, 0.775] AU, corresponding to log ratios [-0.899, -0.599, -0.300, 0.000, 0.300, 0.599]. Linear least-squares regression yields an empirical slope m = 1.00124 (unitless) and Y-intercept b = pKa = 7.10002 with R² = 0.9999997, isolating an experimental pKa = 7.100 ± 0.005 and Ka = 7.94 × 10⁻⁸ M (difference = 0.0003% from literature benchmark 7.100), with standard Gibbs free energy of dissociation ΔG° = +40.53 kJ·mol⁻¹.
High-precision split-beam optical spectrophotometer with deuterium and tungsten-halogen lamps, blazed holographic grating monochromator, and matched photodiode detectors for measuring absorbance (A = -log₁₀ T) from 190 to 900 nm with photometric accuracy ±0.002 AU.
Pair of precision optical quartz cuvettes with certified 10.00 ± 0.01 mm internal optical path length and optical transmission matching within ±0.001 AU across the entire visible spectrum.
High-impedance research-grade pH meter with combined glass-reference electrode calibrated against standard IUPAC buffers (pH 4.01, 7.00, and 10.01) with readability ±0.01 pH units and integrated temperature probe.
Circulating constant-temperature water bath with external jacketed cuvette holder maintaining the sample cell at 25.00 ± 0.02 °C to eliminate thermal shifting of the acid-base equilibrium.
P1000 and P100 micropipettes (calibrated to ISO 8655) and Class A 50.00 mL volumetric flasks used for preparing precision buffer dilutions and dispensing exact indicator aliquots.
Four-decimal analytical balance (readability ±0.0001 g) used to weigh anhydrous sodium dihydrogen phosphate (NaH₂PO₄) and disodium hydrogen phosphate (Na₂HPO₄) for buffer synthesis.
Determine the thermodynamic acid dissociation constant (pKa) and standard Gibbs free energy of ionization of Bromothymol Blue indicator by precision spectrophotometric absorbance measurements at 616 nm across buffered solutions from pH 6.20 to 7.70 at 25.0 °C. Suggested independent volumetric settings: 6.2, 6.5, 6.8, 7.1, 7.4, 7.7 pH.
Power on the dual-beam UV-Vis spectrophotometer and allow deuterium/tungsten lamp sources to warm up for 30 minutes to achieve photometric baseline stability. Set the monochromator to 616.0 nm with a 1.0 nm spectral bandwidth. Verify wavelength calibration using the 656.1 nm deuterium emission line.
Prepare strongly acidic (0.10 M HCl) and strongly alkaline (0.10 M NaOH) standard solutions containing identical total indicator concentration (4.00 × 10⁻⁵ M BTB). Measure the limiting absorbance of pure protonated yellow acid (A_acid = 0.040 AU at pH 1.0) and pure deprotonated blue base (A_base = 0.960 AU at pH 12.0) at 616.0 nm against a deionized water blank.
Formulate a series of six 0.100 M phosphate buffer solutions spanning the pH transition range (pH 6.20, 6.50, 6.80, 7.10, 7.40, and 7.70). Calibrate the combined glass electrode with certified pH 4.01 and 7.00 buffers at 25.00 °C. Measure and record the exact equilibrium pH of each buffer solution to ±0.01 pH units.
Transfer exactly 2.00 mL of 1.00 × 10⁻³ M stock Bromothymol Blue into each 50.00 mL volumetric flask, dilute to the mark with the respective phosphate buffer, and invert twenty times to ensure thorough homogenization. Place the flasks in the 25.00 °C water bath for 15 minutes to establish complete thermodynamic equilibrium.
Rinse the sample quartz cuvette twice with the buffered indicator solution, then fill to 80% capacity. Wipe the exterior optical windows with lint-free lens paper, inspect for microbubbles or dust, and insert into the sample beam holder. Insert the matched buffer blank into the reference beam and record the steady-state absorbance A₆₁₆ to three decimal places.
Repeat the spectrophotometric measurement across all six buffered indicator solutions in ascending order of pH. Compute the ionization ratio [In⁻]/[HIn] = (A - A_acid)/(A_base - A) and its logarithm for each solution. Perform ordinary least-squares regression of pH versus log([In⁻]/[HIn]) to extract the acid dissociation constant pKa from the intercept and verify theoretical unity slope.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
| # | Buffer Solution pH (pH) | Absorbance at 616 nm (A₆₁₆) (AU) | log([In⁻]/[HIn]) | Buffer Solution pH | Remove |
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