Determine the surface tension of aqueous 1-butanol solutions, evaluate the maximum surface excess concentration Γ_max using the Gibbs adsorption equation, and calculate the minimum surface area occupied per molecule A_min at the air-water interface. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
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Adjust C 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.
['The linear logarithmic model applies strictly to the saturated monolayer regime (C > 0.05 M); at very low concentrations, surface tension approaches pure water non-linearly (Szyszkowski curvature).', 'Harkins-Brown correction factors are derived for static or quasi-static drop detachment; dynamic surface tension effects may introduce minor deviations if drop formation is too rapid (< 2 s).', 'The activity coefficient of 1-butanol is approximated as unity (a ≈ C); at the highest concentration (0.80 M), non-ideal solute-solute interactions in the bulk introduce a minor systematic deviation of ~1.5%.'] The physical chemistry simulation model evaluates aqueous solutions of 1-butanol (CH3(CH2)3OH, M = 74.12 g/mol) at 25.00 °C (298.15 K). Thermodynamic parameters: universal gas constant R = 8.31446 J/(mol·K), R·T = 2478.96 J/mol = 0.00247896 N·m/μmol. Reference surface tension of pure water: γ₀ = 71.97 mN/m. Capillary tip radius: r = 3.500 mm. Saturated monolayer parameters: theoretical maximum surface excess Γ_max = 5.500 μmol/m² (5.500 × 10⁻⁶ mol/m²), theoretical slope dγ/dln C = −R·T·Γ_max = −13.634 mN/m. Across the six concentration coordinates C = [0.050, 0.100, 0.200, 0.350, 0.500, 0.800] M, the natural logarithms are x = ln(C) = [−2.9957, −2.3026, −1.6094, −1.0498, −0.6931, −0.2231] and the measured surface tensions are y = γ = [64.30, 54.85, 45.40, 37.77, 32.91, 26.50] mN/m. Ordinary least-squares regression yields an empirical slope S = −13.6330 mN/m and intercept b = 23.4591 mN/m with Pearson correlation coefficient R² = 0.999999995. Applying the Gibbs adsorption equation extracts an empirical maximum surface excess Γ_max = −(S · 10⁻³ / RT) · 10⁶ = 5.4995 μmol/m² (relative difference = 0.009% from the 5.50 μmol/m² literature benchmark). From Γ_max, the minimum cross-sectional area per molecule is calculated as A_min = 10²⁰ / (N_A · Γ_max) = 30.19 Ų/molecule, confirming a close-packed monolayer of vertically oriented 1-butanol molecules at the air-water interface.
Precision-bore borosilicate glass stalagmometer with an optically flat ground capillary tip (radius r = 3.500 ± 0.005 mm) and two etched fiducial volume marks (V = 5.000 ± 0.005 mL) for drop-weight and drop-volume surface tensiometry.
Double-walled glass circulating water jacket connected to an external constant-temperature circulator regulating stalagmometer liquid to 25.00 ± 0.05 °C.
High-sensitivity electronic balance (readability ±0.01 mg) with light-weight, ground-glass weighing bottles to record dropped liquid masses with negligible evaporation.
Anhydrous 1-butanol (CH3(CH2)3OH, purity ≥ 99.8%, M = 74.12 g/mol, bp = 117.7 °C, density ρ = 0.8098 g/cm³), fractionally distilled to ensure absence of surface-active homologue impurities.
Degassed ultra-pure water (resistivity ≥ 18.2 MΩ·cm at 25 °C, surface tension γ0 = 71.97 mN/m, TOC < 3 ppb) used as the surface tension reference calibrant.
Specialized oxidizing acid bath and ultrasonic cleaning tank to strip all organic, lipid, and surfactant residue from the glass capillary bore and drop-forming tip.
Determine the surface tension of aqueous 1-butanol solutions, evaluate the maximum surface excess concentration Γ_max using the Gibbs adsorption equation, and calculate the minimum surface area occupied per molecule A_min at the air-water interface. Suggested independent volumetric settings: 0.05, 0.1, 0.2, 0.35, 0.5, 0.8 M.
Clean the stalagmometer with hot chromic-sulfuric acid cleaning solution, rinse thoroughly with ten volumes of deionized water, and dry with filtered nitrogen. Mount the stalagmometer inside the 25.00 ± 0.05 °C water jacket. Draw degassed pure water above the upper mark, adjust the needle valve to deliver 15–20 drops/min, and count the number of drops (n0) and total mass (m0) required to empty the 5.000 mL volume.
Prepare six aqueous 1-butanol solutions with concentrations C = 0.050, 0.100, 0.200, 0.350, 0.500, and 0.800 M (mol/L) in 100.0 mL Class-A volumetric flasks using degassed Milli-Q water. Stopper flasks tightly and allow them to thermally equilibrate in a 25.0 °C water bath for 30 minutes.
Rinse the stalagmometer capillary twice with the 0.050 M butanol solution. Draw solution above the top graduation, control detachment rate to 1 drop every 3–4 seconds to prevent kinetic neck snapping, and collect falling drops into a tared, ground-glass weighing bottle across the 5.000 mL graduation window. Record the drop count n and net mass m to ±0.1 mg. Repeat in triplicate.
Repeat the drop-weight procedure sequentially for all remaining solutions: C = 0.100, 0.200, 0.350, 0.500, and 0.800 M. Ensure the stalagmometer tip is inspected between runs to confirm optical cleanliness and the complete absence of wetting pinning artifacts.
Compute the average single-drop volume V_drop = V / n. Look up the Harkins-Brown correction factor Φ(r / V_drop^(1/3)) corresponding to the tip radius r = 3.500 mm. Calculate the true surface tension γ = (m_drop · g / (2π r)) · Φ in mN/m (equivalent to dyn/cm) for each concentration.
Evaluate the natural logarithm of concentration x = ln(C) for all six solutions. Plot surface tension γ against ln(C) and execute ordinary least-squares linear regression to determine the slope S = dγ/d(ln C). Apply the Gibbs equation to compute the maximum surface excess concentration Γ_max = −(1 / RT) · (dγ/d(ln C)) in μmol/m² and the minimum surface area per molecule A_min = 1 / (N_A · Γ_max) in Ų/molecule, evaluating agreement with the 5.50 μmol/m² benchmark.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
| # | 1-Butanol Concentration C (M) | Surface Tension γ (mN/m) | Natural Logarithm of Concentration ln(C) | Surface Tension γ (mN/m) | Remove |
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