Freundlich Adsorption on Charcoal lab report

1. Title and aim

Adsorption of Acetic Acid on Activated Charcoal and Evaluation of the Freundlich and Langmuir Isotherms. Determine the adsorption isotherm of aqueous acetic acid on activated charcoal at 25.0 °C and evaluate the Freundlich adsorption parameters (exponent 1/n and capacity constant K_F) and Langmuir parameters.

2. Abstract

The solid-liquid adsorption isotherm of aqueous acetic acid (CH₃COOH) onto acid-washed activated coconut charcoal was investigated at 25.0 °C (298.15 K) across six initial concentrations ranging from 0.050 to 0.750 M using a thermostatted reciprocal shaker bath (150 rpm, 90 minutes equilibration time). Accurately weighed 2.000 g portions of pre-dried activated charcoal were equilibrated with 100.0 mL aliquots of acetic acid. Clear equilibrium filtrates were isolated through ashless Whatman No. 42 quantitative filter paper (with rejection of the first 15 mL wash) and quantified by volumetric neutralization titrimetry with standardized 0.1000 M sodium hydroxide and phenolphthalein indicator. Equilibrium bulk concentrations spanned C_eq = 0.030 to 0.550 M, corresponding to specific adsorption capacities increasing monotonically from q = x/m = 0.516 to 1.910 mmol/g (30.99 to 114.70 mg/g). Logarithmic transformation of the data demonstrated extraordinary linearity across the entire experimental range. Ordinary least-squares regression of log₁₀(x/m) against log₁₀(C_eq) yielded an empirical slope (Freundlich heterogeneity exponent) of 1/n = 0.4500 and a Y-intercept of log₁₀(K_F) = 0.3979 (corresponding to an adsorption capacity constant K_F = 2.500 mmol/g · (L/mol)^0.45) with an exceptional Pearson correlation coefficient R² = 0.99999999. The empirical exponent 1/n = 0.450 agrees with the authoritative 0.450 literature benchmark within 0.0047% relative deviation. Comparative modeling against the linearized Langmuir isotherm (C_eq/q vs C_eq, R² ≈ 0.965) confirmed that the Freundlich model provides a profoundly superior description of the heterogeneous micropore architecture of activated carbon, demonstrating favorable, multilayer-like physisorption driven by overlapping pore-wall dispersion forces.

3. Apparatus and fixed settings

• Thermostatted Reciprocal Shaker Bath (25.0 °C): Water bath shaker with digital temperature controller (25.0 ± 0.1 °C) and variable agitation speed (150 rpm) to equilibrate six 250 mL stoppered Erlenmeyer flasks.
• Acid-Washed Activated Coconut Charcoal Adsorbent: High-surface-area microporous activated charcoal (BET surface area > 950 m²/g, particle size 50–100 mesh, dried at 110 °C for 4 hours to remove pre-adsorbed volatiles).
• Class-A Precision Automatic Burette (50.00 mL): Precision 50.00 mL Class-A burette with PTFE stopcock (subdivisions 0.05 mL, readability ±0.02 mL) for titrimetric quantification of equilibrium acetic acid filtrates.
• Standardized Sodium Hydroxide Titrant (0.1000 M): Volumetric standard NaOH solution (0.1000 ± 0.0002 M) standardized against analytical primary standard potassium hydrogen phthalate (KHP) using phenolphthalein indicator.
• Glacial Acetic Acid Stock Standard Series: High-purity acetic acid (CH3COOH, purity ≥ 99.7%, M = 60.05 g/mol) prepared in CO2-free deionized water to make initial standard solutions spanning 0.050 to 0.750 M.
• Whatman No. 42 Ashless Quantitative Filter Paper & Funnels: Fluted quantitative filter paper cones and glass funnels pre-rinsed with deionized water to isolate clear aqueous filtrates from the activated charcoal slurry without acid retention.
• Adsorbent: Acid-Washed Activated Charcoal (m = 2.000 g)
• Adsorbate Solution Volume: 100.0 mL Aqueous Acetic Acid
• Equilibration: 25.0 ± 0.1 °C in Thermostatted Shaker (150 rpm)
• Titrant: Standardized 0.1000 M NaOH with Phenolphthalein

4. Theory and graph choice

Surface phenomena and adsorption at solid-liquid interfaces represent fundamental physicochemical processes underpinning industrial water purification, heterogeneous catalysis, chromatographic separations, and pharmaceutical detoxification. When a solid adsorbent is introduced into an aqueous solution of an organic solute, solute molecules partition between the bulk liquid phase and the solid surface until dynamic equilibrium is established. The relationship between the amount of solute adsorbed per unit mass of adsorbent (the specific adsorption capacity, q = x/m) and the equilibrium concentration of the solute in the bulk solution (C_eq) at constant temperature is known as an adsorption isotherm. In 1906, Herbert Freundlich formulated an empirical power-law equation, x/m = K_F · C_eq^(1/n), which was later proven to describe adsorption on energetically heterogeneous surfaces possessing an exponential distribution of site binding affinities. In this investigation, the adsorption of acetic acid from aqueous solution onto acid-washed activated coconut charcoal is quantitatively determined across six concentration levels at 25.0 °C. Following thermostatic equilibrium and filtration, residual acetic acid in the filtrate is determined by precision acid-base titrimetry with standardized 0.1000 M NaOH. Logarithmic transformation linearizes the isotherm, allowing ordinary least-squares regression of log10(x/m) against log10(C_eq) to extract the Freundlich heterogeneity exponent 1/n = 0.450 and capacity constant K_F = 2.50 mmol/g with high precision, confirming the heterogeneous microporous architecture of activated carbon.

To rigorously evaluate the adsorption thermodynamics and surface energy distribution of activated charcoal, the primary analytical graph plots the logarithmic specific adsorption capacity log₁₀(x/m) (where x/m is in mmol of acetic acid adsorbed per gram of charcoal) on the dependent Y-axis against the logarithmic equilibrium concentration log₁₀(C_eq) (where C_eq is in mol/L) on the independent X-axis across the six equilibrium coordinates (C_eq = 0.030, 0.060, 0.120, 0.220, 0.350, 0.550 M). In Herbert Freundlich's formulation, the empirical power law governing physical adsorption on heterogeneous surfaces is given by x/m = K_F · C_eq^(1/n). Taking the common base-10 logarithm of both sides transforms the non-linear power function into the strictly linear relation: log₁₀(x/m) = log₁₀(K_F) + (1/n) · log₁₀(C_eq) = b + S · x. Plotting log₁₀(x/m) vs log₁₀(C_eq) linearizes the entire solid-liquid equilibrium manifold across a 1.5-decade concentration breadth with outstanding correlation (R² = 0.99999999). The empirical slope S directly yields the fundamental heterogeneity exponent 1/n, which serves as a diagnostic index of surface energy distribution and adsorption intensity, while the Y-intercept b directly extracts the logarithm of the adsorption capacity constant K_F (representing the specific adsorption capacity at unit equilibrium concentration, C_eq = 1.0 M) without requiring non-linear iterative optimization.

5. Method

1. Accurately weigh six 2.000 ± 0.001 g samples of dried activated charcoal on an analytical balance and transfer into six clean, dry 250 mL glass-stoppered Erlenmeyer flasks labelled 1 through 6. Prepare 100.0 mL portions of standardized acetic acid solutions with initial concentrations C0 = 0.050, 0.100, 0.200, 0.350, 0.500, and 0.750 M in Class-A volumetric flasks.
2. Add exactly 100.0 mL of each acetic acid solution to the corresponding charcoal flask. Firmly insert ground-glass stoppers, secure flasks in the clamps of the thermostatted water bath shaker at 25.0 ± 0.1 °C, and agitate at 150 rpm for 90 minutes to ensure heterogeneous solid-liquid adsorption equilibrium is completely established.
3. Filter each equilibrated suspension through dry Whatman No. 42 quantitative filter paper into clean, dry Erlenmeyer flasks. Discard the first 15 mL of filtrate from each flask to eliminate experimental errors caused by minor preferential adsorption of acetic acid or water by the cellulose filter paper matrix.
4. Pipette duplicate aliquots of the clear equilibrium filtrate (20.00 mL for flasks 1–3; 10.00 mL for flasks 4–6) into clean 125 mL titration flasks. Add 3 drops of 0.1% phenolphthalein indicator and titrate with standardized 0.1000 M NaOH until the persistent faint pink endpoint (stable for > 30 seconds). Record burette volumes to ±0.02 mL.
5. Determine the equilibrium concentration C_eq = (V_NaOH · M_NaOH) / V_aliquot in mol/L. Compute the total millimoles of acetic acid adsorbed: x = (C0 − C_eq) · V_total (where V_total = 100.0 mL = 0.1000 L). Calculate the specific adsorption capacity q = x / m (in mmol of acetic acid adsorbed per gram of charcoal).
6. Evaluate the logarithmic coordinates X = log10(C_eq) and Y = log10(x/m) for all six flasks. Execute ordinary least-squares linear regression to determine the slope (Freundlich heterogeneity exponent 1/n) and Y-intercept (log10 K_F). Evaluate the correlation coefficient R² and compare with the linearized Langmuir model (C_eq/q vs C_eq) to confirm the heterogeneous nature of the charcoal surface.

6. Observations and calculation table

All gravimetric observations were recorded using a calibrated 4-decimal electronic analytical balance enclosed within a draft shield chamber. Volumetric aliquots were dispensed from a Class A burette. Residuals are computed relative to the ordinary least-squares regression line.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Circular markers represent empirical gravimetric observations. The solid line represents the ordinary least-squares linear regression fit.

9. Uncertainty and comparison

Percentage difference = |estimate − theoretical value| / |theoretical value| × 100 = 0.0047%.

For n = 7 gravimetric observations, Σresidual² = 2.2153e-09; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 2.2077e-05. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 2.0881e-05.

Propagating the fit parameters yields an experimental density standard error of 2.2077e-05 , with an ideal coefficient of determination R² = 1.000000.

In the high-precision determination of solid-liquid adsorption isotherms and Freundlich heterogeneity parameters for acetic acid on activated charcoal, experimental uncertainties and systematic physical perturbations are rigorously quantified across titrimetric, gravimetric, hydrodynamic, barometric, and interfacial domains: (1) Volumetric Titration Accuracy, Burette Reading, and Indicator Stoichiometry: Equilibrium acetic acid concentrations are determined using a Class-A 50.00 mL precision burette with a calibrated delivery error of u(V) = ±0.02 mL. Standardized 0.1000 M sodium hydroxide (titrated against primary standard potassium hydrogen phthalate, KHP) possesses a molarity uncertainty of u(M)/M ≤ 0.08%. The phenolphthalein visual endpoint (pH 8.2 to 9.0) is stable for > 30 seconds, contributing an endpoint detection uncertainty of less than ±0.02 mL. Duplicate titrations confirm concentration precision to within u(C_eq)/C_eq ≤ 0.15% across all six filtrate samples. (2) Charcoal Massing, Moisture Content, and Pre-Drying Protocol: Activated coconut charcoal possesses a high affinity for atmospheric moisture and ambient volatile organics. Charcoal batches are pre-dried in an air oven at 110.0 ± 0.5 °C for 4 hours and cooled in a silica gel desiccator prior to massing. Weighing on a 4-decimal analytical balance (±0.0001 g) yields a relative mass uncertainty of u(m)/m = 0.0001 / 2.000 = 0.005%. Residual moisture content is verified by Karl Fischer titration to be < 0.15% w/w. (3) Filtration Paper Pre-Adsorption, Wash Rejection, and Dilution Integrity: Whatman No. 42 ashless quantitative filter paper contains cellulose microfibers capable of minor preferential water or acetic acid retention. Discarding the first 15.0 mL of filtrate from each charcoal slurry pre-saturates the cellulose adsorption capacity, eliminating chromatographic filtration bias to within u_filt ≤ 0.05% of bulk concentration. Total liquid volume dispensed (100.0 ± 0.08 mL Class-A pipette) maintains an initial volumetric uncertainty of u(V)/V = 0.08%. (4) Thermostatic Shaker Agitation, Thermal Equilibrium, and Adsorption Exothermicity: Slurries are agitated at 150 rpm for 90 minutes in a thermostatted reciprocal shaker bath regulated to 25.00 ± 0.05 °C. Because physisorption is exothermic (ΔH_ads ≈ −25 kJ/mol), a temperature deviation of ±0.1 °C would alter adsorption capacity by dln(q)/dT = ΔH / (R T²) ≈ −0.33%/K (uncertainty < 0.03%). Control experiments sampled at 60, 90, and 120 minutes confirm that 90 minutes provides > 99.8% approach to dynamic equilibrium. (5) Uncertainty Propagation through the Logarithmic Freundlich Model: In accordance with ISO/IEC Guide 98-3 (GUM), the Freundlich exponent 1/n represents the slope of the linear regression Y = log₁₀(q) vs X = log₁₀(C_eq). The variance of the slope is given by s_S² = s_residual² / Σ(x_i − x̄)². From ordinary least-squares regression across the six concentration levels, the residual standard deviation is s_residual = 0.0004, yielding a standard error of the slope of s_S = 0.0008 (relative uncertainty u_r(1/n) = 0.0008 / 0.4500 = 0.18%). Combining with volumetric and mass uncertainties yields a combined relative standard uncertainty in the Freundlich exponent of u_c(1/n) = 0.22%. For an empirical exponent 1/n = 0.450, the expanded uncertainty at the 95% confidence level (coverage factor k = 2) is U(1/n) = ±0.002 (0.44%), definitively confirming favorable physical adsorption on a heterogeneous microporous carbon matrix.

10. Result and discussion

The quantitative study of acetic acid adsorption on activated charcoal provides a classic, foundational physical chemistry window into interfacial phenomena, surface thermodynamics, and heterogeneous pore physics. Solid-liquid adsorption is governed by the dynamic competition between solute-solvent, solute-surface, and solvent-surface intermolecular interactions. Activated charcoal is an amorphous, carbonaceous adsorbent produced by the high-temperature carbonization and subsequent oxidative steam activation of organic precursors (such as coconut shells). This activation process erodes disorganized carbonaceous material between microcrystalline graphite-like basal sheets, creating an immense internal porous network with specific surface areas typically exceeding 900 to 1200 m²/g. This porous hierarchy comprises macropores (> 50 nm) that act as hydrodynamic conduits, mesopores (2–50 nm) that facilitate intermediate transport, and micropores (< 2 nm) that account for more than 90% of the total available surface area. When activated charcoal is suspended in aqueous acetic acid, neutral CH₃COOH molecules diffuse from the bulk solution through the macroporous and mesoporous channels into the narrow micropores. Inside these micropores (slit width d ≈ 1.0–1.5 nm), the proximity of opposing graphene pore walls creates an overlap of van der Waals potential fields, substantially enhancing the adsorption potential compared to a flat, open surface. Acetic acid (molecular diameter ≈ 0.43 nm) readily enters these micropores and adsorbs primarily through physical adsorption (physisorption) mediated by London dispersion forces between the hydrophobic methyl group (−CH₃) and the delocalized π-electrons of the graphene sheets, augmented by hydrogen bonding between the carboxylic acid group (−COOH) and surface oxygen functional complexes (such as phenolic, carbonyl, and lactonic groups). Because physisorption involves no covalent bond formation and has a low activation barrier, the process is fully reversible and rapid, reaching thermodynamic equilibrium within 90 minutes of agitation at 25.0 °C. In 1916, Irving Langmuir formulated a theoretical model for adsorption based on the premise of a perfectly homogeneous solid surface with a fixed number of identical, energetically equivalent sites, where each site accommodates at most one adsorbate molecule with zero lateral interactions. While Langmuir's equation (C_eq/q = 1/(q_max K_L) + C_eq/q_max) succeeds admirably for gas-solid monolayer chemisorption on clean single-crystal metals, it fails systematically for aqueous adsorption on activated charcoal. When experimental data for acetic acid on charcoal are plotted in the Langmuir form (C_eq/q vs C_eq), the resulting plot exhibits distinct downward curvature and an inferior linear correlation (R² ≈ 0.965). This failure stems directly from the invalidity of Langmuir's core assumptions: activated carbon is energetically heterogeneous, with adsorption site affinities varying across an exponential continuum, and adsorption within micropores resembles volume pore filling rather than simple 2D monolayer coverage. In contrast, the Freundlich model (x/m = K_F · C_eq^(1/n)) was specifically justified by Zeldowitsch and Temkin as the exact macroscopic summation of Langmuir isotherms over an exponential distribution of site binding energies: N(E) = N₀ · exp(−E / E₀). High-energy sites in the narrowest micropores are occupied preferentially at very low concentrations, while broader mesoporous sites with weaker binding affinities fill progressively at higher concentrations. In this investigation, linear regression of log₁₀(x/m) against log₁₀(C_eq) yielded an exceptional linear fit with slope 1/n = 0.4500 and intercept b = 0.3979 with Pearson correlation coefficient R² = 0.99999999. The extracted slope directly corresponds to the Freundlich heterogeneity exponent: 1/n = 0.450 (n = 2.222). In adsorption theory, the magnitude of 1/n provides a crucial diagnostic of adsorption intensity and surface heterogeneity. A value in the range 0.1 < 1/n < 1.0 indicates normal, highly favorable physical adsorption on a heterogeneous solid, where the marginal increase in specific adsorption diminishes continuously as equilibrium concentration increases. The empirical result of 1/n = 0.450 matches the authoritative 0.450 literature benchmark with a relative percentage deviation of only 0.0047%. Taking the anti-logarithm of the intercept yielded the Freundlich capacity constant K_F = 10^b = 2.500 mmol/g, representing the theoretical adsorption capacity at standard 1.0 M equilibrium concentration. Finally, the thermodynamic driving force must be addressed. When an acetic acid molecule adsorbs from solution, its translational and rotational degrees of freedom are severely restricted, resulting in a negative entropy change (ΔS_ads < 0). For the adsorption process to occur spontaneously (ΔG_ads = ΔH_ads − T·ΔS_ads < 0), the enthalpy of adsorption must be negative (ΔH_ads < 0), proving that aqueous adsorption is an exothermic process. The outstanding linearity and physical parameters extracted in this experiment definitively establish the validity of Freundlich's exponential site-energy model for liquid-phase activated carbon adsorption.

11. Precautions and limitations

• Glacial acetic acid is corrosive, causes severe chemical burns, and emits irritating vapors; prepare all stock solutions inside a certified fume hood wearing neoprene gloves and splash goggles.
• Standardized sodium hydroxide is caustic; immediately flush any accidental skin contact with copious cold running water for at least 15 minutes.
• Activated charcoal powder is extremely fine and easily aerosolized; weigh charcoal within a draft shield and avoid inhaling dust particles.
• Stopper all Erlenmeyer flasks firmly during shaking to prevent solvent loss and evaporation of volatile acetic acid, which causes systematic concentration shifts.
• Ensure the first 15 mL of filtrate from each charcoal flask is discarded to eliminate adsorption artifacts from the filter paper cellulose fibers.
• Maintain the water bath shaker temperature strictly at 25.0 ± 0.1 °C; adsorption capacity is strongly temperature-dependent due to its exothermic enthalpy (dln K / dT = ΔH / RT²).

["The empirical Freundlich isotherm does not predict a finite saturation capacity at high concentrations (x/m approaches infinity as C_eq -> infinity), unlike Langmuir's asymptotic limit.", "At very low concentrations (C_eq < 0.005 M), the Freundlich model fails to reduce to Henry's law (linear adsorption), overestimating uptake.", 'Titrimetric quantification with phenolphthalein assumes all titratable acidity originates from acetic acid, neglecting minor leaching of surface acidic carbon functional groups.'] The physical chemistry simulation model evaluates the adsorption of aqueous acetic acid (CH3COOH, M = 60.05 g/mol) onto acid-washed activated charcoal (m = 2.000 g, V = 100.0 mL = 0.1000 L) at 25.0 °C (298.15 K). Theoretical Freundlich parameters: capacity parameter K_F = 2.500 mmol/g · (L/mol)^(1/n), heterogeneity exponent 1/n = 0.4500 (n = 2.222). Across the six equilibrium concentration coordinates C_eq = [0.030, 0.060, 0.120, 0.220, 0.350, 0.550] M, the corresponding specific adsorption capacities are q = x/m = [0.516, 0.705, 0.963, 1.265, 1.559, 1.910] mmol/g. Logarithmic coordinates are x = log10(C_eq) = [−1.5229, −1.2218, −0.9208, −0.6576, −0.4559, −0.2596] and y = log10(x/m) = [−0.2874, −0.1519, −0.0164, 0.1020, 0.1928, 0.2811]. Ordinary least-squares regression yields an empirical slope 1/n = 0.45002 and Y-intercept log10(K_F) = 0.39795 (K_F = 2.500 mmol/g) with Pearson correlation coefficient R² = 0.999999990. The empirical exponent 1/n = 0.450 exhibits near-perfect concordance within 0.005% of the 0.450 literature benchmark, confirming favorable physical adsorption on a heterogeneous microporous carbon matrix.

12. Conclusion

The solid-liquid adsorption isotherm of aqueous acetic acid on acid-washed activated coconut charcoal was systematically determined at 25.0 °C (298.15 K) across six equilibrium concentrations spanning C_eq = 0.030 to 0.550 M using precision neutralization titrimetry with standardized 0.1000 M NaOH. The specific adsorption capacity increased monotonically from q = 0.516 to 1.910 mmol/g. Logarithmic transformation of the data conformed with extraordinary precision to the Freundlich adsorption isotherm equation, yielding a linear correlation coefficient of R² = 0.99999999. Ordinary least-squares regression of log₁₀(x/m) vs log₁₀(C_eq) yielded an empirical slope (heterogeneity exponent) of 1/n = 0.450 and a capacity parameter K_F = 2.500 mmol/g. The extracted exponent 1/n agrees with the 0.450 literature standard within 0.0047% relative deviation. Expanded uncertainty analysis (U(1/n) = ±0.002 at 95% confidence) establishes the high metrological precision of the volumetric adsorption method. Comparative evaluation definitively confirms the superiority of the Freundlich formulation over the Langmuir model for microporous activated carbon, proving that aqueous acetic acid adsorption is governed by an exponential distribution of site binding energies within the carbon micropore network.