Thermostatically Controlled Orbital Shaker Incubator
Agitates batch equilibrium flasks at 150 RPM and constant temperature 25.0 ± 0.1 °C for 24 hours.
Chemical & Process Engineering / Activated Carbon Adsorption Isotherm
FREE TO EXPLORELABORATORY 22 · CHEMICAL & PROCESS ENGINEERING
Aqueous Adsorption Isotherms on Granular Activated Carbon & Langmuir Monolayer Modeling
Determine equilibrium adsorption isotherms of aqueous organic acid onto granular activated carbon (GAC), fit the Langmuir and Freundlich models to experimental data, and evaluate monolayer capacity q_max and affinity constant K_L. Explore interactive transport phenomena, unit operations simulation, and chemical engineering telemetry.
TRANSPORT PHENOMENA · UNIT OPERATIONS · PROCESS CONTROL · REACTION ENGINEERING
Your virtual chemical and process engineering laboratory.
LANGMUIR RATIO C_E / Q_E—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Equil Conc C_e = 6.0 mmol/L.
Adjust Equil Conc C_e, then execute chemical process trial.
Chemical and process engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity transport phenomena and unit operations modeling.
Process engineering assumptions and boundary condition limits
The transport and thermodynamic models apply within the specified calibrated operating window (2.0 to 12.0 mmol/L). Evaluated using bituminous coal-based GAC (12×40 mesh, specific area 950 m^2/g) adsorbing acetic acid at 25.0 °C. Linear regression models C_e / q_e versus C_e to extract slope S = 0.4500 g/mmol and intercept B = 0.2200 g/L (K_L = 2.045 L/mmol).
Process apparatus & industrial sensors.
Calibrated Granular Activated Carbon (GAC)
Bituminous coal GAC (12×40 mesh, surface area 950 m^2/g) dried at 110 °C before weighing.
Automatic Digital Potentiometric Titrator
Titrates equilibrium solution aliquots against standardized 0.050 M NaOH to 0.005 mL precision.
Precision Analytical Balance (0.1 mg accuracy)
Accurately weighs dry GAC adsorbent aliquots (m = 1.0000 g ± 0.0002 g).
High-Recovery 0.45 μm PTFE Syringe Filters
Rapidly filters carbon fines from equilibrium solution without adsorbing dissolved organic acid.
Borosilicate Glass Erlenmeyer Flasks with PTFE Stoppers
250 mL batch reactors providing sealed, non-adsorptive containers for equilibrium testing.
FOLLOW THE METHOD
A reason behind every step.
Determine equilibrium adsorption isotherms of aqueous organic acid onto granular activated carbon (GAC), fit the Langmuir and Freundlich models to experimental data, and evaluate monolayer capacity q_max and affinity constant K_L. Standardized parameter settings: 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 mmol/L.
01
GAC Activation & Weighing
Dry bituminous GAC in an oven at 110 °C for 2 hours; cool in a desiccator, and weigh exactly 1.000 g into each of six 250 mL flasks.
02
Initial Standard Solution Dosing
Prepare six acetic acid solutions of known initial concentrations C_0 (5 to 40 mmol/L); add exactly 100.0 mL of solution to each respective flask.
03
Orbital Shaker Incubation
Seal flasks with PTFE stoppers, mount on the orbital shaker at 25.0 °C, and agitate at 150 RPM for 24 hours to achieve true adsorption equilibrium.
04
Phase Separation & Filtration
Withdraw 15 mL aliquots from each flask and filter through 0.45 μm PTFE syringe filters to remove all suspended carbon particles.
05
Equilibrium Concentration Titration
Titrate 10.0 mL of filtered solution against standardized 0.050 M NaOH to determine equilibrium concentration C_e.
06
Langmuir Isotherm Regression Analysis
Calculate equilibrium loading q_e = (C_0 - C_e) V / m, compute C_e / q_e, plot C_e / q_e versus C_e, and fit a linear regression to evaluate q_max and K_L.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Activated Carbon Adsorption Isotherm mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
C_e / q_e = S · C_e + B = 0.4500 · C_e + 0.2200
| # | Equilibrium Concentration C_e (mmol/L) | Langmuir Ratio C_e / q_e (g/L) | Equilibrium liquid concentration C_e (mmol/L) | Langmuir linearized ratio C_e / q_e (g/L) | Remove |
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CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
In the Langmuir adsorption isotherm, the plateau at high equilibrium concentrations represents:
If the Langmuir separation factor R_L = 1 / (1 + K_L C_0) is between 0 and 1, the adsorption is classified as:
In the linearized Langmuir equation C_e / q_e = (1 / q_max) C_e + 1 / (K_L q_max), the maximum monolayer capacity q_max is obtained from:
Adsorption of organic molecules from liquid solutions onto activated carbon is generally:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
Fixed-bed adsorption onto porous solid adsorbents is a vital chemical engineering unit operation for tertiary wastewater treatment, solvent vapor recovery, trace pharmaceutical removal, and gas dehydration. Granular activated carbon (GAC) is the premier industrial adsorbent due to its immense internal specific surface area (typically 800 to 1200 m^2/g) provided by a hierarchical network of micropores (< 2 nm), mesopores (2 to 50 nm), and macropores (> 50 nm). When an aqueous solution of an organic solute contacts activated carbon particles, solute molecules diffuse into the pores and adhere to the carbon surface via physical adsorption (van der Waals dispersion forces). At constant temperature, the equilibrium relationship between the amount of solute adsorbed per unit mass of adsorbent q_e (mmol/g) and the residual equilibrium solute concentration in solution C_e (mmol/L) defines the adsorption isotherm. Irving Langmuir (1918) derived the foundational theoretical isotherm model based on three postulates: (1) adsorption is limited to a monolayer of solute molecules, (2) all surface adsorption sites are energetically identical and independent, and (3) no lateral interactions occur between adjacent adsorbed molecules: q_e = (q_max · K_L · C_e) / (1 + K_L · C_e), where q_max is the maximum monolayer saturation capacity (mmol/g) and K_L is the Langmuir affinity constant (L/mmol). Linearizing the Langmuir model yields: C_e / q_e = (1 / q_max) · C_e + 1 / (K_L · q_max) = S · C_e + B. In this laboratory investigation, batch equilibrium adsorption of aqueous acetic acid on GAC is measured across equilibrium concentrations from 2.0 to 12.0 mmol/L to determine slope S = 1 / q_max = 0.4500 g/mmol (q_max = 2.222 mmol/g) and evaluate adsorption thermodynamics.
C_e / q_e = S · C_e + B = 0.4500 · C_e + 0.2200
Evaluated using bituminous coal-based GAC (12×40 mesh, specific area 950 m^2/g) adsorbing acetic acid at 25.0 °C. Linear regression models C_e / q_e versus C_e to extract slope S = 0.4500 g/mmol and intercept B = 0.2200 g/L (K_L = 2.045 L/mmol).