Power-Compensation Isothermal Titration Calorimeter (ITC)
Maintains sample cell at 25.0000 °C using active thermoelectric feedback, measuring heat pulses down to 0.1 μJ.
Chemical & Process Engineering / Excess Enthalpy of Mixing ITC
FREE TO EXPLORELABORATORY 38 · CHEMICAL & PROCESS ENGINEERING
Excess Enthalpy of Mixing (H^E) & Heat of Solution via Isothermal Titration Calorimetry (ITC)
Operate a power-compensation isothermal titration calorimeter (ITC) at 25.000 °C to measure the heat of mixing during incremental microliter injections of ethanol into water across composition factors x_1·(1 - x_1) from 0.05 to 0.25, evaluate the molar excess enthalpy H^E, and determine the Redlich–Kister excess enthalpy parameter A_0. 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.
MEASURED MOLAR EXCESS ENTHALPY H^E—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Composition Factor x_1·x_2 = 0.13 dimensionless.
Adjust Composition Factor x_1·x_2, 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 (0.05 to 0.25 dimensionless). Evaluated using a MicroCal PEAQ-ITC power-compensation isothermal titration calorimeter with 1.40 mL Hastelloy cell, 250 μL injection syringe, and active Peltier feedback control (±0.0001 °C). Calibrated against standard water-water dilution blank and 2-propanol/water heat-of-mixing standards.
Process apparatus & industrial sensors.
Coin-Shaped 1.40 mL Hastelloy Sample & Reference Cells
Resists chemical corrosion and provides rapid thermal equilibration with surrounding heat sink.
Precision 250 μL Automated Injection Syringe with Integral Stirrer
Dispenses reproducible 10.0 μL liquid titrant pulses while stirring continuously at 750 RPM.
Dual Peltier Thermoelectric Cryo-Cooling Jacket
Establishes a steady reference temperature difference of 0.50 °C for power-compensation baseline.
Degassing Station with Vacuum and Magnetic Stirring
Degasses all aqueous and organic feedstocks for 15 minutes to prevent injection bubble artifacts.
Digital Microbalance and Karl Fischer Coulometer
Verifies moisture content and exact gravimetric purity of feedstock absolute ethanol.
FOLLOW THE METHOD
A reason behind every step.
Operate a power-compensation isothermal titration calorimeter (ITC) at 25.000 °C to measure the heat of mixing during incremental microliter injections of ethanol into water across composition factors x_1·(1 - x_1) from 0.05 to 0.25, evaluate the molar excess enthalpy H^E, and determine the Redlich–Kister excess enthalpy parameter A_0. Standardized parameter settings: 0.05, 0.09, 0.13, 0.17, 0.21, 0.25 dimensionless.
01
Degassing & Cell Thermal Equilibration
Degas HPLC water and absolute ethanol under vacuum for 15 minutes; fill reference cell with degassed water and establish 25.000 °C baseline.
02
Sample Cell & Syringe Charging
Load sample cell with 1.40 mL degassed pure water; fill automated injection syringe with 250 μL pure absolute ethanol, purging air bubbles.
03
Injection Parameters Configuration
Program ITC sequence for 20 successive injections of 10.0 μL with 150 s spacing at 750 RPM stirring speed.
04
Initial Injection & Titration Execution
Discard initial 0.4 μL pre-injection; initiate automated titration run, logging power compensation response curves (μcal/s) versus time.
05
Peak Integration & Cumulative Enthalpy Calculation
Integrate power compensation peaks for each injection to determine differential heats of mixing dQ; calculate cumulative molar excess enthalpy H^E.
06
Redlich–Kister Polynomial Regression
Plot molar excess enthalpy H^E versus composition factor x_1·(1 - x_1); fit linear regression through origin to extract A_0.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Excess Enthalpy of Mixing ITC mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
H^E = A_0 · [x_1 · (1 - x_1)] = -3450.0000 · [x_1 · (1 - x_1)]
| # | Mixture Composition Product x_1·(1 - x_1) (dimensionless) | Measured Molar Excess Enthalpy H^E (J/mol) | Composition factor x_1·(1 - x_1) | Molar excess enthalpy H^E (J/mol) | Remove |
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CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
For an ideal solution, the molar excess enthalpy of mixing H^E is:
An exothermic heat of mixing (H^E < 0) indicates that unlike molecular interactions (A-B) are:
The Redlich–Kister expansion models excess enthalpy H^E as a polynomial in:
The temperature dependence of liquid-phase activity coefficients is governed by excess enthalpy via:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
Excess enthalpy of mixing (H^E, also referred to as heat of mixing or excess enthalpy of solution) is a critical thermodynamic property in chemical engineering process design, heat exchanger sizing, reactor thermal management, and flash separation calculations. For an ideal solution, the enthalpy of mixing is strictly zero (ΔH_mix^ideal = 0), meaning mixing pure components at constant temperature and pressure releases or absorbs no heat. In real mixtures, however, breaking like-molecule intermolecular bonds (A-A and B-B) and creating unlike-molecule bonds (A-B) results in an energy imbalance. In the binary ethanol-water system, mixing is exothermic at ambient temperatures (H^E < 0) due to strong cross-association hydrogen bonding between water molecules and ethanol hydroxyl groups, releasing significant heat. The molar excess enthalpy is modeled using the Redlich–Kister polynomial expansion: H^E = x_1 · x_2 · [A_0 + A_1 · (x_1 - x_2) + A_2 · (x_1 - x_2)^2 + ...], where x_1 and x_2 = 1 - x_1 are mole fractions and A_k are temperature-dependent empirical interaction coefficients. In a symmetric first-approximation formulation, excess enthalpy scales directly with the product of the mole fractions: H^E = A_0 · [x_1 · (1 - x_1)], where A_0 is the leading Redlich–Kister parameter. Isothermal Titration Calorimetry (ITC) provides the highest precision method for measuring heats of mixing. Operating under active power-compensation feedback, the ITC sample cell (volume 1.40 mL) is maintained at strictly constant temperature (25.000 ± 0.0001 °C) while automated precision syringe injections (10.0 μL) deliver titrant into the stirred sample cell. Thermal compensation power pulses are integrated to quantify the enthalpy change of each injection with sub-microjoule resolution. In this laboratory experiment, an automated ITC unit measures the heat of mixing across composition products x_1·(1 - x_1) from 0.05 to 0.25 at 25.000 °C to determine the Redlich–Kister parameter A_0 = -3450.0000 J/mol.
H^E = A_0 · [x_1 · (1 - x_1)] = -3450.0000 · [x_1 · (1 - x_1)]
Evaluated using a MicroCal PEAQ-ITC power-compensation isothermal titration calorimeter with 1.40 mL Hastelloy cell, 250 μL injection syringe, and active Peltier feedback control (±0.0001 °C). Calibrated against standard water-water dilution blank and 2-propanol/water heat-of-mixing standards.