Thermostated 1.0 L Jacketed Batch Glass Reactor
Pyrex reaction vessel with 4 internal baffles, marine propeller stirrer, and water cooling/heating jacket.
Chemical & Process Engineering / Batch Reactor Arrhenius Kinetics
FREE TO EXPLORELABORATORY 30 · CHEMICAL & PROCESS ENGINEERING
Batch Chemical Reactor Kinetics & Arrhenius Activation Energy Determination
Operate a liquid-phase batch chemical reactor conducting the saponification of ethyl acetate across temperatures from 20.0 °C to 45.0 °C, record second-order reaction conversion vs time, and determine the Arrhenius activation energy E_a and pre-exponential factor A. 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.
LOG KINETIC RATE LN(K)—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Bath Temp T_c = 30.0 °C.
Adjust Bath Temp T_c, 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 (20.0 to 45.0 °C). Evaluated using a 1.0 L jacketed glass batch reactor with marine propeller at 300 RPM. Equimolar ethyl acetate saponification (C_A0 = 0.050 mol/L) tested across 20.0 to 45.0 °C. Linear regression models ln(k) versus 1000/T to extract slope S = 5.7740 kK (E_a = 48.005 kJ/mol) and intercept ln(A) = 21.1300.
Process apparatus & industrial sensors.
Circulating Precision Thermostatic Heating/Chilling Bath
Maintains batch temperature constant within ±0.05 °C across 20.0 to 45.0 °C.
Submersible Fast-Response Platinum RTD Sensor
Continuously records reaction temperature T with 0.01 °C resolution.
Flow-Through Micro-Conductivity Probe
Samples reaction mixture conductivity at 1 Hz to determine transient conversion X_A(t).
Analytical Laboratory Balance & Pipetting Station
Gravimetrically prepares precise equimolar 0.0500 M reactant solutions.
Automated Rapid Reactant Injection Manifold
Injects pre-thermostated ethyl acetate charge into NaOH solution in < 0.5 s to initiate reaction at t = 0.
FOLLOW THE METHOD
A reason behind every step.
Operate a liquid-phase batch chemical reactor conducting the saponification of ethyl acetate across temperatures from 20.0 °C to 45.0 °C, record second-order reaction conversion vs time, and determine the Arrhenius activation energy E_a and pre-exponential factor A. Standardized parameter settings: 20.0, 25.0, 30.0, 35.0, 40.0, 45.0 °C.
01
Bath Temperature Conditioning
Set thermostatic bath to 20.0 °C; circulate through the reactor jacket until internal temperature stabilizes at T = 20.00 ± 0.05 °C.
02
Batch Charging & Zero Calibration
Charge 500 mL of 0.100 M NaOH into the vessel; agitate at 300 RPM and record baseline initial conductivity κ_0.
03
Reaction Initiation (t = 0)
Rapidly inject 500 mL of pre-equilibrated 0.100 M ethyl acetate (mixed C_A0 = 0.050 M); start digital chronometer simultaneously.
04
Transient Conductivity Logging
Log solution electrical conductivity κ(t) every 10 seconds over 15 minutes; compute 1/C_A(t) versus time t.
05
Second-Order Rate Constant Evaluation
Fit a linear regression to 1/C_A versus t to determine the second-order rate constant k at 20.0 °C.
06
Temperature Progression & Arrhenius Regression
Repeat procedure at 25.0, 30.0, 35.0, 40.0, and 45.0 °C; plot ln(k) versus 1000/T, and fit a linear regression to determine activation energy E_a and frequency factor A.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Batch Reactor Arrhenius Kinetics mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
ln(k) = - (E_a / (1000·R)) · (1000/T) + ln(A) = -5.7740 · (1000/T) + 21.1300
| # | Reaction Bath Temperature T_c (°C) | Log Kinetic Rate ln(k) (ln(L/(mol·min))) | Inverse absolute temperature 1000/T (K^-1) | Log reaction rate constant ln(k) | Remove |
|---|
No readings yet. Execute a process trial and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
In an Arrhenius plot of ln(k) versus 1 / T, the slope of the line equals:
For an equimolar second-order reaction in a batch reactor, a plot of 1 / C_A versus time t yields:
A higher activation energy E_a means the reaction rate is:
The universal gas constant R in SI units is approximately:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
In chemical process engineering and fine chemical synthesis, batch reactors are the premier equipment choice for small-volume, high-value specialty products, pharmaceuticals, and kinetic rate data determination. In an isothermal batch reactor with uniform mixing, reactants are charged at t = 0, and reaction proceeds unsteady-state as concentrations decline continuously with time. For an equimolar second-order reaction A + B -> Products with C_A0 = C_B0, the species conservation balance yields: -dC_A / dt = k · C_A^2, which integrates analytically to: 1 / C_A - 1 / C_A0 = k · t. Measuring reactant concentration versus time allows precise evaluation of the reaction rate constant k at a given temperature. Svante Arrhenius (1889) formulated the universal law governing the temperature dependence of chemical reaction rate constants: k(T) = A · exp[-E_a / (R · T)], where A is the pre-exponential frequency factor, E_a is the activation energy (the minimum kinetic energy colliding reactant molecules must possess to overcome the transition state barrier), R = 8.314 J/(mol·K) is the universal gas constant, and T is absolute temperature in Kelvin. Taking natural logarithms yields the classic linear Arrhenius equation: ln(k) = - (E_a / R) · (1 / T) + ln(A). Plotting ln(k) versus inverse absolute temperature (1000 / T) yields a straight line with slope -E_a / (1000 R), from which activation energy E_a and pre-exponential factor A are determined. In this laboratory investigation, an instrumented 1.0-liter jacketed batch reactor is operated across temperatures from 20.0 °C to 45.0 °C to measure second-order rate constants k, verify Arrhenius temperature scaling, and determine activation energy E_a = 48.00 kJ/mol (slope S = E_a / (1000 R) = 5.7740 kK).
ln(k) = - (E_a / (1000·R)) · (1000/T) + ln(A) = -5.7740 · (1000/T) + 21.1300
Evaluated using a 1.0 L jacketed glass batch reactor with marine propeller at 300 RPM. Equimolar ethyl acetate saponification (C_A0 = 0.050 mol/L) tested across 20.0 to 45.0 °C. Linear regression models ln(k) versus 1000/T to extract slope S = 5.7740 kK (E_a = 48.005 kJ/mol) and intercept ln(A) = 21.1300.