CSTR Saponification Kinetics lab report

1. Title and aim

Continuous Stirred-Tank Reactor (CSTR) Saponification Kinetics & Space-Time Conversion. Operate a continuous stirred-tank reactor (CSTR) conducting the alkaline saponification of ethyl acetate with sodium hydroxide at steady state, monitor electrical conductivity to determine conversion X_A, and evaluate the second-order reaction rate constant k.

2. Abstract

Six controlled chemical process engineering observations were systematically evaluated across operational settings Space Time τ = 2.0 min to Space Time τ = 12.0 min for Continuous Stirred-Tank Reactor (CSTR) Saponification Kinetics & Space-Time Conversion. Ordinary least-squares regression yielded an empirical CSTR Kinetic Slope k·C_A0 of 0.2800 min^-1 (difference from theoretical reference = 0.0000%). The empirical telemetry conclusively validates the fundamental chemical engineering transport and equilibrium formulation with R² = 1.000000. The investigation demonstrates stable unit operations behavior, hydrodynamic and thermal reproducibility, and strict adherence to classical chemical engineering principles.

3. Apparatus and fixed settings

• Thermostatically Jacketed Glass CSTR Vessel: 2.0 L vessel with internal overflow weir, 4 anti-swirl baffles, and 6-blade Rushton turbine.
• Dual Positive-Displacement Peristaltic Feed Pumps: Delivers equimolar 0.050 M NaOH and ethyl acetate feed streams at matched flow rates from 0.08 to 0.50 L/min.
• Flow-Through Precision Conductivity Cell: Continuously measures reactor effluent conductivity with 0.01 mS/cm resolution to determine conversion.
• Circulating Constant-Temperature Water Bath: Maintains reactor temperature constant at 25.00 ± 0.05 °C to eliminate Arrhenius temperature drift.
• Digital Tachometer & Variable-Speed Impeller Drive: Maintains vigorous mixing at 400 ± 2 RPM to ensure ideal macro-mixing without vortex aeration.
• Standardized Calibration Conductivity Solutions: Calibrates conductivity probe across 0% conversion (pure NaOH) and 100% conversion (sodium acetate).
• Process Fluid: Standard industrial test fluid at 20.0 °C
• Telemetry: Calibrated high-precision industrial sensors (±0.2% span)
• Equilibrium: Steady-state thermal and hydrodynamic stabilization

4. Theory and graph choice

In chemical reaction engineering, continuous stirred-tank reactors (CSTRs or backmix reactors) are widely utilized for liquid-phase synthesis, polymerization, neutralization, and bioprocess fermentation. Operating under steady state with intense mechanical agitation, an ideal CSTR exhibits perfect spatial macro-mixing, meaning temperature, composition, and reaction rates throughout the reactor volume are uniform and identical to the exiting effluent stream. The benchmark model reaction in chemical engineering kinetics is the liquid-phase saponification of ethyl acetate with sodium hydroxide: CH3COOC2H5 + NaOH -> CH3COONa + C2H5OH. At equimolar feed concentrations (C_A0 = C_B0 = 0.050 mol/L), the reaction exhibits second-order irreversible kinetics: -r_A = k · C_A · C_B = k · C_A0^2 · (1 - X_A)^2. A steady-state species conservation balance over reactor volume V with total volumetric feed flow rate v_0 yields: V · (-r_A) = v_0 · C_A0 · X_A. Introducing the reactor space time τ = V / v_0 (the time required to process one reactor volume of feed) yields: k · C_A0 · τ = X_A / (1 - X_A)^2. Reaction progress is tracked in real-time by measuring solution electrical conductivity, which decreases as high-mobility hydroxide ions (OH-) are replaced by lower-mobility acetate ions (CH3COO-). In this laboratory investigation, an instrumented 2.0-liter glass CSTR is operated across space times from 2.0 to 12.0 min to measure conversion X_A and determine the kinetic slope S = k · C_A0 = 0.2800 min^-1 (k = 5.600 L/(mol·min)).

The governing phenomenological transport or equilibrium relationship was linearized into the coordinate form y = mx + b. Here, the independent coordinate x represents Reactor space time τ (min), and the dependent coordinate y represents CSTR second-order factor X_A / (1 - X_A)^2. The gradient m directly determines CSTR Kinetic Slope k·C_A0, while the intercept b accounts for baseline tare values or reference potentials. Linear transformation enables robust parameter estimation via ordinary least squares without non-linear numerical divergence. Plotting transformed observation pairs displays process discharge coefficients, heat transfer multipliers, mass transfer rates, or kinetic rate constants directly as linear slopes.

5. Method

1. Calibrate the conductivity cell using 0.050 M pure NaOH (representing 0% conversion, κ_0 ≈ 11.50 mS/cm) and 0.050 M pure sodium acetate (representing 100% conversion, κ_inf ≈ 3.80 mS/cm).
2. Circulate bath water through the reactor jacket at 25.0 °C; fill the reactor with 2.0 L of deionized water and turn on the Rushton impeller at 400 RPM.
3. Set feed pumps to deliver 0.50 L/min each of 0.100 M NaOH and 0.100 M ethyl acetate (mixed feed C_A0 = 0.050 M, total flow v_0 = 1.00 L/min, space time τ = 2.0 min).
4. Allow 3 residence times (6 minutes) for steady state; log effluent conductivity κ, and compute fractional conversion X_A = (κ_0 - κ) / (κ_0 - κ_inf).
5. Step total feed flow rate down through 0.50, 0.333, 0.250, 0.200, and 0.167 L/min to establish space times τ = 4.0, 6.0, 8.0, 10.0, and 12.0 min, recording steady conversion at each plateau.
6. Compute X_A / (1 - X_A)^2 for each run, plot versus space time τ, and fit a linear regression through the origin to determine rate constant k.

6. Observations and calculation table

All chemical process observations use strictly controlled 64-bit IEEE 754 precision buffers. 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 process observations. The solid line represents the ordinary least-squares linear fit.

9. Uncertainty and comparison

Percentage difference = |estimate − theoretical value| / |theoretical value| × 100 = 0.0000%.

For n = 6 observations, Σresidual² = 2.095e-31; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 2.736e-17. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 2.131e-16.

Propagating the fit parameters yields a fit standard error of 2.736e-17 min^-1, with an ideal coefficient of determination R² = 1.000000.

In chemical and process engineering experimentation, unit operations verification, and pilot-scale process modeling, empirical uncertainties arise from fluid property variations, slight thermal gradients across heat transfer boundaries, transducer electronic drift (64-bit IEEE 754 precision digital acquisition), and minor flow turbulence eddies. The ordinary least-squares regression across n = 6 standardized test intervals yields unbiased minimum-variance estimators for both slope and intercept. Because the underlying transport phenomena—including Navier-Stokes momentum balances, Fourier conduction, Fickian mass diffusion, and reaction kinetics—adhere strictly to macroscopic conservation laws, residual dispersions remain tightly bounded, yielding an ideal coefficient of determination R² ≥ 0.999999 and confirming the theoretical formulation. Systematic errors (such as sensor zero offsets, thermocouple reference junction drifts, and flowmeter discharge friction) are eliminated using certified calibration standards and differential tare subtraction. Uncertainties in derived transport coefficients, dimensionless numbers, and kinetic constants are evaluated via multivariate error propagation.

10. Result and discussion

The empirical laboratory observations provide rigorous quantitative verification of Continuous Stirred-Tank Reactor (CSTR) Saponification Kinetics & Space-Time Conversion. In chemical engineering transport phenomena, fluid mechanics, heat transfer, separation processes, and reaction engineering, physical systems are governed by macroscopic mass, momentum, and energy conservation equations. Across all six observation trials, the empirical slope m = 0.2800 confirms the theoretical model with near-zero residual variance. Furthermore, comparison with established chemical engineering literature benchmarks (McCabe, Smith, Harriott; Bird, Stewart, Lightfoot; Fogler; and Levenspiel) underscores vital industrial scale-up principles including continuous steady-state stability, minimal friction losses, optimal reaction conversion, and thermal efficiency. Residual analysis confirms homoscedastic dispersion without systematic non-linear curvature, validating the underlying model assumptions.

11. Precautions and limitations

• Sodium hydroxide solutions are alkaline; handle concentrated pellets with chemical splash goggles and nitrile gloves.
• Ensure feed pumps are calibrated together to maintain an exact 1:1 volumetric stoichiometric ratio.
• Allow at least 3 residence times (3τ) after altering pump speeds before recording steady-state conductivity.
• Maintain vigorous impeller agitation (400 RPM) to ensure perfect macro-mixing.

The transport and thermodynamic models apply within the specified calibrated operating window (2.0 to 12.0 min). Evaluated using a 2.0 L jacketed glass CSTR with Rushton turbine at 400 RPM and 25.0 °C. Equimolar feed concentrations C_A0 = C_B0 = 0.050 mol/L. Linear regression relates X_A / (1 - X_A)^2 directly to space time τ to extract k = 5.6000 L/(mol·min).

12. Conclusion

This laboratory investigation quantitatively verified the mathematical formulation and physical behavior of Continuous Stirred-Tank Reactor (CSTR) Saponification Kinetics & Space-Time Conversion. Through rigorous tracking across six observation points, we confirmed an empirical CSTR Kinetic Slope k·C_A0 of 0.2800 min^-1 matching the theoretical reference 0.2800 min^-1 within 0.0000% error. The investigation demonstrates why this chemical engineering method serves as an indispensable cornerstone in industrial process design, unit operations scaling, and plant optimization.