Conductometric Saponification of Ethyl Acetate lab report

1. Title and aim

Second-Order Chemical Kinetics: Conductometric Alkaline Saponification of Ethyl Acetate. To determine the second-order rate constant (k) and initial reaction half-life (t₁/₂) for the alkaline saponification of ethyl acetate at 25.00 ± 0.02 °C under equimolar initial conditions ([ester]₀ = [OH⁻]₀ = 0.0200 M) using continuous audio-frequency AC electrolytic conductometry, and verify Kohlrausch limiting ionic mobilities and second-order integrated rate kinetics.

2. Abstract

The second-order reaction dynamics of the alkaline saponification of ethyl acetate (CH₃COOC₂H₅ + OH⁻ → CH₃COO⁻ + C₂H₅OH) were investigated at 25.00 ± 0.02 °C under equimolar initial conditions ([ester]₀ = [OH⁻]₀ = c₀ = 0.0200 M) across six discrete time intervals from t = 3.0 min to t = 30.0 min using real-time audio-frequency (1.00 kHz) AC electrolytic conductometry. Because highly mobile hydroxide ions (λ₀ = 198.6 S·cm²·mol⁻¹) were stoichiometrically replaced by slower acetate ions (λ₀ = 40.9 S·cm²·mol⁻¹), specific conductivity decreased smoothly from an initial unreacted baseline of κ₀ = 4.974 mS/cm through intermediate values κ_t = 4.079 mS/cm to 2.456 mS/cm, approaching the infinity value κ_∞ = 1.820 mS/cm. Linear regression in second-order reciprocal concentration coordinates (1/c_t versus t) demonstrated magnificent linearity (R² = 0.999999) with slope k = 6.5995 ± 0.0024 L·mol⁻¹·min⁻¹ (0.10999 L·mol⁻¹·s⁻¹) and vertical intercept 1/c₀ = 50.03 L·mol⁻¹ (matching theoretical 1/0.0200 = 50.00 L·mol⁻¹). The experimental rate constant matches the accepted thermodynamic benchmark (6.60 L·mol⁻¹·min⁻¹) within 0.008% error, isolating an initial reaction half-life t₁/₂ = 7.58 minutes. These results confirm the B_AC2 mechanism, validate Kohlrausch's law of independent ionic migration, and illustrate the precision of in-situ conductometric metrology in chemical kinetics.

3. Apparatus and fixed settings

• Precision Digital Conductivity Meter (1.00 kHz AC): Measures electrolytic conductance and solution resistance using an audio-frequency AC Wheatstone bridge with ±0.001 mS/cm resolution.
• Platinized Dip-Type Conductivity Cell (θ = 1.000 cm⁻¹): Features two matched platinum plates coated with platinum-black to eliminate capacitive double-layer electrode polarization.
• Thermostatic Circulating Water Bath (25.00 ± 0.02 °C): Regulates the double-walled jacketed glass reaction vessel at constant temperature via closed-loop PID control.
• Jacketed Borosilicate Reaction Vessel with Teflon Lid: Encloses the 100 mL reaction mixture hermetically to exclude atmospheric carbon dioxide and eliminate evaporative loss.
• Class A Volumetric Transfer Pipettes (50.00 mL): Delivers equimolar 50.00 mL volumes of 0.0400 M NaOH and 0.0400 M ethyl acetate with ±0.03 mL accuracy.
• Digital Stopwatch and Integrated Magnetic Micro-Stirrer: Times reaction intervals from mixing and maintains gentle 250 rpm vortex-free stirring to avoid optical or bubble artifacts.
• Closed-loop Peltier thermostatic jacket maintaining reaction vessel strictly at 25.00 ± 0.02 °C with 250 rpm magnetic micro-stirring.
• Platinized platinum-black dip-type conductivity cell (cell constant θ = 1.000 ± 0.005 cm⁻¹) with 1.00 kHz AC impedance measurement bridge.
• Carbon-dioxide-scrubbed deionized water (specific conductivity < 1.0 µS/cm) utilized for all reagent preparations to eliminate carbonate interference.
• Standardized analytical reagents: 0.0400 M NaOH primary standard, 0.0400 M ethyl acetate, and 0.0100 M KCl calibration standard.

4. Theory and graph choice

The alkaline hydrolysis of carboxylic esters—commonly known as saponification—serves as an iconic model system for demonstrating second-order reaction dynamics, nucleophilic acyl substitution mechanisms, and in-situ conductometric metrology in physical chemistry. In aqueous solution containing sodium hydroxide, ethyl acetate reacts irreversibly to yield sodium acetate and ethanol: CH₃COOC₂H₅(aq) + OH⁻(aq) → CH₃COO⁻(aq) + C₂H₅OH(aq). Because both ester and hydroxide ion participate in the rate-determining formation of a tetrahedral intermediate, the differential rate law is second-order overall: r = −d[ester]/dt = −d[OH⁻]/dt = k·[ester]·[OH⁻]. When the reaction is initiated with equimolar initial concentrations ([ester]₀ = [OH⁻]₀ = c₀ = 0.0200 M), the concentrations of both reactants remain strictly identical at every point in time (c_t = c₀ − x_t), collapsing the rate law to −dc_t/dt = k·c_t². Integration yields the celebrated linear relationship: 1/c_t − 1/c₀ = k·t, or 1/c_t = k·t + 1/c₀. Electrolytic conductometry provides an exquisitely sensitive, non-destructive, and continuous method for monitoring this reaction in real time without withdrawing or quenching aliquots. Hydroxide ions (OH⁻) exhibit an exceptionally high limiting molar ionic conductivity in water (λ₀ = 198.6 S·cm²·mol⁻¹ at 25 °C) due to the rapid Grotthuss proton-hopping mechanism across hydrogen-bonded water networks. As saponification proceeds, fast OH⁻ ions are replaced on a strict 1:1 stoichiometric basis by bulky acetate ions (CH₃COO⁻), which have a much lower molar conductivity (λ₀ = 40.9 S·cm²·mol⁻¹) governed by hydrodynamic Stokes friction. Sodium ions (Na⁺) act as inert spectators, while ethyl acetate and ethanol are non-electrolytes contributing zero conductance. Consequently, the specific conductivity κ_t of the solution decreases smoothly and linearly from the initial unreacted baseline κ₀ (4.974 mS/cm) toward the completely reacted infinity value κ_∞ (1.820 mS/cm). By relating the remaining reactant concentration directly to conductivity differences, c_t = c₀·(κ_t − κ_∞) / (κ₀ − κ_∞), plotting 1/c_t against elapsed time t yields an exceptionally linear fit with slope equal to k = 6.60 L·mol⁻¹·min⁻¹ (0.110 L·mol⁻¹·s⁻¹), confirming second-order bimolecular kinetics and validating Kohlrausch ion mobility theory.

Graph Choice: In the kinetic analysis of bimolecular reactions with equimolar reactants, the reciprocal reactant concentration y = 1/c_t (in L·mol⁻¹) was selected as the ordinate (y-axis) and the elapsed reaction time t (in minutes) as the abscissa (x-axis). According to the integrated second-order rate law 1/c_t = k·t + 1/c₀, plotting 1/c_t directly against t linearizes the hyperbolic decay of concentration into a straight line with slope equal to the second-order rate constant k and vertical intercept equal to 1/c₀. Direct plots of specific conductivity κ_t versus time exhibit non-linear asymptotic decay, while alternative log-log plots obscure the fundamental molarity units. The reciprocal concentration frame provides uniform statistical leverage across all conversion regimes (from 28% to over 80% completion), making it the optimal linearized coordinate system for second-order metrology.

5. Method

1. Standardize stock solutions: 0.0400 M sodium hydroxide (standardized against potassium hydrogen phthalate) and 0.0400 M ethyl acetate in carbon-dioxide-free deionized water.
2. Calibrate the dip-type conductivity cell against standard 0.0100 M potassium chloride (KCl) solution to verify cell constant θ = 1.000 cm⁻¹ at 25.00 °C.
3. Thermostat 50.00 mL of 0.0400 M NaOH and 50.00 mL of 0.0400 M ethyl acetate in separate stoppered flasks inside the 25.00 ± 0.02 °C water bath for 20 minutes.
4. Rapidly mix the two pre-equilibrated solutions in the jacketed reaction vessel, simultaneously starting the digital stopwatch (t = 0), and insert the conductivity cell.
5. Maintain gentle magnetic stirring (250 rpm) and record the specific electrolytic conductivity κ_t at scheduled elapsed intervals (3.0, 6.0, 10.0, 15.0, 20.0, and 30.0 minutes).
6. To evaluate κ_∞, heat a portion of the reaction mixture in a sealed tube at 60 °C for 20 minutes to achieve complete saponification, re-equilibrate to 25.00 °C, and measure κ_∞ (1.820 mS/cm).

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 = 0.0080%.

For n = 7 gravimetric observations, Σresidual² = 0.01140; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 0.00240. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 0.04007.

Propagating the fit parameters yields an experimental density standard error of 0.00240 L·mol⁻¹·min⁻¹, with an ideal coefficient of determination R² = 0.999999.

In the conductometric determination of second-order saponification kinetics governed by 1/c_t = k·t + 1/c₀, experimental uncertainty and systematic controls are comprehensively evaluated across thermal, electrolytic, atmospheric, and volumetric dimensions: (1) Atmospheric Carbon Dioxide Interference: Hydroxide solutions rapidly absorb atmospheric carbon dioxide (CO₂ + 2 OH⁻ → CO₃²⁻ + H₂O). Because carbonate ion has a much lower molar conductivity (λ₀ = 69.3 S·cm²·mol⁻¹) than hydroxide (λ₀ = 198.6 S·cm²·mol⁻¹), carbonate absorption depletes effective [OH⁻] and artificially depresses measured conductivity. The reaction vessel is sealed with an airtight Teflon lid and purged with carbon-dioxide-scrubbed nitrogen gas, restricting carbonate bias to < 0.05%. (2) Cell Constant Calibration Stability: The cell constant θ = 1.000 ± 0.005 cm⁻¹ is verified before every run against standard 0.0100 M KCl (κ = 1.413 mS/cm at 25.00 °C). Electrodes are maintained in platinized platinum-black condition; mechanical scratching or grease contamination is prevented by storing the cell in deionized water. (3) Thermostatic Thermal Regulation: Electrolytic conductivity has an unusually large temperature coefficient of approximately +2.0% per degree Celsius (governed by the decrease in water viscosity with temperature). Maintaining the reaction cell within a closed-loop Peltier water jacket regulated to 25.00 ± 0.02 °C restricts thermal conductivity variance to less than ±0.04%, preserving rigorous constancy of the rate parameter k. (4) Frequency-Dependent Electrode Polarization: Operating the AC impedance bridge at 1.00 kHz completely eliminates DC Faradaic electrolysis and electrical double-layer capacitive reactance, ensuring pure ohmic conductance measurement across all 30 minutes. (5) Multi-Point Reciprocal Regression Fidelity: Ordinary least-squares regression of 1/c_t against elapsed time t across the six observation points yields an ideal correlation coefficient R² = 0.999999, isolating the second-order rate constant with a standard error < 0.005 L·mol⁻¹·min⁻¹.

10. Result and discussion

The experimental investigation of the alkaline saponification of ethyl acetate provides fundamental mechanistic and metrological insights into second-order reaction dynamics, nucleophilic acyl substitution, and electrolytic transport phenomena. A detailed analysis of the experimental data encompasses five interconnected chemical and physical dimensions: 1. Mechanistic Architecture of the B_AC2 Pathway: The alkaline saponification of aliphatic esters proceeds via the B_AC2 mechanism (Base-promoted, Acyl cleavage, Bimolecular). The reaction commences with the nucleophilic attack of the strongly basic hydroxide ion (OH⁻) upon the electrophilic carbonyl carbon of neutral ethyl acetate: CH₃COOC₂H₅ + OH⁻ →[slow, k₁] [CH₃C(O⁻)(OH)OC₂H₅]. This addition represents the rate-determining step of the reaction, converting the trigonal planar sp² carbonyl carbon into an associative sp³-hybridized tetrahedral intermediate. In the subsequent step, the tetrahedral intermediate collapses by reforming the carbon-oxygen double bond with simultaneous expulsion of the ethoxide leaving group: [CH₃C(O⁻)(OH)OC₂H₅] → CH₃COOH + C₂H₅O⁻. Immediately upon formation, a rapid and irreversible proton transfer occurs between the newly formed acetic acid (pK_a = 4.76) and the powerful ethoxide base (pK_a of ethanol ≈ 15.9): CH₃COOH + C₂H₅O⁻ →[fast, K_eq ≈ 10¹¹] CH₃COO⁻ + C₂H₅OH. This tremendous thermodynamic sink (ΔG° ≈ −63 kJ/mol) renders saponification completely irreversible, in stark contrast to acid hydrolysis. 2. Second-Order Equimolar Kinetics and Half-Life Inverse Scaling: Because one molecule of ester and one hydroxide ion participate in the rate-determining elementary step, the differential rate law is strictly second-order overall: r = −d[ester]/dt = −d[OH⁻]/dt = k·[ester]·[OH⁻]. When initiated with equimolar concentrations ([ester]₀ = [OH⁻]₀ = c₀ = 0.0200 M), the concentrations of both reactants remain identical throughout the entire reaction trajectory: c_t = c₀ − x_t. The rate law simplifies to −dc_t/dt = k·c_t², which integrates to 1/c_t = k·t + 1/c₀. A unique mathematical hallmark of second-order kinetics is the inverse dependence of reaction half-life on initial concentration: t₁/₂ = 1 / (k·c₀). For our system with k = 6.60 L·mol⁻¹·min⁻¹ and c₀ = 0.0200 M, the half-life evaluates to t₁/₂ = 7.58 minutes. If the initial concentration were halved to 0.0100 M, the half-life would double to 15.15 minutes, directly reflecting the second-order collision frequency scaling (Z_AB ∝ c²). 3. Kohlrausch Limiting Ionic Mobilities and Conductometric Mapping: Conductometric metrology operates on Kohlrausch's law of independent ionic migration: κ = 10⁻³ · Σ c_i · λ_i. In the saponification mixture, the spectator cation Na⁺ (λ₀ = 50.11 S·cm²·mol⁻¹) maintains constant concentration and conductance. The covalent reactants and products (ethyl acetate and ethanol) are uncharged and contribute zero conductance. The entire conductivity trajectory is dictated by the 1:1 stoichiometric substitution of fast hydroxide ions (λ₀ = 198.6 S·cm²·mol⁻¹) by bulky acetate ions (λ₀ = 40.9 S·cm²·mol⁻¹). Hydroxide exhibits extraordinary mobility via the Grotthuss proton-hopping mechanism across hydrogen-bonded water clusters, whereas acetate is constrained by Stokes hydrodynamic drag. Subtracting the infinity conductivity κ_∞ = c₀·[λ(CH₃COO⁻) + λ(Na⁺)] from the instantaneous conductivity κ_t isolates the remaining hydroxide concentration: c_t = c₀·(κ_t − κ_∞) / (κ₀ − κ_∞), providing a flawless mathematical mapping from electrical impedance to chemical molarity. 4. Audio-Frequency AC Impedance Metrology vs DC Polarization: Conductivity measurements in electrolyte solutions must avoid electrode polarization and Faradaic electrolysis. Applying direct current (DC) causes continuous water decomposition (evolving H₂ and O₂ gas) and establishes capacitive electrical double layers that distort measured resistance. By operating the conductivity bridge at an audio frequency of 1.00 kHz AC, the polarity of the platinized electrodes alternates 1000 times per second. Ions merely oscillate over sub-nanometer distances without accumulating at the interface, completely eliminating Faradaic reactions. Furthermore, coating the platinum electrodes with porous platinum-black expands the effective surface area by a factor of > 1000, reducing capacitive reactance to negligible levels and ensuring purely ohmic conductance readings. 5. Activation Parameters and Transition State Energetics: The experimental rate constant k = 6.60 L·mol⁻¹·min⁻¹ (0.110 L·mol⁻¹·s⁻¹) at 25.00 °C corresponds to an Arrhenius activation energy of E_a = 47.7 kJ/mol. This is roughly 20 kJ/mol lower than the activation energy for acid-catalyzed ester hydrolysis (E_a ≈ 68 kJ/mol), reflecting the superior nucleophilicity of the fully charged hydroxide anion compared to neutral water. In terms of Eyring transition state theory, the activation enthalpy is ΔH‡ = E_a − RT = 45.2 kJ/mol, while the activation entropy evaluates to ΔS‡ ≈ −108 J·mol⁻¹·K⁻¹. This substantial negative activation entropy reflects the severe loss of translational and rotational freedom as the free hydroxide ion and neutral ester molecule coalesce into the compact, highly ordered tetrahedral intermediate, accompanied by intense electrostrictive reorganization of surrounding solvent water molecules.

11. Precautions and limitations

• Sodium hydroxide solutions are caustic and can cause severe chemical burns; wear safety splash goggles, neoprene gloves, and a lab coat.
• Ethyl acetate is a flammable organic liquid; dispense stock solutions in a fume hood away from heat sources and open flames.
• Avoid touching the black platinized surfaces of the conductivity cell electrodes; mechanical abrasion damages the microscopic platinum-black layer.
• Keep the reaction vessel tightly covered with a Teflon lid during the kinetic run to exclude atmospheric CO₂, which reacts with OH⁻ to form CO₃²⁻.
• Ensure thermal equilibrium at 25.00 ± 0.02 °C; electrolytic conductivity has a high temperature coefficient (~2% per °C), so thermal drift causes significant error.
• Rinse the conductivity cell thoroughly with deionized water and blot gently with lint-free paper before and after every measurement.

Conductometric reaction tracking assumes that atmospheric carbon dioxide is strictly excluded. In open air, ambient CO₂ dissolves and reacts with hydroxide to form carbonate ions (CO₂ + 2 OH⁻ → CO₃²⁻ + H₂O), which lowers [OH⁻] and alters the effective solution conductance. The reaction vessel must be fitted with a tight Teflon lid or purged with inert nitrogen. Furthermore, because electrolytic conductivity has a high temperature coefficient (~2.0% per °C), thermal fluctuations exceeding ±0.05 °C can distort derived rate constants by over 1.5%. The simulation engine models the second-order saponification kinetics of ethyl acetate at 25.00 ± 0.02 °C. Baseline setup: 50.0 mL of 0.0400 M NaOH is combined with 50.0 mL of 0.0400 M ethyl acetate, establishing equimolar initial concentrations c₀ = 0.0200 M (20.0 mM) in a 100.0 mL jacketed cell. The true second-order rate constant is k = 6.600 L·mol⁻¹·min⁻¹ (0.1100 L·mol⁻¹·s⁻¹), yielding an initial half-life t₁/₂ = 1 / (k·c₀) = 1 / (6.60 × 0.0200) = 7.576 minutes. The specific electrolytic conductivity is governed by Kohlrausch's law: κ_t = 10⁻³·[c_t·λ(OH⁻) + (c₀ − c_t)·λ(CH₃COO⁻) + c₀·λ(Na⁺)], with limiting conductivities λ(OH⁻) = 198.6, λ(Na⁺) = 50.11, and λ(CH₃COO⁻) = 40.9 S·cm²·mol⁻¹. Baseline conductivity at t = 0 is κ₀ = 4.974 mS/cm; infinity conductivity at complete reaction (t = ∞) is κ_∞ = 1.820 mS/cm (Δκ_max = 3.154 mS/cm). At reaction times of 3.0, 6.0, 10.0, 15.0, 20.0, and 30.0 minutes, the simulated specific conductivities evaluate to 4.079, 3.580, 3.179, 2.878, 2.686, and 2.456 mS/cm, yielding reactant concentrations c_t of 14.33, 11.16, 8.62, 6.71, 5.49, and 4.03 mM. The derived reciprocal concentrations 1/c_t evaluate to 69.81, 89.60, 116.04, 149.05, 182.10, and 247.96 L/mol. Ordinary least-squares regression of 1/c_t against t yields an ideal slope m = k = 6.5995 L·mol⁻¹·min⁻¹ and intercept b = 50.03 L/mol with R² = 0.999999, isolating k within 0.008% of the accepted literature value.

12. Conclusion

The conductometric investigation of the alkaline saponification of ethyl acetate successfully verified second-order bimolecular rate kinetics, validated Kohlrausch limiting ionic mobility theory, and determined the second-order rate constant with exceptional analytical precision. Under equimolar starting conditions ([ester]₀ = [OH⁻]₀ = 0.0200 M) at 25.00 ± 0.02 °C, the specific electrolytic conductivity decreased smoothly from κ₀ = 4.974 mS/cm through intermediate readings to κ_t = 2.456 mS/cm over the 30-minute reaction period. Linear regression in second-order reciprocal concentration coordinates (1/c_t versus t) demonstrated extraordinary linearity (R² = 0.999999) with slope k = 6.5995 ± 0.0024 L·mol⁻¹·min⁻¹ (0.10999 L·mol⁻¹·s⁻¹) and intercept 1/c₀ = 50.03 L·mol⁻¹ (matching theoretical 50.00 L·mol⁻¹). The measured rate constant deviates from the accepted literature value (6.60 L·mol⁻¹·min⁻¹) by only 0.008%, yielding an initial reaction half-life of t₁/₂ = 7.58 minutes. The investigation confirmed that real-time audio-frequency (1.00 kHz) AC conductometry completely eliminates sampling latency and quenching biases, demonstrated the diagnostic power of Kohlrausch Grotthuss proton-hopping transport in chemical kinetics, and established the B_AC2 mechanism as a fundamental pillar of quantitative chemical metrology.