Assignment Sample: Reaction Kinetics of Ester Hydrolysis

Model Answer

Introduction

The alkaline hydrolysis of ethyl acetate, CH₃COOC₂H₅ + OH⁻ → CH₃COO⁻ + C₂H₅OH, is one of the most widely used teaching reactions in physical chemistry because it proceeds at a convenient rate at room temperature, can be followed by simple titration or conductivity measurements, and displays clean second-order kinetics under the standard experimental conditions used here (Atkins and de Paula, 2014). This assignment analyses concentration–time data recorded for this reaction at two temperatures, with the aims of confirming the reaction order from the shape of the integrated rate data, determining the rate constant, k, at each temperature, and combining the two rate constants via the Arrhenius equation to obtain the activation energy, E_a, of the hydrolysis.

Theoretical Background

The rate law for this reaction is first order in ester and first order in hydroxide ion, giving an overall second-order reaction:

rate = k[ester][OH⁻]

Because the experiment was set up with equal initial concentrations of ester and sodium hydroxide, [ester]₀ = [OH⁻]₀ = a, the two reactant concentrations remain equal to one another throughout the reaction, and the rate law integrates to the standard second-order form:

1/a_t = 1/a₀ + kt

where a_t is the common concentration of ester and hydroxide remaining at time t. This predicts that a plot of 1/a_t against t should be a straight line of gradient k passing through an intercept of 1/a₀, and it is this linearity, rather than the shape of a_t against t alone, that provides the clearest confirmation of second-order behaviour (Laidler, 1987). By contrast, a first-order rate law would predict a straight-line plot of ln a_t against t, and a zero-order rate law would predict a_t itself falling linearly with t; testing all three linearised forms against the same dataset, and identifying which one gives the best straight line, is the standard method for confirming reaction order from concentration–time data when the stoichiometric mechanism is not already known with certainty.

Method

The reaction was initiated by mixing equal volumes of ethyl acetate and sodium hydroxide solutions, both pre-equilibrated to the reaction temperature in a thermostatted water bath, so that the initial concentration of each reactant in the combined mixture was 0.0200 mol dm⁻³. At each recorded time point, a fixed 10 cm³ aliquot of the reaction mixture was withdrawn by pipette and immediately quenched by running it into a flask containing a known excess of standard hydrochloric acid, which instantaneously stops the hydrolysis by neutralising the remaining hydroxide ion and effectively “freezes” the reaction at that instant. The unreacted (excess) HCl in each quenched sample was then back-titrated against standard sodium hydroxide solution using phenolphthalein indicator, and the volume of NaOH used was converted, via the known excess of HCl originally added, into the concentration of hydroxide ion remaining in the reaction mixture at the sampling time. This quench-and-back-titrate approach is preferred over titrating the reaction mixture directly, because it avoids the reaction continuing to proceed during the several minutes a live titration would otherwise take, and the entire procedure was repeated at a second, higher temperature using an identical protocol.

Experimental Data

Table 1 gives the residual hydroxide concentration, determined by back-titration of unreacted NaOH with standard HCl, at seven time points for a reaction carried out at 25 °C with initial concentrations of 0.0200 mol dm⁻³ for both ethyl acetate and sodium hydroxide.

Table 1. Residual hydroxide concentration and its reciprocal at 25 °C.

Determination of Reaction Order and Rate Constant

The final column of Table 1 was calculated by taking the reciprocal of each measured concentration; for example, at t = 30 min, 1/0.01871 = 53.45 dm³ mol⁻¹. Plotting 1/[OH⁻]_t against t gives a good straight line over the full 90-minute run, confirming second-order kinetics; by contrast, a plot of ln[OH⁻]_t against t (the test for a first-order reaction) shows measurable curvature over the same interval and can be rejected as the correct kinetic model.

The rate constant is the gradient of the 1/[OH⁻]_t versus t line. Using the two most widely separated points to illustrate the calculation, t = 0 min (1/a = 50.00) and t = 90 min (1/a = 60.35):

k(25 °C) = (60.35 − 50.00) ÷ (90 − 0) = 10.35 ÷ 90 = 0.1150 dm³ mol⁻¹ min⁻¹

A least-squares fit through all seven points gives the same gradient to three significant figures, confirming that the reaction obeys the second-order rate law closely across the whole time range studied and that k(25 °C) = 0.115 dm³ mol⁻¹ min⁻¹, a value consistent with literature reports for this reaction at room temperature (Laidler, 1987).

An identical run carried out at 35 °C, processed in the same way, gave a rate constant of k(35 °C) = 0.230 dm³ mol⁻¹ min⁻¹, almost exactly double the 25 °C value, illustrating the characteristically strong temperature sensitivity of reaction rate constants that motivates the Arrhenius analysis below.

Activation Energy Determination

The Arrhenius equation, k = A exp(−E_a/RT), can be applied to two rate constants measured at different absolute temperatures, T₁ and T₂, by taking the ratio of the two forms of the equation and rearranging to eliminate the pre-exponential factor, A:

ln(k₂/k₁) = −(E_a/R)(1/T₂ − 1/T₁)

With k₁ = 0.115 dm³ mol⁻¹ min⁻¹ at T₁ = 298 K and k₂ = 0.230 dm³ mol⁻¹ min⁻¹ at T₂ = 308 K:

ln(k₂/k₁) = ln(0.230/0.115) = ln(2.000) = 0.6931

1/T₂ − 1/T₁ = 1/308 − 1/298 = 0.0032468 − 0.0033557 = −1.089 × 10⁻⁴ K⁻¹

Rearranging for E_a, with the gas constant R = 8.314 J mol⁻¹ K⁻¹:

E_a = −R × ln(k₂/k₁) ÷ (1/T₂ − 1/T₁) = −8.314 × 0.6931 ÷ (−1.089 × 10⁻⁴) = 52,910 J mol⁻¹ ≈ 52.9 kJ mol⁻¹

This value falls within the range of 40–55 kJ mol⁻¹ typically reported for the alkaline hydrolysis of simple aliphatic esters (Atkins and de Paula, 2014), supporting the reliability of the two-temperature dataset. The pre-exponential factor, A, can then be recovered by substituting E_a and either rate constant back into the single-temperature Arrhenius equation:

A = k₁ × exp(E_a/RT₁) = 0.115 × exp(52,910 ÷ (8.314 × 298)) = 0.115 × exp(21.36) ≈ 2.2 × 10⁸ dm³ mol⁻¹ min⁻¹

an order of magnitude consistent with a bimolecular reaction between two small, moderately polar species in aqueous solution (Connors, 1990).

Evaluation

The strong linearity of the 1/[OH⁻]_t versus t plot at both temperatures, together with a doubling of the rate constant for a 10 °C rise consistent with the well-known rule of thumb for solution-phase organic reactions, and an activation energy that sits comfortably within the literature range for ester saponification, together give good confidence in the second-order kinetic model adopted here. Several factors, however, limit the precision of the derived rate constants and activation energy. Temperature control is critical: because k roughly doubles for every 10 °C rise, a water-bath fluctuation of even ±0.5 °C could shift an individual rate constant by several per cent, and this uncertainty propagates directly into the Arrhenius calculation, which uses only two temperatures and therefore cannot detect or average out a systematic offset in either bath. The end-point of each back-titration also carries a small, operator-dependent uncertainty; because the reaction is quenched (for example by adding excess standard acid) at the moment of sampling, any delay between withdrawing the sample and quenching it allows the reaction to continue and would bias the apparent concentration downward, artificially increasing the apparent rate constant. Finally, the assumption of a clean, single-step second-order mechanism neglects the reverse (ester-forming) reaction between ethanol and acetate ion; this is a reasonable approximation early in the reaction, when little product has accumulated, but would introduce increasing error if the analysis were extended to high conversions, and a more rigorous treatment would fit the data to the full reversible second-order rate law rather than assuming the reaction goes to completion (Espenson, 1995).

A more robust version of this exercise would use at least three or four temperatures rather than two, allowing E_a to be obtained from the gradient of a full ln k versus 1/T plot together with a standard error on that gradient, and would repeat each titration in duplicate to quantify the precision of the individual concentration measurements that underpin every subsequent calculation.

An alternative to the titrimetric method used here is to follow the reaction by conductivity, since the highly mobile hydroxide ion is progressively replaced by the much less mobile acetate ion as the reaction proceeds, producing a continuous, measurable fall in the conductivity of the mixture without the need to withdraw and quench discrete samples. A conductometric run would give many more data points per unit time at the cost of requiring a conductivity-to-concentration calibration, and comparing the rate constant obtained by both methods on the same reaction mixture would be a useful cross-check that neither the quenching step nor the titration end-point introduces a significant systematic bias into the titrimetric results reported here (Connors, 1990). It is also worth noting that the excellent agreement between the two-point and least-squares estimates of k at 25 °C in this dataset (both 0.115 dm³ mol⁻¹ min⁻¹ to three significant figures) is itself evidence that the underlying concentration–time data are close to ideal second-order behaviour over the range studied, with no obvious curvature that would indicate a competing side reaction or a significant reverse reaction at these early-to-moderate conversions.

Conclusion

The concentration–time data confirm that the alkaline hydrolysis of ethyl acetate under these conditions is second order overall, with rate constants of 0.115 dm³ mol⁻¹ min⁻¹ at 25 °C and 0.230 dm³ mol⁻¹ min⁻¹ at 35 °C. Combining these via the Arrhenius equation gives an activation energy of 52.9 kJ mol⁻¹ and a pre-exponential factor of approximately 2.2 × 10⁸ dm³ mol⁻¹ min⁻¹, both consistent with published values for this well-characterised reaction. Tighter temperature control, replicate titrations and a multi-temperature Arrhenius plot would all improve the precision of a repeat determination.

References

• Atkins, P. and de Paula, J. (2014) Atkins’ Physical Chemistry. 10th edn. Oxford: Oxford University Press.
• Laidler, K.J. (1987) Chemical Kinetics. 3rd edn. New York: Harper & Row.
• Connors, K.A. (1990) Chemical Kinetics: The Study of Reaction Rates in Solution. New York: VCH.
• Espenson, J.H. (1995) Chemical Kinetics and Reaction Mechanisms. 2nd edn. New York: McGraw-Hill.
• Levine, I.N. (2009) Physical Chemistry. 6th edn. New York: McGraw-Hill.
• Housecroft, C.E. and Constable, E.C. (2010) Chemistry: An Introduction to Organic, Inorganic and Physical Chemistry. 4th edn. Harlow: Pearson.
• Harris, D.C. (2015) Quantitative Chemical Analysis. 9th edn. New York: W.H. Freeman.
• Royal Society of Chemistry (2015) Kinetics of the Saponification of Ethyl Acetate: A Practical Guide. London: Royal Society of Chemistry.