Lab Report Example: Determining the Rate of Reaction by Titration

Aim

The aim of this experiment was to determine the observed rate constant for the acid-catalysed hydrolysis of ethyl ethanoate at a constant temperature of 25 °C, and to demonstrate, using a volumetric (titrimetric) method, that the reaction is pseudo-first-order with respect to the ester. A secondary aim was to calculate the half-life of the reaction from the experimentally determined rate constant and to evaluate the reliability of the titration technique as a means of following a slow reaction over time.

Introduction and Theoretical Background

The Reaction Under Investigation

Esters undergo hydrolysis in aqueous solution to regenerate the parent carboxylic acid and alcohol. In this experiment, ethyl ethanoate was hydrolysed in the presence of hydrochloric acid, which acts as a catalyst, according to the equation below:

CH₃COOC₂H₅(aq) + H₂O(l) → CH₃COOH(aq) + C₂H₅OH(aq)

The hydrogen ions supplied by the hydrochloric acid protonate the carbonyl oxygen of the ester, making the carbonyl carbon more susceptible to nucleophilic attack by water. Because the catalyst is regenerated at the end of each catalytic cycle, the concentration of hydrogen ions remains effectively unchanged throughout the experiment. A particularly convenient feature of this reaction is that ethanoic acid is produced as the ester is consumed. The total quantity of acid present in the mixture therefore increases steadily with time, and this increase can be followed quantitatively by titration against a standardised alkali. The titration measures the combined acidity of the unchanged hydrochloric acid catalyst and the ethanoic acid generated by hydrolysis, since both are fully neutralised at the phenolphthalein end point.

Pseudo-First-Order Kinetics

The intrinsic rate of the reaction depends on the concentrations of the ester, water and the catalysing hydrogen ions. In dilute aqueous solution, however, water is present in very large excess, so its concentration is essentially constant, and the hydrogen ion concentration is held constant by its role as a catalyst. Under these conditions the rate law collapses to a pseudo-first-order expression that depends only on the concentration of the ester:

rate = k_obs[ester]

Integration of this expression gives a linear relationship between the natural logarithm of the ester concentration and time. Since the amount of ester remaining at any time is directly proportional to the difference between the titre at infinite time (when hydrolysis is complete) and the titre at time t, the integrated rate equation can be written in terms of the experimental titres as:

ln(V_∞ − V_t) = ln(V_∞ − V₀) − k_obst

Here V₀ is the titre at the start (corresponding to the hydrochloric acid alone), V_t is the titre at time t, and V_∞ is the titre once the reaction has gone to completion. A plot of ln(V_∞ − V_t) against time should therefore yield a straight line of gradient −k_obs, confirming first-order behaviour and allowing the rate constant to be read directly from the slope.

Materials and Apparatus

• Ethyl ethanoate (laboratory reagent grade)
• Hydrochloric acid, 1.00 mol dm⁻³ (catalyst and reaction medium)
• Sodium hydroxide, standardised at 0.100 mol dm⁻³ (titrant)
• Phenolphthalein indicator solution
• Thermostatically controlled water bath set to 25 °C
• 50 cm³ burette, 25 cm³ and 5 cm³ pipettes with safety fillers
• Conical flasks, beakers and a supply of crushed ice
• Stopclock, thermometer and a white tile

Method

1. A 50 cm³ volume of 1.00 mol dm⁻³ hydrochloric acid was pipetted into a clean, dry conical flask and clamped in the water bath. The acid was left for fifteen minutes to reach the bath temperature of 25 °C, confirmed with a thermometer.
2. A 5.00 cm³ portion of ethyl ethanoate, pre-equilibrated to the same temperature, was pipetted into the acid. The stopclock was started at the moment half of the ester had been added, and the mixture was swirled briefly to ensure thorough mixing.
3. Immediately, a 5.00 cm³ aliquot of the reaction mixture was withdrawn and run into a conical flask containing approximately 25 cm³ of ice-cold deionised water. The cold water dilutes the mixture and lowers its temperature, effectively quenching the reaction so that negligible further hydrolysis occurs during titration. This provided the initial titre, V₀.
4. The quenched aliquot was titrated without delay against the standardised 0.100 mol dm⁻³ sodium hydroxide using two drops of phenolphthalein, the end point being taken as the first permanent pale pink colour.
5. Further 5.00 cm³ aliquots were withdrawn, quenched and titrated in the same way at 10, 20, 30, 40, 50 and 60 minutes after the start of the reaction.
6. To obtain the infinity titre, V_∞, a final aliquot was removed, sealed in a stoppered tube and warmed in a 60 °C bath for approximately one hour to drive the hydrolysis to completion. It was then cooled to 25 °C and titrated in the same manner.
7. All glassware was rinsed with deionised water between titrations, and each titre was recorded to the nearest 0.05 cm³.

Results

The volume of 0.100 mol dm⁻³ sodium hydroxide required to neutralise each 5.00 cm³ aliquot is recorded below, together with the derived quantities used to test for first-order behaviour. The infinity titre was measured as V_∞ = 24.50 cm³. All figures are representative values generated to illustrate the calculation and should be treated as indicative rather than as measurements of a specific real sample.

When ln(V_∞ − V_t) was plotted against time, the data points fell on a convincing straight line, which is the diagnostic test for a first-order process. The line of best fit had a gradient of approximately −0.0180 min⁻¹ and an intercept of 3.00, in close agreement with the predicted value of ln(20.00) = 3.00. Taking the magnitude of the gradient gives the observed rate constant:

k_obs = 0.0180 min⁻¹ = 3.0 × 10⁻⁴ s⁻¹

The half-life of the reaction, which for a first-order process is independent of the starting concentration, was calculated from the rate constant as t_½ = ln2 / k_obs = 0.693 / 0.0180 = 38.5 minutes. This value is consistent with the raw data, since the titre change between consecutive measurements falls to roughly half of its initial increment over a comparable interval.

Discussion

The linearity of the logarithmic plot confirms that the hydrolysis of ethyl ethanoate under these conditions obeys pseudo-first-order kinetics with respect to the ester. This outcome is fully consistent with the accepted mechanism: although the true rate law depends on the concentrations of ester, water and hydrogen ions, the large excess of water and the catalytic regeneration of hydrogen ions mean that only the ester concentration changes appreciably during the measurement. The observed rate constant, k_obs, is therefore a composite quantity that incorporates the effectively constant concentrations of water and catalyst, and it would be expected to increase if a more concentrated acid were used.

The close match between the measured intercept and the calculated value of ln(V_∞ − V₀) gives confidence that the infinity titre was determined correctly, since an inaccurate V_∞ would systematically distort every data point and introduce curvature into the plot. The steady decrease in the titre increments with time also provides a qualitative, independent check on the first-order assignment without relying on the logarithmic transformation alone. Taken together, these observations show that a relatively simple volumetric technique can yield quantitatively meaningful kinetic information.

Evaluation and Sources of Error

Several factors could affect the reliability of the result and should be considered when interpreting the rate constant:

• Incomplete quenching. Hydrolysis continues, albeit slowly, between withdrawing an aliquot and reaching the end point. Chilling the aliquot in ice-cold water reduces this error, but titrating promptly is essential; any delay would make the measured titre slightly too high.
• Determination of V_∞. Forcing the reaction to completion by warming is the single most sensitive step. If hydrolysis is not fully complete, V_∞ is underestimated and the calculated rate constant is biased. Repeating the infinity measurement until a constant titre is obtained would improve accuracy.
• Temperature control. Rate constants are strongly temperature-dependent, so small drifts in the water bath temperature introduce scatter. Equilibrating both reagents before mixing minimised this effect.
• End point judgement. The phenolphthalein end point is subjective; over-titration of even one or two drops shifts the apparent titre. Using the same observer and a white tile under consistent lighting improves reproducibility.

To strengthen the investigation, the experiment could be repeated at several temperatures so that an Arrhenius plot could be constructed and the activation energy determined. Repeating the run in triplicate would also allow random error to be quantified, and an alternative monitoring method such as conductivity or polarimetry could be used to corroborate the titrimetric result.

Conclusion

The acid-catalysed hydrolysis of ethyl ethanoate was successfully followed by titrating timed aliquots of the reaction mixture against standardised sodium hydroxide. The linear plot of ln(V_∞ − V_t) against time confirmed that the reaction is pseudo-first-order with respect to the ester, and the observed rate constant was determined to be approximately 0.0180 min⁻¹ (3.0 × 10⁻⁴ s⁻¹), corresponding to a half-life of about 38.5 minutes at 25 °C. The experiment demonstrates that a straightforward volumetric method can provide reliable kinetic data, provided that quenching, temperature control and the infinity measurement are handled with care.

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