In a study of chemical reaction kinetics, one must select for observation some physical property of the reacting system which is related in a known manner to the progress of the reaction. Spectroscopic changes in the visible or near ultraviolet region are particularly convenient as a measure of the extent of reaction. For the present investigation we will examine the hydrolysis of the ester p-nitrophenylacetate in buffered aqueous solution. The ester and the acid are nearly colorless, but the ionized p-nitrophenylate anion has a high molar absorptivity at 400 nm. Above pH 8.5, where both acetic and p-nitrophenol are fully ionized, the reaction can be represented as (eq (1)):
The hydrolysis is catalyzed by OH- ion, which in our work will be controlled by addition of very dilute sodium hydroxide to a buffer of pH 6.86-7.00. Based upon the observations of others (consult an organic or physical organic text for a discussion of the mechanism of this reaction), the proposed rate equation for the reaction is
The condition of constant OH- ion allows us to treat the reaction as if it were a first order process; the second order rate law has been reduced to "pseudo first order":
We will follow reaction progress photometrically by observing the increase in light absorption at 400 nm, caused by the formation of the phenolate anion. Letting A be the absorbance of the reaction solution at 400 nm, and assuming that no other species absorb at this wavelength, we can write
e is the molar absorptivity of the phenolate ion. The differential rate equation integrates to yield at t=0, A=A0,
The integrated rate equation is suitable for linear regression, but both A0 and Ainfinity and must be known to calculate values of the dependent variable in equation 5a; in eqn. 5b, only Ainfinity need be known in advance. A0 can be estimated by observing the absorbance at t = 0; Ainfinity can be estimated from knowledge of the molar absorptivity of the product and the initial concentration of ester used, or by direct observation of the absorbance of the solution after the reaction has "gone to completion". The need for prior knowledge of the limiting experimental absorbances can be avoided by using nonlinear regression directly upon the integrated rate equation written in the form
In this approach, A0 and Ainfiinity are treated as adjustable regression parameters, along with the pseudo first order rate constant k. Both linear and nonlinear regression methods seek the minimum in the function
In linear regression the (successful) answer is unique, whereas nonlinear regression (which requires initial estimates of the regression parameters at the start of the analysis) proceeds by iterative approximation and may give "false" answers. Nonetheless the nonlinear approach has much to recommend it, and it is the only method available for models which cannot be linearized.
EXPERIMENTAL PROCEDURE
We require a spectrophotometer and means of controlling and measuring hydroxyl ion concentration. By observing the reaction at several different concentrations of hydroxyl ion, we will be able to test the validity of the second order rate law which is thought to represent this reaction. The Cary 1E UV-Vis Spectrophotometer interfaced to a PC will be used to collect kinetic data, which will be obtained by following the absorbance of the reaction solution at fixed wavelength. A pH meter, a buffer, and dilute aqueous NaOH are used to measure and control pH; careful measurement of pH is critical to the success of this project.
SOLUTIONS
Prepare a solution of 9 - 12 mg of p-nitrophenylacetate in 10 ml of acetone in a 10 ml volumetric flask; this solution must be prepared at the start of the laboratory period.
A small amount of dilute aqueous NaOH should be added to water to obtain the desired initial pH, near 9.5. The stirred solution will be monitored continuously with a pH meter. A pH range from about 9.5 to 11 will provide a suitable data set. Particular pH values are obtained by adding small amounts of dilute NaOH to the solution being monitored with the pH meter. Be certain that the pH readings are stable before starting any runs.
Turn on the Cary and the PC; the instrument should warm up for at least two hours prior to the experiment. From start button/All programs/Cary WinUV, select the Scanning Kinetics feature. Set the wavelength to 400 nm, the absorbance maximum to 1, the signal averaging time to 1.00, and the spectral bandwidth to 1.00. Zero the instrument with respect to the blank; use 2.00 mL of the aqueous NaOH solution for a reference. The sample compartment is at the front of the Cary (the reference compartment is at the rear). Place the blank in the front compartment, close the lid, and left-click on Zero to zero the instrument. Remove the cell containing the reference solution. Note that the Cary is a double-beam instrument, but in this experiment we will not be using this feature.
TO START THE REACTION: To prepare the reaction mixture, add 15 to 25 microliters of the ester solution (via a Hamilton syringe) to 2.00 mL of aqueous NaOH in a spectrophotometric cell, cap the cell, and mix by inverting several times; place the cell in the front compartment of the instrument, replace the cell compartment lid, and click Collect. This sequence should be done with calm dispatch, to minimize the time between the start of the reaction and the start of data collection. Remember, data are invalid if the absorbance exceeds 1.0, so watch the monitor on the controlling PC. In a successful run, the absorbance versus time curve will initially rise, and then level out at some absorbance (ideally) close to 1.0.
For the next data set, adjust the NaOH solution to the desired pH by addition of dilute NaOH solution, re-zero the Cary, and repeat the absorbance/time measurement. At least four different pH values are required for an adequate analysis.
For runs at or below pH=10, make measurements for 30 minutes. For runs above pH=10, make runs for about 15 minutes. Set the stop time feature accordingly. You may stop a measurement if the absorbance seems to be constant over a period of about 10 measurements. Be sure that the absorbance does not exceed 1.0; if it does, redo the run, and use a little less of the ester solution (see below). When a run is complete, export the absorbance-time data as ASCII files suitable for use with Mathcad.
Upon completion of the work, those persons wishing to rise in the esteem of their fellows (lacking social responsibility, simple fear is an adequate motive) will conscientiously perform the lab cleanup tasks, a list of which is prominently displayed at the work place.
DATA ANALYSIS
You will use the Mathcad linear and nonlinear regression procedures developed for the "Determination of Rate Laws and Nonlinear Curvefitting" simulated data analysis. In this case we use only the first order model. Once the first order results are obtained for each different pH data set, the pseudo first order rate constants must be pooled and a suitable linear regression performed to find the second order rate constant and its relative standard deviation. You can see that data analysis in this case is a two step process: first the separate data sets must yield their apparent first order rate constants, and then those are combined to obtain (in a final regression) the second order rate constant.
THE REPORT
The general guidelines apply. In addition, respond to these requests:
The value of the report will be enhanced by preparing tables which present the regression parameters and their quality estimates obtained for each pseudo first order data set; the final regression results for the evaluation of the second order rate constant should be presented separately. Remarks and conclusions should be referenced to supporting evidence in the Mathcad document and accompanying tables.