Methyl acetate hydrolyzes to form acetic acid and methanol, according to the following reaction:
The reaction is extremely slow in pure water, but is catalyzed by both hydronium and hydroxide ions. In this experiment the kinetics of the reaction catalyzed by HCl will be studied.
Hydrolysis reactions of this type are reversible; the back reaction is called esterification. For any equilibrium the overall rate is the difference in rates of the forward and reverse reactions:
If, however, the reaction is not allowed to proceed very far to the right, the concentrations of products will be very small and the reverse rate term can be neglected. Thus, during the early stages of the reaction the rate law is written:
The reaction is first-order with respect to both methyl acetate and water and of order q (to be determined in the experiment) with respect to H3O+. For dilute solutions the [H2O] remains essentially constant during the reaction and equation (3) simplifies to
The [H3O+] also remains constant during the reaction, because the HCl is not consumed and its presence suppresses the ionization of acetic acid. Thus, the reaction is pseudo-first-order and equation (4) can be further simplified to give
where kH, the acid-dependent rate constant, is equal to kF'[H3O+]q. The value of q can be determined if kH is evaluated for more than one concentration of HCl.
The integrated form of the first-order rate law is
where C0 and Ct are the molar concentrations of methyl acetate initially present and at time t. The initial concentration (C0) is readily calculated from the known solution volumes and the density of methyl acetate. The value of Ct can be obtained by taking the difference between the initial concentration and the number of moles per liter of methyl acetate consumed at time t. From the stoichiometry of the reaction the number of moles per liter of methyl acetate consumed is equal to the number of moles per liter of acetic acid formed. At suitable time intervals during the reaction, aliquots of the solution are withdrawn and titrated with standard base. The number of moles of base is equal to the sum of the number of moles of HCl plus the number of moles of HC2H3O2 in the aliquot. The number of moles of HCl in each aliquot is constant and may be calculated from the concentration of HCl in the reaction mixture.
Equation 6 shows that the acid-dependent rate constant, kH, is the negative slope of a plot of ln(Ct)-versus-t. Because the slope will be the same if a quantity proportional to concentration is used in the log term, ln(nt)-versus-t can be plotted, where nt is the difference between the initial number of moles of methyl acetate and the number of moles of acetic acid at time t. Likewise, the titration volume data can be used directly, if the volume of base equivalent to the number of moles of methyl acetate is calculated.
Once q is known, the acid-independent rate constant kF' may be calculated. Evaluation of kF' at more than one temperature provides information about the activation parameters for the reaction. The Arrhenius equation,
may be integrated to give
A plot of ln kF' versus the reciprocal of the absolute temperature should be linear. The slope of the line is equal to the negative of Ea/R, where R is the gas constant and Ea is the Arrhenius activation energy. If only two temperatures, T1 and T2, are used, integration of (7) between fixed limits gives
from which Ea may be obtained directly.
According to the transition state theory, the rate constant of an elementary reaction is given by
where kB and h are Boltzmann's and Planck's constants, and K+ is similar to an equilibrium constant for the formation of the activated complex from the reactant molecules. It is possible to define the free energy of activation,, as
where and are the corresponding enthalpy and entropy of activation. Combination of equations (10) and (11), followed by differentiation with respect to temperature, gives for reactions in solution
which is similar in form to equation (7) with Ea equal to + RT. Once has been evaluated, may be calculated by using equations (10) and (11).
Note: Careful pipetting and titrating techniques are essential if good data are to be obtained. The temperature should be controlled as precisely as possible.
1. Obtain about 50 mL methyl acetate in a large test tube and 300 mL 1.0 M HCl in an Erlenmeyer flask. Allow these solutions to equilibrate in a 25oC bath. Also equilibrate a flask containing about 200 mL of deionized water.
2. Into a dry 250 mL Erlenmeyer flask pipet 50 mL of the HCl and 50 mL of water. To initiate the reaction add from a pipet 10 mL of methyl acetate. Start the timer when the pipet is half emptied. Mix the solution thoroughly and keep it in the bath.
3. As soon as possible, withdraw a 5 mL aliquot of the reaction mixture and transfer it to a 150 mL Erlenmeyer which contains approximately 50 mL of water. The receiver should be pre-chilled in an ice bath to make sure that the hydrolysis is sufficiently slowed. Note the time at which the pipet has been half emptied.
4. Titrate the diluted aliquot as soon as possible with standard NaOH using phenolphthalein as the indicator.
5. Repeat steps 3 and 4 at 10 minute intervals for one hour and for 20 minute intervals for another hour, if possible. Make sure that the pipet used to withdraw each 5 mL aliquot is clean and dry.
6. At some convenient time titrate 2 or 3 aliquots of the equilibrated HCl so that the molarity at 25oC will be known accurately.
Repeat the above procedure using 100 mL 1.0 M HCl and 10 mL methyl acetate as the reaction mixture. This reaction will proceed more rapidly, so aliquots should be withdrawn at shorter intervals. Duplicate runs should be performed if possible. An efficient student pair should be able to follow two or more properly spaced reactions at the same time.
Repeat the procedure at 35oC using the reaction conditions given in step 2. Remember that the rate will be about double that at 25oC, so aliquots will have to be withdrawn at shorter intervals. Determine the molar concentration of the HCl at 35oC.
As described in the Introduction, the progress of the reaction will be monitored by titrating aliquots of the solution at known time intervals. A Metrohm 702 Automatic Titrator will be used. It is equipped with a Brinkmann Fiber Optic Probe Colorimeter to detect the pink phenolphthalein endpoint. Information about these instruments can be found in Reference 1.
Successive aliquots will be added to the same titration vessel, which (except as noted in Steps 8 and II) will not be cleaned between titrations. This means that each aliquot will be added to a solution containing a small amount of excess NAOH from the previous titration. Because the titrator is programmed to stop adding base when a set %T value is reached (90.0%T for endpoint detection; 88.0%T to stop adding titrant), the error should be small. As in any kinetics experiment, the temperature should be controlled as precisely as possible.
1. Obtain about 30 mL of methyl acetate in a large test tube and about 200 mL 1.0 M HCI in a 250 mL Erlenmeyer flask. Allow these solutions to equilibrate in the constant temperature bath.
2. Into a dry 125 mL Erlenmeyer flask, pipet volumes of HCI and water, as specified in the Table below. Proceed to Step 3, while the flask is equilibrating in the water bath.
3. The HCI must be standardized at each reaction temperature. Why? This also provides an opportunity to become familiar with the titrator. Make sure that the titrator and the calorimeter are both turned on and that the method called 4411 is loaded (upper right comer of the titrator display). The filter wheel must be set to the 520 nm position. The piston should already be filled with standard NAOH. Be sure to record the concentration. Immerse the fiber optic probe tip in a beaker of water, and set the calorimeter Zero knob to 100%T.
4. Put about 100 mL of water and a stir bar into a 250 mL beaker and add about 4-6 drops of phenolphthalein. Immerse the dispensing tube and the fiber optic probe tip in the water, and adjust the stirring rate to a give efficient mixing, without vortexing around the probe tip (stable %T reading on the calorimeter meter).
5. To generate the initial pink color (i.e., a mock endpoint from a previous titration), set the dV/dt knob on the titrator to the 1 position. Press and release the DOS keypad, until the calorimeter meter reads about 80 %T. (Note: This is not critical, but if the %T is very low, it may be wise to prepare another solution.) Then press STOP to refill the piston.
6. Transfer 1.000 mL of the 1.0 M HCI to the titration vessel, and press the START keypad. At the end of the titration, record the endpoint volume on the display. The 4411 method specifies an initial dose of titrant close to the endpoint volume. For efficient work, it will be necessary to change this parameter to about 0.2 mL below the expected endpoint value. On the titrator handset, press PARAMETERS, and then press ENTER repeatedly, until "Start V: abs" appears. Press ENTER once more and then insert the desired volume. Press ENTER, followed by QUIT, QUIT to return to the operating mode. (Note: If the original Start V was too large, the titrator will never observe an endpoint, and the solution will contain too much excess base. Press STOP on the titrator, prepare a new titration solution, and decrease the Start V before proceeding.)
7. Obtain at least three more standardization results. (Note: If time is short, these titrations may be performed at convenient times during the kinetics runs.)
8. Before starting the kinetics run, decrease Start V to about 0.2 mL less than the value used for the standardizations. Why? If several titrations have been performed, it is advisable to prepare a fresh titration solution (Step4).
9. To initiate the reaction use a pipet to transfer 5.000 mL of methyl acetate to the equilibrated HCI/water solution. Start the timer when the pipet is half emptied. Mix the solution thoroughly and keep it in the bath.
10. As soon as possible, withdraw an aliquot (volume given in the Table) of the reaction mixture and transfer it to the titration solution. Record the time at which the pipet has been half emptied. Press START on the titrator, and record the volume when the endpoint is reached.
11. Repeat Step 10 at the approximate intervals specified in the Table. (Note: The pipet should not have to be cleaned between aliquots, but it may be desirable to draw the solution above the line and drain it back into the reaction mixture, before withdrawing the actual aliquot.) Because the titration volumes increase during the reaction (Why?), it will be desirable to change Start V frequently. The titration solution should be replaced after about five or six titrations, to make sure that the indicator does not become too dilute.
12. Repeat Steps 8-11 for the remaining kinetics runs specified in the Table (below). An efficient student pair should be able to follow two properly spaced reactions at the same time.
1. For each aliquot calculate Ct (or a quantity proportional to Ct). (The density of methyl acetate is 0.9273 g/mL at 25oC and 0.9141 g/mL at 35oC, and the molecular weight is 74.08.) Plot ln Ct versus t for each set of data. Evaluate the acid-dependent rate constant, kH, in seconds-1. Use the uncertainty in the slope to evaluate the 95% confidence limits of kH.
2. From runs at 25oC with different concentrations of HCl determine the order with respect to H3O+ and its uncertainty. Use the nearest whole-number value of q to calculate kF' for each run. Also obtain the uncertainty in kF'. (Assume negligible error in q for these calculations.)
3. Evaluate Ea, , and using the temperature dependence data.
Consult a good organic chemistry text for a plausible mechanism (or propose your own) for acid catalyzed hydrolysis. Show that the mechanism is supported by the rate law given by equation (4) using your nearest whole-number value of q.
1. Williams, K. R. Laboratory Manual for Introductory Analytical Chemistry; Fall, 1995 (or later edition); pp44-47.