Date:	April 9, 1998
To:	K.J. Sampson
From:	J.Q. Student
Subject:	Esterification of Butyric Acid with Methanol in the Sampson Reactor

Summary. This memo contains the results of recent experiments and analysis of the Sampson reactor located in the Unit Operations Laboratory in Stocker Center. A total of 13 experimental runs were completed at different temperatures and with different feed compositions, in order to establish the characteristics of this reaction. The results indicate that the reaction rate can be expressed by the formula

R = k1[B][M] - k2[E]                                                                                     (1)

where R is the rate of consumption of butyric acid, k1 and k2 are the reaction rate constants, [B] is the butyric acid concentration, [M] is the methanol concentration, and [E] is the ester concentration. k1 has a value of 0.894 lit/min/mol at 210 °C with an activation energy of 34.3 kcal/mol/K. k2 has a value of 0.0035/min at 210 °C with an activation energy of 25.7 kcal/mol/K. Heat effects were not quantified, however it appears that the reaction is nearly athermal, as expected [1]. The reactor temperature followed the jacket temperature to within 2 °C at all times after the initial heat-up phase was complete. The Sampson reactor easily withstood the pressure generated during the experiments. The maximum pressure observed was 275 psi while the operating limit for the reactor is 650 psi.

Experimental Procedure. The standard Sampson reactor procedure was used for these experiments. After charging the raw materials and sealing the reactor, the jacket temperature controller was set at the desired value and the reactor temperature was monitored until the desired value was achieved to within 2 °C. At that point the reactant bundling board was removed and the rocker was turned on, initiating the reaction. Samples were withdrawn at ten minute intervals and analyzed using a Hightower Model 45 mass spectrometer. The concentration of E as a function of time was then fit, using multiple linear regression, to a second order polynomial. Finally, the polynomial was differentiated and evaluated at zero time yielding an estimate of the initial reaction rate.

Results. The complete set of experimental conditions and results is listed in Table 1. The method of initial rates was used to isolate the forward and reverse reactions. The method of excess was used to isolate the concentration effects for the forward reaction in runs 1-6. The reverse reaction order was determined in runs 7-9. The activation energies were determined by repeating the experiments at three different temperatures in runs 1,4, 7, and 10-13. Concentration vs. time data are given elsewhere [2]. Table 1 reports the initial concentrations, temperature, initial reaction rate, the correlation coefficient for the curve fit, and estimated values of the rate constants.

Table 1. Experimental Results

Run	Initial Concentrations				Temperature	Initial	Curve	Forward	Reverse
	(mol/lit)				(° C)	Rate	Fit	Rate	Rate
						(mol/lit/min	R2	Constant	Constant
	[B]	[M]	[E]	[I]		x 1000)		(lit/min/mol)	(1/min)

1	0.87	0.018	0.0	0.0	210	0.172	0.975	11.0
2	0.87	0.012	0.0	0.033	210	0.115	0.964	11.0
3	0.87	0.006	0.0	0.066	210	0.065	0.978	12.4
4	0.036	0.78	0.0	0.0	210	0.394	0.956	14.0
5	0.024	0.78	0.0	0.045	210	0.222	0.876	11.8
6	0.012	0.78	0.0	0.090	210	0.140	0.988	15.0
7	0.0	0.0	0.69	0.0	210	-0.0131	0.976		0.0190
8	0.0	0.0	0.46	0.55	210	-0.0086	0.989		0.0156
9	0.0	0.0	0.23	1.10	210	-0.0043	0.991		0.0187
10	0.87	0.018	0.0	0.0	190	0.089	0.967	5.68
11	0.87	0.018	0.0	0.0	230	0.360	0.967	23.0
12	0.0	0.0	0.69	0.0	190	-0.0067	0.938		0.00971
13	0.0	0.0	0.69	0.0	230	-0.0280	0.978		0.0406

The concentration dependence was found to be first order in all three species. Figure 1 gives a plot of the initial reaction rate vs. concentration. The data was fit to a straight line for each species using linear regression, while forcing a zero intercept. The correlation coefficient was found to be 0.92 for species B, 0.94 for species M, and 0.93 for species E indicating an acceptable fit to the first order equation (straight line).

Rate constants were then calculated from

k1 = R/([B][M])                                                                                     (2)

for the forward reaction and

k2 = -R/[E]                                                                                     (3)

for the reverse reaction. Calculated values of the rate constants are listed in Table 1. Figure 2 gives an Arrhenius plot, from which the activation energies, 34.3 kcal/mol/K for the forward reaction and 25.7 kcal/mol/K for the reverse reaction, were calculated.

[1] Z.X. Zwyky, "Heat Effects for Various Esterifications," J. Cat., 14, 3456 (1956).

[2] J.Q. Student, ChE Unit Operations Laboratory Notebook, pp. 11-15 (1998).

(Last modified on 4/28/98)