Saponification Reaction to Determine Rate Constant

Reactors Lab HW assignment 2                                                                Jesse Braun

Determination of reaction order, activation energy and pre-exponential factor

Data was collected from the reaction of Sodium Hydroxide (NaOH) with Ethyl Acetate to produce Ethanol and Sodium Acetate (NaAc):

[pic 1]

As the reaction was occurring, total conductivity was measured at 30 second intervals up to 10 minutes. This was carried out at three different temperatures; 35°C, 40°C, and 50°C. From this data and previous calibration results obtained, the concentration was determined. This was done by the following equations where (m) is the slope obtained from the calibration curves previously calculated:

                                        (1)[pic 2]

                                        (4)[pic 3]

                                        (3)[pic 4]

                                        (4)[pic 5]

Equations (1)-(4) can be used in conjunction to find the concentration of NaOH based on the total conductivity (Vtotal) as follows:

                                        (5)[pic 6]

Once the experimental concentration was determined from collected data, a calculated value for each time interval was created using the following equation:

                        (6)[pic 7]

Equation 6 can be derived from the rate equation for a batch reactor and is equation 7.15 in Essentials of Chemical Reactions Engineering. Utilizing equation (5) and (6), a NLLS regression technique was utilized in excel to produce values for both the reaction order (α) and rate constant (k). This same series of calculations and regression was done with the data collected at each temperature to obtain 3 different (k) values. The reaction order was seen to not change much between the different temperature experiments and staying relative around a value of 2 so that was chosen and held constant to give the best results for k variance with temperature. The results of these calculations are located in tables 2-4.

After determining values for reaction order and rate constant, the next step was to determine the pre-exponential factor (A) and activation energy (Ea) from the thermodynamic relationship for (k) as follows:

                                                (7)[pic 8]

Another NLLS regression was performed in excel using the experimental (k) values and those calculated based on temperature using equation (7) and values were obtained for both (A) and (Ea) which are located in Table 4. Another way used to calculate these values is to graph ln(k) as a function of 1/T and create a trend line. This was done to compare with the results from the NLLS regression and the results found were almost identical. These results are depicted in Table 5 and Graph 1. The graph trend line equation is used to determine the variables by the following set of equations:

                                                (8)[pic 9]

                        (9)[pic 10]

                                (10)[pic 11]

 The results from the experiment are presented in the Table 1 below, comparing them to those found in literature.  

[pic 12]

       Table 1: Experimental results compared to literature values

Using these results, and the results obtained from literature, a plot can be made to determine concentration of NaOH in a scaled up 1L batch reactor.

[pic 13][pic 14]

Experimental data collected and calculated

[pic 15]

      Table 2: Data obtained from experiment 1 at 35°C

[pic 16]

             Table 3: Data obtained from experiment 2 at 40°C

Trial 2 was picked to use further from the data in Table 2 due to error in running trial 1 in reading the conductivity correctly. This error resulted in a lower value for (k) then what was expected as well.

[pic 17]

 Table 4: Data obtained from experiment 3 at 50°C

[pic 18]

Table 5: Determination of Ea and A from rate constant change with temperature

[pic 19]

Graph 1: Relationship between rate constant as a function of temperature