2.3.2. Kinetic Study

To calculate the reaction rate, the samples from the Zn/CaO-mediated amidation of JO were withdrawn regularly every 10 min and then centrifuged to remove the catalyst; the rotary evaporated was used to remove any remaining amount of diethanolamine; and the samples were finally subjected to FTIR studies to analyze the fatty acid diethanolamide yield. As the reaction progressed, the intensity of the ester carbonyl peak at 1739 cm<sup>−</sup><sup>1</sup> decreased regularly, and the intensity of the fatty acid amide carbonyl band at 1617 cm<sup>−</sup><sup>1</sup> increased due to the conversion of triglyceride to corresponding amide (Figure S3, Supplementary Materials). The amidation of JO in the presence of Zn/CaO was found to follow pseudo-first-order kinetics, and the reaction rate constant (*k*) could be given as

$$\mathbf{k} = -\ln \| (1 - \chi\_{\rm FAD}) / \mathbf{t} \|,\tag{1}$$

where *XFAD* is the fatty acid diethanolamide yield at time *t*.

The kinetics of the Zn/CaO-catalyzed amidation of JO were studied at a 5:1 diethanolamine/JO molar ratio in the temperature range of 30–90 ◦C. The linear nature of the −ln(1 − *XFAD*) versus *t* (time) plots (Figure 6a) supported the idea that the reaction followed pseudo-first-order kinetics. The rate constant values were calculated as 0.171, 0.043, 0.019, and 0.011 min−<sup>1</sup> at 90, 70, 50, and 30 ◦C, respectively.

**Figure 6.** (**a**) Plot of −ln(1 − *XFAD*) versus *kt* at di fferent reaction temperatures for the 2-Zn/CaO-400-catalyzed aminolysis of JO. (**b**) The Arrhenius equation curve for the aminolysis of JO. Reaction conditions: diethanolamine/JO = 5:1 (m/m), catalyst amount = 4 wt%, temperature = 90 ◦C.

To calculate the activation energy (*Ea*) and the pre-exponential factor ( *A*) for the amidation reaction, an Arrhenius model was used, as given in Equation (2):

$$
\ln \text{k} = -E\_{\text{3}} / RT + \ln A\_{\text{\textdegree}} \tag{2}
$$

where *R* = the gas constant (8.31 J K−<sup>1</sup> mol−1), and *T* is the reaction process temperature in kelvin.

The values of *Ea* and *A* calculated from the graph between 1/*T* and ln *k* were found to be 47.8 kJ mol−<sup>1</sup> and 4.75 × 10<sup>8</sup> min−1, respectively (Figure 6b). The resulting activation energy (47.8 kJ mol−1) for the amidation of JO was observed within the range for the heterogeneous catalysis (33–84 kJ mol−1).

#### **3. Materials and Methods**

All chemical reagents were purchased from Sigma-Aldrich (St. Louis, MO, USA) and were used without further purification. Transition metal-doped CaO, MgO, and ZnO catalysts were synthesized in nanoparticle form by following a modified incipient-wetness impregnation method.
