**4. Conclusions**

This study developed the noncatalytic oleic acid esterification with ethanol using microwave irradiation for biodiesel production. The microwave-mediated esterification was more efficient than conventional-heating-based esterification. The oleic acid conversion decreased with increasing molar ratio of ethanol to oleic acid but increased by enhancing the temperature, reaction time, and microwave power levels. The high R<sup>2</sup> values of the second-order kinetic model were established in describing the esterification. In addition, a linear relation of microwave power to pre-exponential factors was observed, in which microwave power positively influenced the reaction. This work suggested that microwave-assisted noncatalytic esterification is an ecofriendly and energy-efficient approach for biodiesel synthesis.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1073/13/9/2167/s1, Figure S1: Kinetic model for calculating forward reaction rate constant of esterification of oleic acid with ethanol at different reactant molar ratios, Figure S2: Kinetic model for calculating forward reaction rate constant of esterification of oleic acid with ethanol at different temperatures, Figure S3: Kinetic model for calculating forward reaction rate constant of esterification of oleic acid with ethanol at different microwave power levels, Table S1: Forward reaction rate constant *k*<sup>1</sup> and equilibrium rate constant *Ke* for esterification using conventional heating.

**Author Contributions:** Conceptualization, H.C.N., H.C.O., and C.-H.S.; methodology, H.C.N., H.C.O., and C.-H.S.; validation, F.-M.W., K.K.D., and H.-Y.J.; formal analysis, H.C.N., F.-M.W., and K.K.D.; investigation, F.-M.W., K.K.D., T.T.P., H.-Y.J., and N.P.N.; resources, C.H.-S. and H.C.O.; writing—original draft preparation, H.C.N., H.C.O., and C.-H.S.; writing—review and editing, C.-H.S. and H.C.O.; supervision, C.-H.S. and H.C.O.; project administration, C.-H.S.; funding acquisition, C.-H.S. and H.C.O. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Ministry of Science and Technology of Taiwan, R.O.C.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

1. Nguyen, H.C.; Liang, S.-H.; Chen, S.-S.; Su, C.-H.; Lin, J.-H.; Chien, C.-C. Enzymatic production of biodiesel from insect fat using methyl acetate as an acyl acceptor: Optimization by using response surface methodology. *Energy Convers. Manag.* **2018**, *158*, 168–175. [CrossRef]


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