In this work, we introduce a kinetic model to study the effectiveness of ester-mediated amide bond formation under prebiotic conditions. In our previous work, we found that a simple system composed of α-hydroxy acids and α-amino acids is capable of forming peptide bonds via esterification followed by the ester-amide exchange reaction. To further understand the kinetic behavior of this copolymerization, we first tracked the growth of initial species from a valine/lactic acid mixture in a closed system reactor. A mathematical model was developed to simulate the reactions and evaluate the rate constants at different temperatures. We found these reactions can be described by the empirical Arrhenius equation even when reaction occurred in the solid (dry) state. Further calculations for activation parameters showed that the ester-mediated pathway facilitates amide bond formation by lowering activation entropies. These results provide a theoretical framework that illustrates why the ester-mediated pathway for peptide bond formation is efficient and why it would have been more favorable on the early Earth, compared to peptide bond formation without the aid of hydroxy acids.