An organic droplet containing thymol acetate (TA) floating on a sodium dodecyl sulfate aqueous phase was examined to develop a novel self-propelled object based on reaction kinetics. Two types of oscillatory motion, without back-and-forth motion (Osc I) and with back-and-forth motion (Osc II), were observed by varying the pH of the aqueous phase. The oscillation frequency reached its maximum at pH 9.6, coinciding with the occurrence of Osc II. The kinetics of the hydrolysis of TA as a reactant and the acid-base equilibrium between thymol (TOH) and the thymolate ion (TO-) as products were evaluated experimentally. The driving force of motion was discussed on the basis of the interfacial tension. The pH dependence of the oscillation frequency and the selection of Osc I or II were attributed to the equilibrium between the TOH and TO-. These results highlight the possibility of designing self-propulsion systems by considering reaction kinetics and chemical properties.