A chemical-technological process of a second-order reaction in a chemical reactor of an ideal displacement, described by a nonlinear partial differential equation of the first order has been considered. Within the framework of the proposed model, the inverse problem of determining the rate constant of a chemical reaction was defined. In this case, an additional condition was set regarding the reagent concentration at the outlet from the reactor. To solve the inverse problem, its discrete analogue was constructed and a special representation was proposed for solving the resulting system of linear algebraic equations. As a result, an explicit formula for determining the approximate value of the rate constant of a chemical reaction was obtained. The possibilities of the proposed numerical method were illustrated by numerical calculations on model problems.