The paradox is well known that the residence time distribution (RTD) is not valid for the estimation of the conversion of a first-order reaction in an open tubular reactor. A case of delta-injection of reactive species into an open flow system is investigated theoretically in this paper. The analytical solution with the Laplace transform demonstrated that the conversion of a first order reaction is identical to that in a closed reactor under steady state. The effect of the background reactant concentration gradient addressed by the authors in a previous paper was employed to this case, and the numerical solution of the tracer dispersion based on this novel argument gave rise to a similar value of conversion, suggesting the validity of the concept and the significance of the subtle difference between RTDs determined with or without the presence of a background reactant in an open now system.