Reaction systems are a formal model for specifying and analysing computational processes in which reactions operate on sets of entities (molecules), providing a framework for dealing with qualitative aspects of biochemical systems. This paper is concerned with reaction systems in which entities can have discrete concentrations and reactions operate on multisets of entities, providing a succinct framework for dealing with quantitative aspects of systems. This is facilitated by a dedicated linear time temporal logic which allows one to express and verify a wide range of behavioural system properties. In practical applications, a reaction system with discrete concentrations may only be partially specified, and effective calculation of the missing details would provide an attractive design approach. To develop such an approach, this paper introduces reaction systems with parameters representing the unknown parts of the reactions. The main result is a method which attempts to replace these parameters in such a way that the resulting reaction system operating in a given external environment satisfies a given temporal logic formula. We provide a suitable encoding of parametric reaction systems in SMT, and outline a synthesis procedure based on bounded model checking for solving the synthesis problem. We also provide a complexity result of the synthesis problem and preliminary experimental results demonstrating the feasibility of the new synthesis method.