TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: Each esterification chamber is: separated from an adjacent electrolyte chamber by an anion exchange membrane and a cation exchange membrane, and each electrolyte chamber is formed between an anion exchange membrane and a cation exchange membrane; or separated from an adjacent electrolyte chamber by an anion exchange membrane, and a bipolar exchange membrane, and each electrolyte chamber is formed between an anion exchange membrane and a bipolar exchange membrane. The electrolyte and esterification chambers have a specified ordering sequence ABAB...A, where A represents an electrolyte chamber and B represents an esterification chamber. Each electrolyte chamber is formed between an anion exchange membrane, and either a bipolar exchange membrane or a cation exchange membrane.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The method further comprises the step of removing the raw biodiesel mixture from the esterification chambers and separating the fatty acid alkyl esters and glycerol. In the method: a portion of the hydroxyl anions and protons migrate to adjacent chambers, the migration of ions being facilitated by the electric potential applied across the EDICR anode and cathode; the biodiesel and glycerol are produced without the use of acid, base, or other homogeneous catalysts; the EDICR serves as a heterogeneous catalyst; the EDICR serves as a heterogeneous catalysts for the transesterification and esterification reactions; the portion of the protons and hydroxyl ions used for the esterification and transesterification reactions are produced by water splitting; the electric current applied to the EDICR provides the driving force for water splitting; the glycerol and biodiesel are produced without contamination from salts; and the glycerol and biodiesel produced in the EDICR can be purified. The EDICR serves as a heterogeneous catalyst for the transesterification and esterification reactions. Preferred Components: The IERW contains anion and cation moieties and the ratio between anion and cation moieties is 3:1-1:3. The glycerol and biodiesel are produced without contamination from salts. The electric current applied to the EDICR provides the driving force for water splitting. At least a portion of the protons and hydroxyl ions used for the esterification and transesterification reactions are produced by water splitting. EXAMPLE - Soybean oil (45 g) and methanol (9 g) were taken into glass beaker and heated to 40-45 degrees C. Two different types of membrane configuration of electrodeionization catalytic reactor stacks were assembled. The mixture of soybean oil and methanol was used in the reaction compartments and an ion conducting electrolyte was used in the other compartment. The water necessary for generation of the hydroxyl ions were supplied with the reaction mixture to give fatty acid alkyl esters.