A chemical processing system is disclosed for the automated dissolution, dispersing and reaction of chemicals, especially for synthesizing proteins. The system includes a plurality of storage cartridges containing a first chemical in fluid communication with a reservoir containing a second chemical to be reacted with the first chemical. Each cartridge includes a pump (e.g., a plunger) which operates by changing the internal volume of the cartridge. The pump permits bi-directional flow of the first chemical into and out of the reservoir and cartridge to promote mixing and reacting with the second chemical in the reservoir to produce a third chemical.