The present disclosure relates to chemical synthesis. The teachings thereof may be embodied in methods for chemical synthesis and/or reactors for synthesis. The teaching may increase the conversion of equilibrium-limited reactions in a single pass through a synthesis reactor. For example, a method may include: introducing a synthesis reactant into a reaction chamber with a prevailing pressure p1; forming a synthesis product; discharging the product and any unreacted reactant; separating the product from the unreacted reactant; and introducing the unreacted reactant into a second reaction chamber with a prevailing pressure p2 lower than the pressure p1.