The equilibrium thermochemistry of the alkali elements in cool dwarf atmospheres is investigated as part of a comprehensive set of chemical equilibrium calculations. The abundances of all important gases and the condensation temperatures of all initial condensates for Li, Na, K, Rb, and Cs are calculated as a function of pressure and temperature. Also discussed is the chemistry of refractory elements such as Al, Ca, Cr, Fe, Mg, Si, Ti, and V. The calculation of the alkali element and refractory element chemistry can help to constrain pressure and temperature conditions in dwarf atmospheres. A relative temperature scale is developed and compared to recent observations of the alkali elements in late-type dwarfs and brown dwarfs, such as the DENIS objects and Gliese 229B. The calculations show (1) Atomic Li gas abundances are expected to be lower than the bulk Li abundance because LiOH gas (at high total pressure) or LiCl gas (at low total pressure) form in very cool objects. Observations of only monatomic Li are therefore not a good test for the substellar nature of very cool objects. (2) The observations of atomic Cs in Gliese 229B can be understood by considering the distribution of Cs between atomic Cs and CsCl gases. (3) Liquid condensates, which may form solutions with complex compositions, form at higher pressures, and need to be considered in further atmospheric structure and opacity modeling.