Grain boundary embrittlement occurs when a solute enriches at a grain boundary and lowers its cohesive energy. While grain boundary enrichment is often attributed to equilibrium segregation effects, most models of embrittlement consider either the energetics of decohesion or the equilibrium adsorption at the boundary, but not both phenomena together. We develop a model for the change in cohesive energy of a grain boundary of a pure metal upon introduction of solute under conditions of equilibrium segregation prior to fracture. A heuristic grain boundary cohesion map is presented to delineate whether a given solute-solvent pair will exhibit weakening or strengthening of grain boundaries. The analysis helps to clarify that grain boundary embrittlement requires a solute that will both lower the cohesive energy of the boundary and segregate to it in the first place. The map reasonably captures known metal-metal embrittling pairs.