We report results from a systematic simulational study of the ultimate mechanical strength of n-alkane glasses for carbon numbers n = 1, 2, 3, 4, 6, 8, 16, 24, and 48. The ultimate isotropic tensile strength was determined by constructing the equation of state of energy landscape for this homologous series. The tensile strength depends nonmonotonically on carbon number, exhibiting a maximum at n = 3. The mass density at which fracture occurs initially increases with chain length and then reaches a plateau value for n > 8. The predictions of the landscape equation of state are entirely consistent with results generated by a direct inherent structure deformation procedure. Although the ultimate isotropic tensile strength maximum at n = 3 would seem to contradict physical intuition regarding chain entanglement, we present a simple mean-field theory that reveals the underlying physics responsible for the tensile strength maximum, namely the simple competition between intermolecular interactions and intramolecular packing effects.