Collision-induced dissociation of (R1OH)Li+(R2OH) with xenon is studied using guided ion beam mass spectrometry. R1OH and R2OH include the following molecules: water, methanol, ethanol, 1-propanol, 2-propanol, and 1-butanol. In all cases, the primary products formed correspond to endothermic loss of one of the neutral alcohols, with minor products that include those formed by ligand exchange and loss of both ligands. The cross-section thresholds are interpreted to yield 0 and 298 K bond energies for (R1OH)Li+-R2OH and relative Li+ binding affinities of the R1OH and R2OH Ligands after accounting for the effects of multiple ion-molecule collisions, internal energy of the reactant ions, and dissociation lifetimes. We introduce a means to simultaneously analyze the cross sections for these competitive dissociations using statistical theories to predict the energy dependent branching ratio. Thermochemistry in good agreement;with previous work is obtained in all cases: In essence, this statistical approach provides, a detailed means of.correcting for the "competitive shift" inherent in multichannel processes.