Pull-off forces for chemically modified atomic force microscopy tips in contact with flat substrates coated with receptor molecules are calculated using a Johnson, Kendall, and Roberts contact mechanics model. The expression for the work of adhesion is modified to account for the formation of discrete numbers of chemical bonds (nbonds) between the tip and substrate. The model predicts that the pull-off force scales as nbonds1/2, which differs from a common assumption that the pull-off force scales linearly with nBonds. Periodic peak progressions are observed in histograms generated from hundreds of computed pull-off forces. The histogram periodicity is the signature of discrete chemical interactions between the tip and substrate and allows estimation of single-bond rupture forces. The effects of solvent, probe tip radius, and chemical binding probability on the detection of single-bond forces are examined systematically. A dimensionless parameter, the effective force resolution, is introduced that serves as a quantitative predictor for determining when periodicity in force histograms can occur. The output of model is compared to recent experimental results involving tips and substrates modified with self-assembled monolayers. An advantage of this contact mechanics approach is that it allows straightforward estimation of solvent effects on pull-off forces.