The molecular oxygen dayglow emissions, O₂(a¹Δ_g → X³Σ_g) at 1.27 µm and O₂(b¹Σ_g → X³Σ_g) at 762 nm, arise in part from processes related to the Hartley band photolysis of ozone. It is therefore possible to derive daytime ozone concentrations from measurements of the volume emission rate of either dayglow. The accuracy to which the ozone concentration can be inferred depends on the accuracy to which numerous kinetic and spectroscopic rate constants are known, including rates which describe the excitation of molecular oxygen by processes that are not related to the ozone concentration. We find that several key rate constants must be known to better than 7% accuracy in order to achieve an inferred ozone concentration accurate to 15% from measurements of either dayglow. Currently, accuracies for various parameters typically range from 5% to 100%.