This paper analyzes dynamic properties of hydrogen bonds in liquid water. We use molecular dynamics simulation to calculate different probability densities that govern the time evolution of the formation and rupture of hydrogen bonds. We provide analytical connections between these functions. Excellent agreement with our simulation results is observed. We prove transition state theory rate constant to be identical to the inverse of the associated mean first passage time (hydrogen bond lifetime). Hence, the analysis establishes its Arrhenius temperature dependence. We give the explicit relation between reactive flux correlation function for the relaxation dynamics of hydrogen bonds, and their first passage time probability densities. All the different observations in the existing literature, associated with various estimates of hydrogen bonding times in liquid water that are affected (or not affected) by particular bond criteria, as well as by different definitions of hydrogen bond lifetimes applied in simulation, can be easily reconciled within the framework of reactive flux correlation function approach.