The kinetic energy distribution of electrons obtained from femtosecond pump/probe ionization of Na-2 is calculated. The pump laser pulse prepares a vibrational wave packet in the (1) Sigma(u)(+) double minimum potential of the molecule which serves as the initial state for subsequent ionization induced by absorption of another photon from the probe pulse. The time dependence of the electron kinetic energy distribution reflects details of the vibrational dynamics. In particular the splitting of the packet can be observed in the case when its mean energy equals the barrier height between the potential wells. The estimate of several molecular properties from a theoretical analysis of the electron spectra is carried through and discussed.