Magnetic reconnection is believed to be the prime mechanism to trigger solar flares and accelerate electrons up to energies of MeV. In the classical two-dimensional reconnection model, the separation motion of chromospheric ribbons manifests the successive reconnection that takes place higher up in the corona. Meanwhile, downward traveling energetic electrons bombard the dense chromosphere and create hard X-ray (HXR) emissions, which provide a valuable diagnostic of electron acceleration. Analyses of ribbon dynamics and HXR spectrum have been carried out separately. In this Letter, we report a study of the comparison of reconnection electric field measured from ribbon motion and hardness (spectral index) of X-ray emission derived from X-ray spectrum. Our survey of the maximum average reconnection electric field and the minimum overall spectral index for 13 two-ribbon flares show that they are strongly anti-correlated. The former is also strongly correlated with flare magnitude measured using the peak flux of soft X-ray emissions. These provide strong support for electron acceleration models based on the electric field generated at reconnecting current sheet during flares.