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The Rare-RI Ring (R3) is a recently commissioned cyclotron-like storage ringmass spectrometer dedicated to mass measurements of exotic nuclei far fromstability at Radioactive Isotope Beam Factory (RIBF) in RIKEN. The firstapplication of mass measurement using the R3 mass spectrometer at RIBF isreported. Rare isotopes produced at RIBF, $^{127}$Sn, $^{126}$In, $^{125}$Cd,$^{124}$Ag, $^{123}$Pd, were injected in R3. Masses of $^{126}$In, $^{125}$Cd,and $^{123}$Pd were measured whereby the mass uncertainty of $^{123}$Pd wasimproved. This is the first reported measurement with a new storage ring massspectrometery technique realized at a heavy-ion cyclotron and employingindividual injection of the pre-identified rare nuclei. The latter is essentialfor the future mass measurements of the rarest isotopes produced at RIBF. Theimpact of the new $^{123}$Pd result on the solar $r$-process abundances in aneutron star merger event is investigated by performing reaction networkcalculations of 20 trajectories with varying electron fraction $Y_e$. It isfound that the neutron capture cross section on $^{123}$Pd increases by afactor of 2.2 and $\beta$-delayed neutron emission probability,$P_\mathrm{1n}$, of $^{123}$Rh increases by 14\%. The neutron capture crosssection on $^{122}$Pd decreases by a factor of 2.6 leading to pileup ofmaterial at $A=122$, thus reproducing the trend of the solar $r$-processabundances. The trend of the two-neutron separation energies (S$_\mathrm{2n}$)was investigated for the Pd isotopic chain. The new mass measurement withimproved uncertainty excludes large changes of the S$_\mathrm{2n}$ value at$N=77$. Such large increase of the S$_\mathrm{2n}$ values before $N=82$ wasproposed as an alternative to the quenching of the $N=82$ shell gap toreproduce $r$-process abundances in the mass region of $A=112-124$.

First application of mass measurement with the Rare-RI Ring reveals the solar r-process abundance trend at A=122 and A=123