C4F7N is one of the most promising candidate to replace SF6 as arc quenching medium. Some buffer gases (N2 and CO2) are usually mixed with C4F7N to reduce the operating temperature. In order to provide priori knowledge of the arc quenching performance for C4F7N mixtures, the plasma properties including equilibrium compositions, thermodynamic properties, transport coefficients, and net emission coefficients (NEC) of C4F7N-N2 and C4F7N-CO2 arc plasmas are calculated and the effects of buffer gases are discussed. Taking these properties as input, a 1D arc decaying model is constructed to describe arc decaying characteristics. According to the evolution of axial temperature and arc conductance over time, the arc decaying process is divided into three stages, i.e. the thermal recovery stage, the pre-dielectric recovery stage, and the post-dielectric recovery stage. We focus on the first two stages and describe them by the thermal recovery time (or rate) and the pre-dielectric recovery time (or rate) respectively. According to the results of 1D arc decaying modelling, the descending order of the thermal recovery ability for the gases studied in this work is: SF6 > C4F7N > 75%C4F7N-25%N2 > 75%C4F7N-25%CO2 > 50%C4F7N-50%N2 > 25%C4F7N-75%N2 > 50%C4F7N-50%CO2 > CO2 > 25%C4F7N-75%CO2 > N2; and the pre-dielectric recovery ability is: N2 > SF6 > CO2 > 25%C4F7N-75%CO2 > 25%C4F7N-75%N2 > 50%C4F7N-50%CO2 > 75%C4F7N-25%CO2 > 50%C4F7N-50%N2 > 75%C4F7N-25%N2 > C4F7N.