A new cyclic model of a class of chemical engines is set up, in which not only finite-rate mass transfer and mass leakage but also the internal irreversibility resulting from friction, eddy currents and other irreversible effects inside the cyclic working fluid are taken into account. The influences of these irreversibilities on the performance of the cycle are revealed. The optimal relation between the power output and the efficiency of the cycle is derived. On the basis of the optimal relation, some optimal performances and important performance bounds of the cycle are determined and evaluated. For example, the maximum power-output and the corresponding efficiency, the maximum efficiency and the corresponding power output, the optimal mass-transfer time, the minimum rate of energy loss and so on are calculated and analyzed. The results obtained here cannot only enrich the application of thermodynamic theory but also provide some theoretical guidance for the effective application of energy resources and for the optimal design and development of a class of chemical engines. Moreover, some important conclusions relative to the isothermal endoreversible chemical engines, which have been investigated previously, can be directly deduced from the results in this paper.