Abstract <p>When describing steady-state mass-transfer processes, time is often omitted in the main mass-transfer equation. Experimental data on the operation of mass-transfer equipment, however, also indicate the influence of phase contact time on the mass-transfer efficiency of internal contact devices. In this paper, the basic mass-transfer equation is presented in differential form and integrated together with the expressions of the material balance of the mass-transfer process in two phases for cross-flow tray contact devices, the hydrodynamic model of flow movement on which is close to ideal displacement for one of the phases and ideal mixing for the other. As a result, by means of transformations of the obtained equations, expressions for the Murphy efficiency for each of the phases on the specified type of contact devices, which establish a relationship between the mass-transfer efficiency and the parameters of the mass-transfer process and the consumptions of the phases, are obtained. The prognostic nature of the obtained dependences and their advantages over empirical expressions are indicated. The necessity of taking into account the time of the mass-exchange process, including steady-state, in order to determine the efficiency of the contact device is substantiated.</p>