Critical constants of mass diffusion through a membrane were related to a critical time, t(c)＇, which designates the conversion between transient and steady-state conditions of the diffusion process. The critical time t(c)＇, is precisely defined and analytically derived. In their dimensionless form, these critical constants depend solely on the Sherwood number (Sh). Values of dimensionless critical constants were determined for the whole range of Sherwood numbers. The results are useful in cases where small amounts of diffused mass must be detectable. E.g. : in production from hazardous materials, in the design and evaluation of diffusion experimental processes and devices. The effect of measurement errors on the determination of the critical constants is also analyzed. The main results show that the evaluation of the critical constants is obtained a with minimum errors? when experiments are being performed under convective boundary conditions (Sh > 100). The results of this study are applicable to heat transfer problems as well.