Interphase Mass Flux

This is the equation the rest of mass transfer exists to serve. A coefficient multiplied by a departure from equilibrium gives the moles crossing each square metre of interface every second, $N_A = K_y(y - y^*)$, and it has the same shape as Ohm's law and Fourier's law: a flux is a driving force divided by a resistance. Everything else in the field — the correlations, the dimensionless groups, the diffusivity estimates — is machinery for putting a number on one of the two terms on the right.

The driving force is a departure from equilibrium, not a concentration difference, and the distinction is the one that trips people. It is tempting to compare the solute in the gas with the solute in the liquid, but those are quantities in different phases and their difference means nothing physical; a solute can and routinely does move from a low concentration to a high one when equilibrium demands it. The starred term converts the liquid's actual composition into the gas composition that WOULD be in equilibrium with it, usually through Henry's law as $y^* = m x$, and the comparison is then legitimate because both quantities live in the same phase.

The subscript on the coefficient carries a second trap. $K_y$ is an OVERALL coefficient, which means $y^*$ must be in equilibrium with the BULK liquid, not with the interface. That is precisely what "overall" buys: both film resistances are absorbed into the coefficient so a bulk-to-bulk driving force can be used, and the interfacial compositions — which nobody can measure anyway — never have to be found. Pairing an overall coefficient with an interfacial driving force double-counts a resistance and understates the flux, and it is a common slip when a text switches between $k_y$ and $K_y$ without flagging it.

Finally, this flux applies at ONE POINT. The driving force changes continuously from the bottom of a column to the top, typically by a large factor, so multiplying a single flux by the total area is wrong except in a well-mixed vessel. Sizing equipment means either using the log-mean driving force, which is exact when both lines are straight, or integrating properly — which is exactly what the transfer-unit method does on your behalf. There is a fourth term hiding here too: the flux is per unit of INTERFACIAL area, and in a packed column or a bubble swarm that area is neither known nor easily measured, which is why the trade so often quotes the product $K_y a$ as a single lumped quantity per unit of column volume.