= Solution
\b[The model allows unlimited column height without weakening the binding or reducing the upward rate as a column grows.] As $bp\to1^-$, successive heights become nearly equally probable and the mean height diverges. At $bp=1$, the putative height weights cannot even be normalized; for $bp>1$ they increase with height and no finite stationary uptake exists.
This is a condensation-like failure of the unbounded-layer idealization, rather than a monolayer reaching its capacity. Finite gas supply, finite geometrical capacity, altered layer binding and interactions can modify or limit the actual uptake. The divergent expression is an equilibrium result only below its convergence threshold.
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