The formalism is developed for scattering of a molecule in a 2Π electronic state by an infinitely massive, uncorrugated surface. A general development of the electrostatic interaction potential is used to obtain matrix elements of the potential between molecular rotational and fine-structure states, described in an intermediate Hund’s coupling case. Explicit expressions for the inelastic S-matrix elements are derived in the energy sudden limit. Semiclassical (high J) expressions for the potential matrix elements and sudden S-matrix elements are obtained. This formal work is then used to make several general predictions for collisions of NO (X 2Π) with Ag(111), which has been recently studied experimentally. In particular, we predict: (1) for moderate to high values of the final rotational quantum number, the molecules will be scattered so that J lies in the plane of the surface, (2) in the energy sudden limit the F1 and F2 rotational manifolds will be equally populated by collisions, (3) and, again in the energy sudden limit, preferential population will occur in either the two Λ-doublet levels which are symmetric with respect to reflection of the NO electronic wave function in the plane of rotation or in the two levels which are antisymmetric with respect to this operation.