Aerosol particle reactions with vapor molecules and molecular clusters are often collision rate limited, hence determination of particle-vapor molecule and particle-molecular cluster collision rates are of fundamental importance. These collisions typically occur in the mass transfer transition regime, wherein the collision kernel (collision rate coefficient) is dependent upon the diffusive Knudsen number, KnD. While this alone prohibits analytical determination of the collision kernel, aerosol particle- vapor molecule collisions are further complicated when particles are non-spherical, as is often the case for particles formed in high temperature processes (combustion). Recently, through a combination of mean first passage time simulations and dimensional analysis, it was shown that the collision kernel for spherical particles and vapor molecules could be expressed as a dimensionless number, H, which is solely a function of KnD. In this work, it is shown through similar mean first passage times and redefinitions of H and KnD that the H(KnD) relationship found for spherical particles applies for particles of arbitrary shape, including commonly encountered agglomerate particles. Specifically, it is shown that to appropriately define H and Kn D, two geometric descriptors for a particle are necessary: its Smoluchowski radius, which defines the collision kernel in the continuum regime (KnD→0) and its orientationally averaged projected area, which defines the collision kernel in the free molecular regime (Kn D→). With these two parameters, as well as the properties of the colliding vapor molecule (mass and diffusion coefficient), the particle-vapor molecule collision kernel in the continuum, transition, and free molecular regimes can be simply calculated using the H(KnD) relationship.