The kinetics of a model of diffusion-influenced enzyme activation is studied in two spatial dimensions. Enzyme molecules diffuse and collide with an immobile, spherical, uniformly reactive receptor-ligand complex. Enzymes do not interact with each other, but interact with the complex via an interparticle potential. No hydrodynamic interactions are included. Inactive enzymes get activated upon collisions with the complex. Enzyme deactivation is modeled as a first-order kinetic process independent of diffusion and collisions, Exact expressions are derived for the steady-state number of active enzymes and for the Laplace transform of the time-dependent activation rate coefficient. The activation kinetics in the time domain can be calculated by numerical inversion of the kinetic expressions in Laplace space.