  We study diffusion-limited coalescence, A+A<-->A$, in one dimension, and
derive an exact solution for the steady state in the presence of a trap.
Without the trap, the system arrives at an equilibrium state which satisfies
detailed balance, and can therefore be analyzed by classical equilibrium
methods. The trap introduces an irreversible element, and the stationary state
is no longer an equilibrium state. The exact solution is compared to that of a
reaction-diffusion equation --- the habitual approximation method of choice.
The exact solution allows us to determine the rate coefficients in the
reaction-diffusion equation, without appealing to renormalization group
techniques.
