We present a phase field model which approximates a one-phase Stefan-like problem with a kinetic condition at the moving boundary, and which models a dissolution and precipitation reaction. The concentration of dissolved ions is variable on one side of the free boundary and jumps across the free boundary to a fixed value given by the constant density of the precipitate. Using a formal asymptotic analysis we show that the phase field model approximates the appropriate sharp interface limit. The existence and uniqueness of solutions to the phase-field model is studied. By numerical experiments the approximating behaviour of the phase-field model is investigated.