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We construct a theoretical model to describe the dynamics of a charged particle undergoing a dissociation reaction on its surface in a weak electrolyte solution.  Theoretical analysis and numerical simulations of the model reveal that phoretic motion of the particle emerges in response to a concentration gradient of the electrolyte.  In our model the concentration gradient cannot generate an electric field in the bulk far from the particle, because the solute is an undissociated (neutral) electrolyte.  However, the dissociation reaction with the solute yields asymmetric charge distribution, which gives rise to net force on the particle and leads to directional motion of the particle.  We show that the direction of the particle motion changes depending on the ratio of the particle radius to the Debye screening length and the ratio of the permittivity of particle to that of dispersion medium.  We also discuss the possibility of self-phoretic motion of the particle under no concentration gradient.