Monte Carlo simulations of linear, weak polyacids and explicit simple ions have been performed in a spherical cell model to study the shift in the apparent dissociation constant. The simulations are performed in a canonical ensemble with the apparent dissociation constant calculated in a procedure based on Widom's particle-insertion method. The effects of model parameters are discussed, for example, the influence of various distances of closest approach, and the results are compared to experiments as well as simulations with effective pair-potentials between monomers, both the screened Coulomb potential and an extended version that takes into account a distance of closest approach between monomers and simple ions. Results of the latter potential are also compared to the experimental data, which are from poly(acrylic acid), poly-D,L-glutamic acid and carboxymethyl cellulose.