We present steady shear rheology data for sodium polystyrene sulfonate (NaPSS) in semidilute unentangled salt-free aqueous solution as a function of polymer concentration (c) and degree of polymerisation (N). The measured terminal modulus (G) agrees with the scaling prediction of G ≃ kBTc/N. The specific viscosity varies with the degree of polymerisation as ηsp ∝ N1.24±0.08. The observed dependence differs with the linear relation expected from the Rouse model for ideal chains as predicted by de Gennes' scaling model and subsequent theories. Together with the diffusion data of Oostwal et al., our results suggest that chains may follow non-Gaussian statistics beyond the correlation length (ξ). Small angle neutron scattering data on salt-free semidilute solutions at low polymer concentrations partially support this hypothesis but do not confirm it. The electrostatic Kuhn length of NaPSS salt-free solutions is found to be proportional and slightly larger than the correlation length (LK,e ≃ 1.3ξ). This result agrees well with the scaling model of Dobrynin et al. Radii of gyration (Rg) data as a function of polymer concentration reveal that a concentrated regime (Rg ∝ c0) does not occur for NaPSS in the concentration range considered (c ≲ 4M). We conclude by comparing the predictions of the scaling model of Dobrynin et al. and Muthukumar's double screening theory with viscosity data for different polyelectrolyte-solvent systems. Dobrynin's model provides a better description of experimental observations. Our findings confirm several aspects of current models for polyelectrolyte solutions but some deviations from theory remain.