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The electrical conductivity is an important parameter in understanding the mechanism by which power is coupled to a radio-frequency (rf) discharge plasma, as well as in determining the external electrical characteristics of the discharge. We present the results of computations of the resistive and reactive components of the collisional impedance of an argon plasma at 13.56 MHz. The plasma conductivity is computed from the two-term solution to the Boltzmann equation, and includes the velocity dependence of the electron collision frequency, as well as non-Maxwellian electron energy distribution functions. We compare these results with those obtained from the widely used classical expression for plasma impedance, in which the electron collision frequency is computed either in the dc or high frequency limit. Our results show that neither of the classical limiting expressions are adequate for discharge pressures in the range of few mTorr to a few Torr, which includes the region of operation for many rf discharges used in many applications of plasma technology. Further, the classical formula assumes that in the high-frequency limit the plasma reactance is due entirely to electron inertia. We demonstrate that the plasma reactance may be strongly influenced, and in some cases dominated, by electron collisions. Results are presented in graphical form, which are useful in evaluating the importance of these effects on the interpretation of experimental results and the modeling of rf discharges.