It is shown that the functioning of glass electrodes in heavy water reflects the same mechanism as that in light water, the quantitative difference being the isotope effect. The central process of this "dissociation mechanism" is an interfacial equilibrium between surface groups of the membrane glass and hydronium and/or alkali ions in the solution involving dissociated surface groups whose charge causes the ion activity-dependent potential of the glass. The dissociation mechanism thus differs from other explanations of the glass electrode functioning in that it is based on verified reactions and is not merely a theory. The common glass electrode mechanism in the isotopic solvents permits the understanding of empirical methods to determine pD ("deuteron effect") and pNa(D2O) ("deuterium oxide effect") in heavy water by the application of correction terms, delta(glass) and delta(glass,Na), which are added, respectively, to the apparent ("operational") pH(D )and the pNa-(H2O)(D2O) values measured by glass electrode cells calibrated in standard solutions in light water. The correction terms depend on glass properties and are not universal constants. delta(glass) is given by the heterogeneous dissociation constants of the surface groups and the subsurface diffusion potentials of the glass ("residual diffusion potential"), whereas delta(glass,Na) does not involve the residual diffusion potential. The different magnitudes of the correction terms predict that the sodium error of glass electrodes is smaller in heavy than in light water.