The heat capacities of (NH4)(2)PbCl6 and (ND4)(2)PbCl6 were measured at temperatures between 13 K and 300 K, A gradual phase transition was found at 77.8+/-0.3 K for (NH4)(2)PbCl6 with an associated transition entropy of 3.0 J K-1 mol(-1). The transition temperature shifted to 81.0+/-0.3 K in (ND4)(2)PbCl6. A sharp first order transition occurred at 38.40+/-0.03 K for (ND4)(2)PbCl6 accompanied by a transition entropy of 7.5 J K-1 mol(-1). There was no corresponding phase change in (NH4)(2)PbCl6. The mechanism of the deuteration-induced transitions in the present compound and similar transitions in (ND4)(2)TeCl6, (ND4)(2)PtCl6, (ND4)(2)PdCl6, and (ND4)(2)SeCl6 is discussed. Tunneling energies involved in the rotational motion of the ND4+ ion in the three-minimum potential were derived from the experimental entropy data, They correlate smoothly with the metal-chlorine bond distance for these five isomorphous compounds, Standard thermodynamic functions calculated from the heat capacity data are tabulated in the Appendix.