The solid-liquid equilibria of the Mg(NO3)(2)-Ln(NO3)(3) (Ln = La, Ce, Pr)-HNO3-H2O systems in the (similar to 21%) HNO3 regions at T= 298.15 K were studied by using the method of isothermal solubility, the phase diagrams were obtained based on the measured data. The Schreinemaker's wet residues method was used to determine the compositions of solid-phases. The three quaternary systems are all composed of three equilibrium solid-phases Mg(NO3)(2)center dot 6H(2)O, 3Mg(NO3)(2)center dot 2Ln(NO3)(3)center dot 24H(2)O, Ln(NO3)(3)center dot 6H(2)O. The new solid phase compounds 3Mg(NO3)(2)center dot 2La(NO3)(3)center dot 24H(2)O, 3Mg(NO3)(2)center dot 2Ce(NO3)(3)center dot 24H(2)O and 3Mg(NO3)(2)center dot 2Pr (NO3)(3)center dot 24H(2)O are congruently soluble in an average medium of similar to 21 mass% HNO3, and they were characterized by chemical analysis, X-ray diffraction (XRD), X-ray diffraction single crystal structure analysis, and thermogravimetric/differential thermogravimetric (TG-DTG) techniques. The XRD graphs of 3Mg (NO3)(2)center dot 2La(NO3)(3)center dot 24H(2)O, 3Mg(NO3)(2)center dot 2Ce(NO3)(3)center dot 24H(2)O and 3Mg(NO3)(2)center dot 2Pr(NO3)(3)center dot 24H(2)O are identical due to their isomorphic structure. The X-ray diffraction single crystal structure analysis show that 3Mg (NO3)(2)center dot 2Ln(NO3)(3)center dot 24H(2)O (Ln = La, Ce, Pr) all belong to hexagonal systems, with space group R-3, for 3Mg(NO3)(2)center dot 2La(NO3)(3)center dot 24H(2)O, a = b = 1.1082 +/- 0.0009 nm, c = 1.7422 +/- 0.0013 nm, V =1.853 +/- 0.002 nm(3), = 3.976 g.cm(-3), Z = 3, for 3Mg(NO3)(2)center dot 2Ce(NO3)(3)center dot 24H(2)O, a= b = 1.1056 +/- 0.0003 nm, c = 1.7438 +/- 0.0009 nm, V = 1.8462 +/- 0.0008 nm(3), Dc= 3.997 g.cm(-3), Z = 3, for 3Mg(NO3)(2)center dot 2Pr(NO3)(3)center dot 24H(2)O, a = b = 1.0992 +/- 0.0009 nm, c = 1.7211 +/- 0.0007 nm, V = 1.8012 +/- 0.0013 nm(3), D = 4.101 g.cm(-3), Z = 3. The Delta H-sol(m)theta(standard molar enthalpies of solution) of the compounds 3Mg(NO3)(2)center dot 2La(NO3)(3)center dot 24H(2)O, 3Mg (NO3)(2)center dot 2Ce(NO3)(3)center dot 24H(2)O and 3Mg(NO3)(2)center dot 2Pr(NO3)(3)center dot 24H(2)O in water (aq) were measured to be (107.96 +/- 0.74) kJ.mol(-1), (110.18 +/- .54) kJ.mol(-1) and (102.96 +/- 0.55) kJ.mol(-1), respectively, and their Delta H-f(m)theta, (standard molar enthalpies of formation) were calculated to be -(12242.6 +/- 2.5) kJ.mol(-1), -(12223.1 +/- 2.4) kJ.mol(-1) and -(12232.6 +/- 2.5) kJ.mol(-1), respectively. (C) 2016 Elsevier Ltd.