Thermodynamic properties of nickel (II) orthophosphate Ni3(PO4)2

Abstract

In this work for the first time for nickel (II) orthophosphate Ni3(PO4)2 in the range of 298–1618 K temperature dependences of the key thermodynamic parameters are received: isobaric Ср and isochoric the Сv molar heat capacities, changes of an enthalpy ∆H, internal energy ∆U, entropy ∆S and energy of Gibbs ∆G. Isobaric heat capacity of nickel (II) orthophosphate was determined by Kellog-Kubaschewski method. As the basic in this work served of Maier-Kelley equation: Cp=A+BT+CT-2, where A, B and C– coefficients, and T– absolute temperature. Nickel (II) orthophosphate has the only crystal modification and up to the temperature of the melting does not undergo any phase transformations.From this it follows that the probability of the abnormal course of a curve on graphic dependence of Ср on T is low. Using of Kellog-Kubaschewski method, we received a equation: Cp=291.05+64.73· 10-3T-5.46·106T-2. The temperature dependence of isochoric heat capacity of Сv for the chosen phosphate was determined by Magnus-Lindeman method. The equation is as a result received: Сv=291.05+64.73· 10-3T-5.46· 106T-2-1.21· 10-3T3/2. Using the known functions, for the first time for Ni3(PO4)2 in the range of 298–1618 K it is received dependences of the important thermodynamic parameters: isobaric Ср and isochoric the Сv molar heat capacities, changes of an enthalpy ∆H, internal energy ∆U, entropy ∆S and energy of Gibbs ∆G. For example, at the room temperature 300 K of Ni3(PO4)2 has such parameters: Ср=249.80 J/(mol×K), Сv=243.51 J/(mol×K), ∆H=0.50 kJ/mol, ∆U=0.49 kJ/mol, ∆S=1.67 J/(mol×K), and ∆G= –0.002 kJ/mol. At temperature 700 K, corresponding to the classical Dulong-Petit limit of nickel (II) orthophosphate has such thermodynamic properties: Ср=325.22 J/(mol×K), Сv=302.81 J/(mol×K), ∆H=119.47 kJ/mol, ∆U=113.93 kJ/mol, ∆S=249.40 J/(mol×K), and ∆G= –55.12 kJ/mol. In a melting point of Ni3(PO4)2 at 1618 K has: Ср=393.70 J/(mol×K), Сv=314.95 J/(mol×K), ∆H=451.09 kJ/mol, ∆U=400.87 kJ/mol, ∆S=548.16 J/(mol×K), and ∆G= –435.83 kJ/mol. From the received results follows that nickel (II) orthophosphate at temperatures 298–1618 K has rather high thermodynamic stability. It, in turn, allows recommending it for high-temperature use.The received sizes are also important for the subsequent thermodynamic calculations and can form a scientific basis for modeling of phase equilibrium in multicomponent systems with participation of Ni3(PO4)2.