A calorimetric and thermodynamic investigation of two magnesium phosphates, MgHPO₄·3H₂O(cr) and MgKPO₄·6H₂O(cr), was undertaken. The synthesis of both phases was performed from magnesium chloride and potassium phosphate solutions at room temperature. The synthetic products were characterized by powder X-ray diffraction and X-ray fluorescence methods. The enthalpies of formation of both phases were determined using hydrofluoric acid solution calorimetry giving Δ_fH_m^o(T = 298.15 K, MgHPO₄·3H₂O,cr) = −2595 ± 3 kJ mol^–1 and Δ_fH_m^o(T = 298.15 K, MgKPO₄·6H₂O,cr) = −3718 ± 3 kJ mol^–1. The low-temperature heat capacity, C_p,m^o, was measured using adiabatic calorimetry from T = 6.1 to 324.6 K for MgHPO₄·3H₂O(cr) and from T = 5.9 to 329.0 K for MgKPO₄·6H₂O(cr). Using these C_p,m^o(T) data, the third law entropy at T = 298.15 K, S_m^o, is calculated as 212.9 ± 1.5 J K^–1 mol^–1 for MgHPO₄·3H₂O(cr) and 352.7 ± 2.1 J K^–1 mol^–1 for MgKPO₄·6H₂O(cr). These new experimental results, together with literature data, are used to calculate the Gibbs free energy of formation, Δ_fG_m^o, for both phases, giving Δ_fG_m^o(=298.15 K, MgHPO₄·3H₂O,cr) = −2292 ± 4 kJ mol^–1·and Δ_fG_m(T = 298.15 K, MgKPO₄·6H₂O,cr) = −3248 ± 4 kJ mol^–1. Smoothed C_p,m^o(T) values between 0 and 320 K are presented, along with the values for S_m^o and the functions [H_m^o(T) – H_m^o(0)] and [G_m^o(T) – H_m^o(0)], for both phases.

中文翻译：

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两种磷酸镁MgHPO ₄ ·3H ₂ O 和MgKPO ₄ ·6H ₂ O热力学性质的实验量热研究

对两种磷酸镁 MgHPO ₄ ·3H ₂ O(cr) 和 MgKPO ₄ ·6H ₂ O(cr) 进行了量热和热力学研究。两相的合成均在室温下由氯化镁和磷酸钾溶液进行。通过粉末X射线衍射和X射线荧光法对合成产物进行了表征。两相的形成焓使用氢氟酸溶液量热法测定，得到 Δ _f H _m ^o ( T = 298.15 K, MgHPO ₄ ·3H ₂ O,cr) = -2595 ± 3 kJ mol ^–1和 Δ _f H _m^o ( T = 298.15 K, MgKPO ₄ ·6H ₂ O,cr) = -3718 ± 3 kJ mol ^–1。低温热容量，Ç _p，米^ø，使用绝热量从测定Ť = 6.1至324.6 K中MgHPO ₄ ·3H ₂ O（CR）和从Ť = 5.9至329.0 K中MgKPO ₄ ·6H ₂ ö (cr)。使用这些C _{p ,m} ^o ( T ) 数据，T = 298.15 K 时的第三定律熵S _m ^o计算为 212.9 ± 1.5 JK^–1 mol ^–1对于 MgHPO ₄ ·3H ₂ O(cr) 和 352.7 ± 2.1 JK ^–1 mol ^–1对于 MgKPO ₄ ·6H ₂ O(cr)。这些新的实验结果与文献数据一起用于计算两相的吉布斯形成自由能 Δ _f G _m ^o，得到 Δ _f G _m ^o (=298.15 K, MgHPO ₄ ·3H ₂ O,cr ) = −2292 ± 4 kJ mol ^–1 ·和 Δ _f G _m ( T = 298.15 K, MgKPO ₄ ·6H ₂O,cr) = -3248 ± 4 kJ mol ^–1。显示了 0 到 320 K 之间的平滑C _{p ,m} ^o ( T ) 值，以及S _m ^o的值和函数 [ H _m ^o ( T ) – H _m ^o (0)] 和 [ G _m ^o ( T ) – H _m ^o (0)]，对于两个相。