The concentration dependences of molar volume, thermal expansion coefficient, and interdiffusion coefficient for liquid lead–magnesium system

2008 ◽  
Vol 377 (3) ◽  
pp. 501-505 ◽  
Author(s):  
R.A. Khairulin ◽  
S.V. Stankus
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hongfang Hou ◽  
Wanjing Cui ◽  
Jiaojiao Chen ◽  
Lingzong Meng ◽  
Yafei Guo ◽  
...  

Densities of sodium arsenite (NaAsO2) aqueous solution with the molality varied from 0.19570 to 1.94236 mol·kg−1 at temperature intervals of 5 K from 283.15 to 363.15 K and 101 ± 5 kPa were measured by a precise Anton Paar Digital vibrating-tube densimeter. Apparent molar volumes (VΦ) and thermal expansion coefficient (α) were obtained on the basis of experimental data. The 3D diagram of apparent molar volume against temperature and molality and the diagram of thermal expansion coefficient against molality were generated. According to the Pitzer ion-interaction equation of the apparent molar volume model, the Pitzer single-salt parameters (βM,X0υ, βM,X1υ, βM,X2υ, and CM,Xυ, MX = NaAsO2) and their temperature-dependent correlation F(i, p, T) = a1 + a2ln (T/298.15) + a3(T − 298.15) + a4/(620 − T) + a5/(T − 227) (where T is temperature in Kelvin and ai are the correlation coefficients) for NaAsO2 were obtained for the first time. The predictive apparent molar volumes agree well with the experimental values, and those results indicated that the single-salt parameters and the temperature-dependent formula are reliable.


2020 ◽  
Vol 92 (10) ◽  
pp. 1673-1682
Author(s):  
Wanjing Cui ◽  
Hongfang Hou ◽  
Jiaojiao Chen ◽  
Yafei Guo ◽  
Lingzong Meng ◽  
...  

AbstractDensities of the sodium arsenate aqueous solution with the molality varied from (0.04165 to 0.37306) mol · kg−1 were determined experimentally at temperature intervals of 5 K from 283.15 K to 363.15 K and ambient pressure using a precise Anton Paar Digital vibrating-tube densimeter. The apparent molar volumes (Vϕ), thermal expansion coefficient (α) and partial molar volume $({\bar V_{\rm{B}}})$ were obtained based on the results of density measurement. The 3D diagram of apparent molar volume against temperature and molality as well as the diagram of thermal expansion coefficient and partial molar volume against molality were plotted, respectively. On the basis of the Pitzer ion-interaction equation of apparent molar volume model, the Pitzer single-salt parameters ($(\beta _{{\rm{M,X}}}^{(0)v},\beta _{{\rm{M,X}}}^{(1)v},{\rm{ }}\beta _{{\rm{M,X}}}^{(2)v}{\rm{ and }}C_{{\rm{M,X}}}^v,MX = N{a_3}As{O_4})$ and their temperature-dependent correlation F(i, p, T) = a1 + a2ln(T/298.15) + a3(T – 298.15) + a4/(620 – T) + a5/(T – 227) (where T is temperature in Kelvin, ai is the correlation coefficient) for Na3AsO4 were obtained on account of the least-squares method. Predictive apparent molar volumes agree well with the experimental values, and those results indicate that the single-salt parameters and their relational coefficients of temperature-dependence for Na3AsO4 obtained are reliable.


1964 ◽  
Vol 42 (10) ◽  
pp. 1857-1864 ◽  
Author(s):  
Alois Schauer

It is shown that a close relation exists between the temperature coefficient of lattice vibration frequencies and the thermal expansion coefficient. The basic equations[Formula: see text](νi being the frequency of the ith mode of vibration, T the temperature, Ci the Einstein function of frequency νi, γ the Grueneisen parameter, and β the volume thermal expansion coefficient) are derived and discussed for various temperature ranges.


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