PARTIAL MOLAR PROPERTIES

Thermodynamic properties like E, H, S, A, and G change with a change in the mass of a system. It is an extensive property. These properties are derived using various equations and considered a closed system. Order to extend the results to an obtained open system, and here mass and composition vary. 

G.N. Lewis introduced a thermodynamic property, ‘X’ known as the partial molar property. Temperature and pressure are not the only functions of partial molar properties; also, a number of moles of components are present in the system.

Extensive thermodynamic properties ‘X’ is defined as,

\[\displaystyle \begin{array}{l}X=f\left( {P,T,{{n}_{1}},{{n}_{2}}....{{n}_{i}}} \right)------(1)\\\end{array}\]

n1,n2.....ni = number of moles of various components 1, 2………i in the system.

Above equation (1) differentiation as,

\[\displaystyle \begin{array}{l}dX={{\left( {\frac{{\partial X}}{{\partial T}}} \right)}_{{P,{{n}_{1}},{{n}_{2}}}}}dT+{{\left( {\frac{{\partial X}}{{\partial P}}} \right)}_{{T,{{n}_{1}},{{n}_{2}}}}}\partial P+{{\left( {\frac{{\partial X}}{{\partial {{n}_{1}}}}} \right)}_{{T,P,{{n}_{2}}}}}\partial {{n}_{1}}+{{\left( {\frac{{\partial X}}{{\partial {{n}_{2}}}}} \right)}_{{T,P,{{n}_{1}}}}}\partial {{n}_{2}}+.....+{{\left( {\frac{{\partial X}}{{\partial {{n}_{i}}}}} \right)}_{{T,P,{{n}_{1}},{{n}_{2}}}}}\partial {{n}_{i}}----(2)\\or\\dX={{\left( {\frac{{\partial X}}{{\partial T}}} \right)}_{{P,{{n}_{1}},{{n}_{2}}}}}dT+{{\left( {\frac{{\partial X}}{{\partial P}}} \right)}_{{T,{{n}_{1}},{{n}_{2}}}}}\partial P+\overline{{{{X}_{1}}}}d{{n}_{1}}+\overline{{{{X}_{2}}}}d{{n}_{2}}+..........+\overline{{X{}_{i}}}d{{n}_{i}}-------(3)\\\text{Here,}\\\overline{{{{X}_{1}}}}={{\left( {\frac{{\partial X}}{{\partial {{n}_{1}}}}} \right)}_{{T,P,{{n}_{2}}}}}-------(4)\\\overline{{{{X}_{2}}}}={{\left( {\frac{{\partial X}}{{\partial {{n}_{2}}}}} \right)}_{{T,P,{{n}_{1}}}}}--------(5)\\-----------\\-----------\\\overline{{X{}_{i}}}={{\left( {\frac{{\partial X}}{{\partial {{n}_{i}}}}} \right)}_{{T,P,{{n}_{1}},{{n}_{2}}}}}-------(6)\\Where,\overline{{{{X}_{1}}}},\overline{{{{X}_{2}}}},\overline{{X{}_{i}}}=\text{partial molar properties for the constituents 1,2,3-------i}\text{.}\end{array}\]

The bar put over the symbol of any property denotes the partial molar property.

“Partial molar properties there is no appreciable change in the concentration at constant temperature and pressure if the addition of one mole of respective constituents and moles of other substance remaining constant.”

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Bhoomika Sheladiya

BSc. (CHEMISTRY) 2014- Gujarat University
MSc. (PHYSICAL CHEMISTRY) 2016 - School of Science, Gujarat University

Junior Research Fellow (JRF)- 2019
AD_HOC Assistant Professor-(July 2016 to November 2021)

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