Summability equation

Sumifix Supra dyes SUMKAEXCEL Sumisdex Sumitomo C KS500 Summability equation Sumycin Sun... 

This summability equation, the counterpart of equation 116, provides for the calculation of solution properties from partial properties. Differentiation of equation 122 yields equation 123 ... 

Since In y is a partial property with respect to G /RT the following form of the summability equation is vahd ... 

These clearly are not the same as the suggested expressions, which are therefore not correct. Note that application of the summability equation to the derived partial-property expressions reproduces the original equation for H. Note further that differentiation of these same expressions yields results that satisfy the Gibbs/Duhem equation, Eq. (11.14), written ... 

At high temperatures and low to moderate pressures the reacting species fonii an ideal-gas mixture. Apphcationof the summability equation to Eq. (11.26) yields ... 

Because qi is a partial property, tire summability equation applies ... 

All three quantities are for the same T, P, and physical state. Eq. (4-126) defines a partial molar property change of mixing, and Eq. (4-125) is the summability relation for these properties. Each of Eqs. (4-93) through (4-96) is an expression for an ideal solution property, and each may be combined with the defining equation for an excess property (Eq. [4-99]), yielding ... 

The summability relation (eq. 122) applied to the special case of an ideal solution is written as equation 194 ... 

Given equations that represent partial properties M, Mf, or Mf as functions of composition, one may combine them by the summability relation to yield a mixture property. Application of the defining (or equivalent) equations for partial properties then regenerates the given equations if and only if the given equations obey the Gibbs/Duhen equation. 

The summability and Gibbs/Duhem equations take on the following forms ... 

Equation (/7.70) is in fact just a special case of Eq. f71.9), obtained by setting = 7, wlriclr also makes ni = xi. Equations (11.11) and (11.12) on tire other hand are new and vital. Krrown as summability relations, tirey allow calculation of mixture properties from partial properties, playiirg a role opposite to that of Eq. f71.7), which provides for the calculation of partial properties from mixtme properties. 

This last equation demonstrates that In Ji is a partial property respect to ( /RT, implying also the validity of the summability reli... 

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