Property relationships chain rule

The simplest case of structure-property relationships are qualitative rules of thumb. For example, the statement that branched polymers are generally more biodegradable than straight-chain polymers is a qualitative structure-property relationship. 

All these variables qualify as state properties of a thermodynamic system. From the fundamental relationship (4.29), we infer from the chain rule that... 

For a system with constant composition, the two properties that we choose to constrain the state of the system become the independent properties. We can write the differential change of any other property, the dependent property, in terms of these two properties, as illustrated by Equation (5.4). From a combined form of the first and second laws, we developed the fundamental property relations. We then used the rigor of mathematics to allow us to form this intricate web of thermodynamic relationships. Included in the web are the Maxwell relations, the chain rule, derivative inversion, the cyclic relation, and Equations (5.22) through (5.24). A set of useful relationships relating partial derivatives with T, P, s, and v is summarized in Figure 5.3. We use these relationships to solve first- and second-law problems similar to those in Chapters 2 and 3, but for real fluids. 

A reaction mechanism is a sequence of elementary processes proposed to account for experimental kinetic results. Pure chemical kinetics proposes a classification of various types of mechanism (non-chain mechanisms, straight-chain and branched-chain mechanisms, etc.), establishes relationships between the properties of a global reaction and those of the elementary processes involved in the corresponding mechanism, and provides rules for writing a priori a reaction mechanism from a knowledge of the thermochemical and kinetic characteristics of the... 

The surface activity of a particular surfactant depends on the balance between its hydrophilic and hydrophobic properties. For the simplest case of a homologous series of surfactants, an increase in the length of the hydrocarbon chain as the series is ascended results in increased surface activity. This relationship between hydrocarbon chain length and surface activity is expressed by Traube s rule which states that in dilute aqueous solutions of surfactants belonging to any one homologous series, the molar concentrations required to produce equal lowering of the surface tension of water decrease three-fold for each additional CH2 group in the hydrocarbon chain of the solute . Traube s rule also applies to the interfacial tension at oil-water interfaces. 

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