Homogeneous closed system

Rate of polymerization. The rate of polymerization for homogeneous systems closely resembles anionic polymerization. For heterogeneous systems the concentration of alkylated transition metal sites on the surface appears in the rate law. The latter depends on the particle size of the solid catalyst and may be complicated by sites of various degrees of activity. There is sometimes an inverse relationship between the degree of stereoregularity produced by a catalyst and the rate at which polymerization occurs. 

Consider a closed PVT system, either homogeneous or heterogeneous, of uniform T and P, which is in thermal and mechanical equilibrium with its surroundings, but which is not initially at internal equilibrium with respect to mass transfer or with respect to chemical reaction. Changes occurring in the system are then irreversible, and must necessarily bring the system closer to an equihbrium state. The first and second laws written for the entire system are... 

A thermodynamic system (closed system) is one that interacts with the surroundings by exchanging heat and work thru its boundary an isolated system is one that does not interact with the surroundings. The state of a system is determined by the values of its various properties, eg, pressure, volume, internal energy, etc. A system can be composed of a finite number of homogeneous parts, called phases, or there can be a single phase. For some applications, it may... 

The rate of a reaction is the number of units of mass of some participating reactants that is transformed into a product per unit time and per unit volume of the system. The rate of a closed homogeneous reaction (that is, no gain or loss of material during the reaction) is determined by the composition of the reaction mixture, the temperature, and pressure. The pressure from an equation of state can be determined together with the temperature and composition. 

Hydrogeochemical reactions involving only a single phase are called homogeneous, whereas heterogeneous reactions occur between two or more phases such as gas and water, water and solids, or gas and solids. In contrast to open systems, closed systems can only exchange energy, not constituents, with the environment. 

Irreversible processes of phase transfer and chemical reaction within a closed system, whether homogeneous (a single phase) or heterogeneous (more than one phase), lead to T djS > 0. At equilibrium, T djS = 0. For fixed S and V constraints, dE = —T djS. A reversible process corresponds to zero internal entropy change and a minimum in dE. 

The dynamic population balance equation for a closed homogenous system considering a single characteristic size is written. 

Next, we want to find the general solution for the system of homogeneous linear equations for the closed polyene chain with N atoms yielding the Nth degree secular equation... 

The internal energy f/ of a closed homogeneous system of constant composition is described by... 

The internal energy U and the enthalpy // of a closed homogeneous system of constant composition are described by the internal state variables p, V and T which are related to each other via the equation of state. 

From the reversible cyclic process carried out in a closed homogeneous system by combination of infinite number of consecutive carnot cycles it follows that ... 

In the case of closed homogeneous system the following relations apply to changes in amount of reaction component... 

Up to this point, with minor exceptions, we have discussed only closed systems, that is, systems having a fixed composition, and have for the most part not bothered to consider whether the system was homogeneous (one phase) or heterogeneous (more than one phase). We must now explicitly consider the implications of having more than one phase, and of the transfer of matter between phases and into and out of the system. 

We shall first consider a closed, homogeneous system in which a single chemical reaction occurs. Using the notation of Sec. 3-5, we may write the expression of a general chemical reaction involving r chemical substances in the form... 

We now consider a closed homogeneous system in which several reactions may occur. We consider a set of s reactions... 

The change in the free energy of a closed homogeneous system in which a chemical reaction is taking place may be written in the form... 

In this section, the general theory of chemical equilibrium is applied to a closed, homogeneous system comprising a real-gas mixture of r components. The approximations inherent in the law of mass action are also indicated. 

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