Isochoric reactions

This result appears to be counterintuitive, especially since we normally allow the energy to depend on mole numbers, as specified by the relation E = E S, V, N( ). However, this problem is apparent rather than real from the viewpoint of chemistry the fundamental species in any chemical reaction are the participating atoms whose numbers are strictly conserved—witness the process of balancing any chemical equation. Thus, while the arrangement or configuration of the atoms changes in a chemical process their numbers are not altered in this process. Under conditions of strict isolation the system behaves as a black box no indication of the internal processes is communicated to the outside. One should not attempt to describe processes to which one has no direct access. However, under conditions illustrated in Remark 1.21.2, even an isochoric reaction carried out very slowly in strict isolation, produces an entropy change dS = dO = 1 Hi dNi > 0. See also Eq. (2.9.3) which proves Eq. (1.21.3) under equilibrium conditions. 

It should be mentioned that even in the absence of dipolar, polarizable, or ionic reaction partners, high electric fields may cause shifts in chemical distributions. Such a field effect requires, however, that the solvent phase has a finite temperature coefficient of the dielectric permittivity or a finite coefficient of electrostriction an additional condition is that the chemical reactions proceed with a finite reaction enthalpy (AH) or a finite partial volume change (A V). Electric field induced temperature and pressure effects of this type are usually very small they may, however, gain importance for isochoric reactions in the membrane phase. 

Looking at the isothermal-isobaric or isothermal—isochoric reaction, it can be concluded that under either constant pressure or constant volume, the thermal effect depends on the reaction temperature, as is described by Kirchhoff equations. In order to derivate them, the expressions for Qp and Qy must be differentiated, e.g. the equation for Qy is as follows ... 

Similarly to thermal effect, specific values are introduced the maximum work of the isothermal-isobaric reaction Lp ax and maximum work of isothermal-isochoric reaction Lvmax- These reactions must therefore take place in a system in contact with an environment of constant temperature in the case of an isothermal-isobaric reaction the pressure in the system must be equal to environmental pressure. Spontaneous chemical reaction tends to be an irreversible process and its implementation as a reversible transformation requires special conditions. 

The Van t Hoff isotherm establishes the relationship between the standard free energy change and the equilibrium constant. It is of interest to know how the equilibrium constant of a reaction varies with temperature. The Varft Hoff isochore allows one to calculate the effect of temperature on the equilibrium constant. It can be readily obtained by combining the Gibbs-Helmholtz equation with the Varft Hoffisotherm. The relationship that is obtained is... 

In order to illustrate this principle, let the effect of temperature on the equilibrium constant of an exothermic reaction, involving the oxidation of a metal to its oxides, be considered. Upon increasing the temperature of this reaction some of the metal oxides will dissociate into the metal and oxygen and thereby reduce the amount of heat released. This qualitative conclusion based on Le Chatelier s principle can be substantiated quantitatively from the Varft Hoff isochore. 

The deficiency can be made up, if no energy is added from the outside, only from the detonation products, with a resulting drop in their temperature from the isochoric adiabatic flame temperature. This may quench the chemical reaction. The deficiency diminishes with decrease of wave-front curvature. For point initiation , enough energy must be added from the outside to make up for the total deficit which accumulates during the time the wave is reaching a diameter at which the curvature drops below a critical value... 

A rational deduction of elemental abundance from solar and stellar spectra had to be based on quantum theory, and the necessary foundation was laid with the Indian physicist Meghnad Saha s theory of 1920. Saha, who as part of his postdoctoral work had stayed with Nernst in Berlin, combined Bohr s quantum theory of atoms with statistical thermodynamics and chemical equilibrium theory. Making an analogy between the thermal dissociation of molecules and the ionization of atoms, he carried the van t Hoff-Nernst theory of reaction-isochores over from the laboratory to the stars. Although his work clearly belonged to astrophysics, and not chemistry, it relied heavily on theoretical methods introduced by and associated with physical chemistry. This influence from physical chemistry, and probably from his stay with Nernst, is clear from his 1920 paper where he described ionization as a sort of chemical reaction, in which we have to substitute ionization for chemical decomposition. [81] The influence was even more evident in a second paper of 1922 where he extended his analysis. [82]... 

Equation (5) represents the variation of equilibrium constant with temperature at constant pressure. This equation is referred to as van t Hoff reaction isochore (Greek isochore = equal space), as it was first derived by van t Hoff for a constant volume system. Since AH is the heat of reaction at constant pressure, the name isochore is thus misleading. Therefore, equation (S) is also called as van s Hoff equation. 

M. Polanyi, Reaction isochore and reaction velocity from the standpoint of... 

The explosion of an industrial explosive is considered as an isochoric process, i.e. theoretically it is assumed that the explosion occurs confined in undestroyable adiabatic environment. Most formulations have a positive oxygen balance conventionally it is assumed, that only C02, H20, N2 and surplus 02 are formed. The reaction equation of the example above is then... 

In the case of isochoric explosion, the value for the energy of formation referring to constant volume has to be employed. The heat of explosion is the difference of the energies between formation of the explosive components and the reaction products, given in... 

The decomposition reactions of both detonation and powder combustion are assumed to be isochoric, i.e., the volume is considered to be constant, as above for the explosion of industrial explosives. 

From this expression it is possible, by making use of the reaction isochore, i.e.,... 

This is the well-known equation for the reaction isochore discovered by van t Hoff. The equation tells us qualitatively that the equilibrium constant increases with the temperature for endothermic reactions (0<0), and diminishes with the temperature for exothermic reactions (Q>0). In other words (since the products of the reaction are in the numerator of the constant), an increase in the temperature favours the production of the substances which are formed with absorption of heat. We can test the equation quantitatively if we assume the heat of reaction to be constant and integrate for a small range of temperature. This assumption is justified by experience, as the quantity... 

As an illustration of the use of the isochore in solution, we may now proceed with the Sixth Method of determining molecular weight Consider a substance not too soluble m a solvent, 1 e one for which a solution of maximum concentration, 1 e its solubility, obeys the gas laws Suppose that at a given temperature the solubility is jj, and at another temper tture T2 the solubility is sz In each case there is equilibnum between the solid phase and the saturated solution If the reaction, t e the process of solution, simply involves the transfer of 1 mole from the one phase to the other, we can regard the equilibrium finally reached... 

The important relation for our present purpose is the last one It shows that (on the basis of Nernst s Theorem) the sum of the integration constants of the vapour pressure curves which can be directly determined may be used to calculate the constant I for a given gaseous reaction, without actually carrying the reaction out at all We can thus rewrite the integrated form of the reaction isochore (viz equation (8)) in the form—... 

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