Homogeneous equilibrium definition

The hole-size relationship between cations and crown ethers has been a part of the lore in the cation binding area for nearly two decades. Although, to our knowledge, no formal definition of this principle has ever been offered, the general concept seems to be that cation binding will be optimized when the cation diameter and macrocycle cavity size are identical. A simple consequence of this concept is the notion that 15-crown-5 is selective (binds more strongly) for Na+ over K+. We have measured the homogeneous (equilibrium) stability constants for the reaction... 

In the absence of the last two terms, we obtain w = [— stress-diffusion couphng. Finally, we remark that our dynamic model ensures the nonnegative definiteness of the heat production rate [10]. Then we can generally prove that the system tends to a homogeneous equilibrium state with W — I = V = w = 0 as t ->QO in the absence of macroscopic flow field. 

Sigma (a) bonds Sigma bonds have the orbital overlap on a line drawn between the two nuclei, simple cubic unit cell The simple cubic unit cell has particles located at the corners of a simple cube, single displacement (replacement) reactions Single displacement reactions are reactions in which atoms of an element replace the atoms of another element in a compound, solid A solid is a state of matter that has both a definite shape and a definite volume, solubility product constant (/ p) The solubility product constant is the equilibrium constant associated with sparingly soluble salts and is the product of the ionic concentrations, each one raised to the power of the coefficient in the balanced chemical equation, solute The solute is the component of the solution that is there in smallest amount, solution A solution is defined as a homogeneous mixture composed of solvent and one or more solutes. 

The definitions of enthalpy, H, Helmholtz free eneigy, A, and Gibbs free energy, G, also give equivalent forms of the fundamental relation (3) which apply to changes between equilibrium states in any homogeneous fluid system ... 

Hence, equilibrium constants of homogeneous electron-transfer reactions between (A) and B are evidently connected to the differences in reduction potentials of A and B. This connection reflects a definite physical phenomenon. Namely, if two redox systems are in the same solution, they react with each other until a unitary electric potential is reached. For the transfer of only one electron at room temperature, the following simplified equation can be employed ... 

Adsorbed films between two immiscible liquids. The question of the meaning of the term pn in the surface layer has been raised by Crax-ford, Gatty, and Teorell,2 without, however, coming to any very clear decision. Danielli s estimate was a very rough one, based on the application of the Donnan equilibrium between the surface layer and the interior, and suffers from the difficulties always attending an attempt to consider concentrations in the surface layer in a similar way to concentrations in a bulk phase the surface layer is not homogeneous. pH is closely related to, and is determined by, the electrochemical potential (see Chap. VIII, pp. 304 ff.), and this depends on the electrostatic potential, which varies rapidly at different levels near to the surface it appears possible that the only satisfactory definition of pa in the surface may be one which varies rapidly at different depths. The question appears one which would repay... 

As mentioned earlier, the state of a pure homogeneous fluid is fixed whenever two intensive thermodynamic properties are set at definite values. However, for more complex systems this number is not necessarily two. For example, a mixture of steam and liquid water in equilibrium at 101.33 kPa can exist only at 100°C. It is impossible to change the temperature without also changing the pressure if vapor and liquid are to continue to exist in equilibrium one cannot exercise independent control over these two variables for this system. The number of... 

When a pure liquid is placed in an evacuated bulb, molecules will leave the liquid phase and enter the gas phase until the pressure of the vapor in the bulb reaches a definite value, which is determined by the nature of the liquid and its temperature. This pressure is called the vapor pressure of the liquid at a given temperature. The equilibrium vapor pressure is independent of the quantity of liquid and vapor present, as long as both phases exist in equilibrium with each other at the specified temperature. As the temperature is increased, the vapor pressure also increases up to the critical point, at which the two-phase system becomes a homogeneous, one-phase fluid. 

A strict definition of a phase is a domain with a homogenous chemical composition and physical state (Atkins 1998). Typically, phase behavior is associated with equilibrium mixtures of hquid, vapor and solid phases in a mixture of two or more substances as a fimctiorr of temperature, pressure and compositiorr. hr fats, when discussing phases, it usually refers to their polymorphic form, sohd/hquid states, or compositionally differerrt ffactiorrs within a complex mixtrrre. Therefore, when phases of fats are discussed it is important to carefully define what is being used as the definition for... 

What we mean in this report by equilibrium and disequilibrium requires a brief discussion of definitions. Natural physicochemical systems contain gases, liquids and solids with interfaces forming the boundary between phases and with some solubility of the components from one phase in another depending on the chemical potential of each component. When equilibrium is reached by a heterogeneous system, the rate of transfer of any component between phases is equal in both directions across every interface. This definition demands that all solution reactions in the liquid phase be simultaneously in equilibrium with both gas and solid phases which make contact with that liquid. Homogeneous solution phase reactions, however, are commonly much faster than gas phase or solid phase reactions and faster than gas-liquid, gas-solid and... 

From the purely thermo-dynamic point of view one might be inclined to content oneself with the empirical composition of such a homogeneous mixture, since under given circumstances, e. g. of temperature and pressure, only one definite arrangement of matter is in equilibrium, and that is given by the quantitative composition. Still, as will be seen below, by working from molecular and atomistic conceptions, it is possible to develop laws, verified by experiment, which... 

The subsequent discussion is based on the theorem that all reactions in a homogeneous system come to a stop when a certain definite chemical equilibrium has been established between the substances which take part in the reaction. In other words, that such reactions never proceed so far that the substances entering into the reaction have disappeared entirely. All the... 

By purely thermodynamical methods we can now deduce the following theorem For every chemical reaction in a homogeneous system under constant external conditions e.g. under constant temperature and pressure, or constant temperature and volume) there is a certain function of the concentrations of the components (no matter how these are expressed) which has a definite constant value when equilibrium is established. We may therefore write... 

MTien several solid substances react with one another in presence of a solvent, the condition for equilibrium may be obtained as follows. In homogeneous solutions which contain definite, although possibly very minute, concentrations of all the molecules taking part in the reaction, the law of mass action will hold, provided that the concentrations are not too high. At constant temperature, however, the concentrations of all the substances which are present in the solid state are determined by their solubilities. The constant values of these concentrations may therefore be included in the equilibrium constant, like the vapour pressures of the solid substances in the calculations of the previous paragraph. For reactions between solids and solutions the law of mass action therefore assumes the same form as for homogeneous solutions, viz. ah... 

A catalyst is a substance that increases the rate at which a chemical reaction approaches equilibrium without, itself, becoming permanently involved in the reaction. The key word in this definition is permanently since there is ample evidence showing that the catalyst and the reactants interact before a reaction can take place. The product of this interaction is a reactive intermediate from which the products are formed. This substratexatalyst interaction can take place homogeneously with both the reactants and the catalyst in the same phase, usually the liquid, or it can occur at the interface between two phases. These heterogeneously catalyzed reactions generally utilize a solid catalyst with the interaction taking place at either the gas/solid or liquid/solid interface. Additional phase transport problems can arise when a gaseous reactant is also present in the liquid/solid system. 

---