State of equilibrium

By convention, species to the left of the arrows are called reactants, and those on the right side of the arrows are called products. As Berthollet discovered, writing a reaction in this fashion does not guarantee that the reaction of A and B to produce C and D is favorable. Depending on initial conditions, the reaction may move to the left, to the right, or be in a state of equilibrium. Understanding the factors that determine the final position of a reaction is one of the goals of chemical thermodynamics. 

After each addition of titrant, the reaction between the analyte and titrant reaches a state of equilibrium. The reaction s electrochemical potential, Frxm therefore, is zero, and... 

To determine the equilibrium constant s value, we prepare a solution in which the reaction exists in a state of equilibrium and determine the equilibrium concentration of H3O+, HIn, and Im. The concentration of H3O+ is easily determined by measuring... 

If a sedimentation experiment is carried out long enough, a state of equilibrium is eventually reached between sedimentation and diffusion. Under these conditions material will pass through a cross section perpendicular to the radius in both directions at equal rates downward owing to the centrifugal field, and upward owing to the concentration gradient. It is easy to write expressions for the two fluxes which describe this situation ... 

It is an inference naturally suggested by the general increase of entropy which accompanies the changes occurring in any isolated material system that when the entropy of the system has reached a maximum, the system will be in a state of equilibrium. Although this principle has by no means escaped the attention of physicists, its importance does not seem to have been duly appreciated. Little has been done to develop the principle as a foundation for the general theory of thermodynamic equilibrium (my italics). ... 

The state of equilibrium differs from the equilibrium between water and pure water vapor in that, in a gas phase, there is also inert gas (dry air) present. This means that the water pressure is equal to the total gas pressure, p -- p, + ph, not to the water vapor pressure p, . 

In a state of equilibrium the chemical potentials of water and water vapor are equal ... 

It appears that the mean chain length (L) in a state of equilibrium polymerization depends essentially on the geometry constraints for sufficiently small T>. In contrast to recent theoretical predictions [47], which treat the... 

Principle of transmissibility. A force acting at a point on a body can be replaced by a second force acting at a different point on the body without changing the state of equilibrium or motion of the body as long as the second force has the same magnitude and line of action as the first. 

The vibration profile that results from motion is the result of a force imbalance. By definition, balance occurs in moving systems when all forces generated by, and acting on, the machine are in a state of equilibrium. In real-world applications, however, there is always some level of imbalance and all machines vibrate to some extent. This section discusses the more common sources of vibration for rotating machinery, as well as for machinery undergoing reciprocating and/or linear motion. 

The term balance means that all forces generated by, or acting on, the rotating element of a machine-train are in a state of equilibrium. Any change in this state of equilibrium creates an imbalance. In the global sense, imbalance is one of the most common abnormal vibration profiles exhibited by all process machinery. 

Redox reactions, like all reactions, eventually reach a state of equilibrium. It is possible to calculate the equilibrium constant for a redox reaction from the standard voltage. To do that, we start with the relation obtained in Chapter 17 ... 

We have seen that, qualitatively, the state of equilibrium for a system is characterized by the... 

A large amount of heat is absorbed in this reaction, 57.8 kcal/mole of water decomposed. If the temperature is lowered, the state of equilibrium is even more favorable to the production of water at room temperature than it is at 2273°K. Yet a mixture of hydrogen and oxygen can remain at room temperature for a long period without apparent reaction. Equilibrium is not... 

A new state of equilibrium is then attained in which more FeSCN+2 is present than was there before the addition of SCN-. Increasing the concentration of SCN- has increased the concentration of the FeSCN+2 ion. This is in accord with Le Chatelier s Principle. The change imposed on the system was an increase in the concentration of SCN-. This change can be counteracted in part by some Fe+3 and SCN- ions reacting to form more FeSCN+2. The same argument applies to an addition of ferric ion from a soluble ferric salt. In each case, the formation of FeSCN+s uses up a portion of the added reactant, partially counteracting the change. 

Now look at the numerical values of the equilibrium constants. The K s listed range from 10+1 to 10 16, so we see there is a wide variation. We want to acquire a sense of the relation between the size of the equilibrium constant and the state of equilibrium. A large value of K must mean that at equilibrium there are much larger concentrations present of products than of reactants. Remember that the numerator of our equilibrium expression contains the concentrations of the products of the reaction. The value of 2 X 10,s for the K for reaction (19) certainly indicates that if a reaction is initiated by placing metallic copper in a solution containing Ag+ (for example, in silver nitrate solution), when equilibrium is finally reached, the concentration of Cu+2 ion, [Cu+2], is very much greater than the square of the silver ion concentration, [Ag+]2. 

What, specifically, is equal in a chemical reaction that has attained a state of equilibrium ... 

What about the state of equilibrium for the reaction represented by equation (11)1 Let us place a strip of metallic copper in a zinc sulfate solution. No visible reaction occurs and attempts to detect the presence of cupric ion by adding H2S to produce the black color of cupric sulfide, CuS, fail. Cupric sulfide has such low solubility that this is an extremely sensitive test, yet the amount of Cu+2 formed cannot be detected. Apparently the state of equilibrium for the reaction (11) greatly favors the products over the reactants. 

The negative voltage shows that the state of equilibrium favors the reactants more than the products for the reaction as written. For standard conditions, the reaction will not tend to occur spontaneously. However, if we place Ag(s) in 1 M H+, the Ag+ concentration is not 1 M— it is zero. By Le Chatelier s Principle, this increases the tendency to form products, in opposition to our prediction of no reaction. Some silver will dissolve, though only a minute amount because silver metal releases electrons so reluctantly compared with H2. It is such a small amount, in fact, that no silver chloride precipitate forms, even though silver chloride has a very low solubility. 

It is found that after the elapse of a sufficient time interval, all reversible reactions reach a state of chemical equilibrium. In this state the composition of the equilibrium mixture remains constant, provided that the temperature (and for some gaseous reactions, the pressure also) remains constant. Furthermore, provided that the conditions (temperature and pressure) are maintained constant, the same state of equilibrium may be obtained from either direction of a given reversible reaction. In the equilibrium state, the two opposing reactions are taking place at the same rate so that the system is in a state of dynamic equilibrium. 

There are three different approaches to a thermodynamic theory of continuum that can be distinguished. These approaches differ from each other by the fundamental postulates on which the theory is based. All of them are characterized by the same fundamental requirement that the results should be obtained without having recourse to statistical or kinetic theories. None of these approaches is concerned with the atomic structure of the material. Therefore, they represent a pure phenomenological approach. The principal postulates of the first approach, usually called the classical thermodynamics of irreversible processes, are documented. The principle of local state is assumed to be valid. The equation of entropy balance is assumed to involve a term expressing the entropy production which can be represented as a sum of products of fluxes and forces. This term is zero for a state of equilibrium and positive for an irreversible process. The fluxes are function of forces, not necessarily linear. However, the reciprocity relations concern only coefficients of the linear terms of the series expansions. Using methods of this approach, a thermodynamic description of elastic, rheologic and plastic materials was obtained. 

The third approach is called the thermodynamic theory of passive systems. It is based on the following postulates (1) The introduction of the notion of entropy is avoided for nonequilibrium states and the principle of local state is not assumed, (2) The inequality is replaced by an inequality expressing the fundamental property of passivity. This inequality follows from the second law of thermodynamics and the condition of thermodynamic stability. Further the inequality is known to have sense only for states of equilibrium, (3) The temperature is assumed to exist for non-equilibrium states, (4) As a consequence of the fundamental inequality the class of processes under consideration is limited to processes in which deviations from the equilibrium conditions are small. This enables full linearization of the constitutive equations. An important feature of this approach is the clear physical interpretation of all the quantities introduced. 

A state of equilibrium which does not satisfy the conditions for true equilibrium is called a state of false equilibrium. A system may remain in a given state for a long period of time, and thus appear to be in an equilibrium state. A small change... 

States of equilibrium may also be classified into states of stable, unstable and neutral equilibrium, according as the system tends to return to its initial state, or to move further away from this state, or simply to remain in the altered state, when the displacing force is removed. Dynamical illustrations are afforded by a sphere resting at the bottom of a bowl, on the top of the inverted bowl, and on a smooth table respectively. 

By the variance, or number of degrees of freedom of the system, we mean the number of independent variables which must be arbitrarily fixed before the state of equilibrium is completely determined. According to the number of these, we have avariant, univariant, bivariant, trivariant,. . . systems. Thus, a completely heterogeneous system is univariant, because its equilibrium is completely specified by fixing a single variable— the temperature. But a salt solution requires two variables— temperature and composition—to be fixed before the equilibrium is determined, since the vapour-pressure depends on both. 

Since 0i(p,T), 02(p,T) depend only on T and p, and since these magnitudes remain constant during the change, it is evident that the total potential of the system has a stationary value in the equilibrium state the system therefore remains in equilibrium in its new state, and the state of equilibrium is neutral ( 49). 

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