Dynamic equilibrium state

A chemical equilibrium results when two exactly opposite reactions are occurring at the same place, at the same time and with the same rates of reaction. When a system reaches the equilibrium state the reactions do not stop. A and B are still reacting to form C and D C and D are still reacting to form A and B. But because the reactions proceed at the same rate the amounts of each chemical species are constant. This state is a dynamic equilibrium state to emphasize the fact that the reactions are still occurring—it is a dynamic, not a static state. A double arrow instead of a single arrow indicates an equilibrium state. For the reaction above it would be ... 

The extent to which DOM abundance and composition can be considered as end products of microbial activity rather than as drivers depends on the relationship between source dynamics and community response time. At one extreme, steady inputs, stable environmental conditions, and long residence time promote a dynamic equilibrium state in which DOM characteristics can be viewed as the product of source-activity interaction. At the other... 

At the equilibrium potential, a dynamic equilibrium state establishes, at which the rates of the forward and the back reactions are equal. 

Figure 3.1.3 The Ag/Ag+ electrode an example of a metal/metal ion electrode. The dynamic equilibrium state is shown (i.e. both the forward and back reaction proceed at the same rate).

In the equilibrium state, the anodic and cathodic partial reactions of an electrochemical reaction have equal rates. The system is in a dynamic equilibrium state, and no net reaction occurs. For example, when a copper sheet is immersed in copper sulfate solution, in the equilibrium state the anodic dissolution rate of copper from sheet to solution equals the cathodic deposition rate from the solution to the surface of the sheet. Theoretically, one can calculate the equilibrium state of an electrochemical reaction from thermodynamic values. This is the standard electrode potential, E°, or equilibrium potential of the electrochemical reaction. The standard electrode potential corresponds to a determined standard state of 0.1 MPa, 25 °C, activity of reactive species of 1 or ideal solution of 1.0 mol L-1, and equilibrium potential of any other state. 

Reversible chemical reactions lead to dynamic equilibrium states. What is dynamic about these states Why are they called equilibrium states ... 

Let us assume that in the atmosphere, or possibly in a certain bounded region of the atmosphere, there are M mass units of the components of interest. If F is the rate of its formation, i.e. supply into the atmosphere (or into the bounded region) and R the rate of its conversion or relea.se from the given region of the atmosphere, then for a dynamic equilibrium state it holds that F = R and the mean time of the residence t = Mf F = M/R. Thus, from the physical standpoint r is the time after which the given component could completely disappear from the atmosphere in the absence of its source. The data in the literature concerning the mean times of the residence are not uniform and values for particular components of the atmosphere are very variable (from several hours to several years). In Table 5.1 the most probable values of r are summarized for certain atmospheric components. 

In this dynamic equilibrium state, charged groups of the protein are almost always located at the surface of the native protein whereas the interior contains hydrophobic groups tucked away from the surrounding water molecules (Figure 1.3). When the protein is denatured it loses functionality and the coil expands as all groups are hydrated and the charge distribution becomes more even [29]. 

In contrast to chemical kinetics, which focuses on the rates of chemical reactions, chemical equilibrium focuses on the final state of reactions. It is defined as the state in which the concentrations of all the components reach a steady-state condition and no further changes occur macroscopically. That means there is no tendency toward changes in molecular concentrations or ion abundances, although they do change microscopically (dynamic equilibrium state). One should keep in mind that chemical equilibria must involve both forward and reverse reactions whereas chemical kinetics only concerns forward reactions. Contrary to the simple reaction represented in Equation 10.1, the equilibrium state involves both the forward and the reverse processes, for example ... 

The incident and reflected waves obtained with X-SiOx samples are shown in Figure 22.14A as a function of time. The positive portion indicates compressive waves and the negative portion denotes tensile waves. The transmitted wave is shown as the output signal. In an SHPB test, a dynamic equilibrium state, indicated by equal stresses applied on both ends of the specimen, must first be established. Such an experiment is then considered valid and the acquired experimental data are processed to deduce the dynamic stress-strain relationships. To examine the dynamic equilibrium condition, following either the first-wave (transmitted wave) or the second-wave (difference between incident wave and reflected wave) method [26, 66, 73], the front stress (at the end of the specimen in contact... 

Figure 22.14. Typical SHPB results. A. Oscilloscope recordings B. dynamic equilibrium state check and strain rate history.

As we can see, the motion of a polymer chain in a non-entangled melt, as represented by the Rouse-model, can be described as a superposition of 3ATr linearly independent Rouse-modes, corresponding to Nr modes in x-, y- and 2-directions respectively. In a dynamic equilibrium state all these Rouse-modes become thermally excited and it is instructive to calculate their mean-squared amplitudes. The displacement pattern of mode m is given by... 

To apply the concept of resilience to complex systems, such as cities, two approaches can be followed the resilience of ecosystems (a) and the engineering resilience (b). In the first, proposed and developed by Holling (1973, 1986, 2001), resilience can be defined as the ability of a system in dynamic equilibrium, subject to external shocks, to move back to a dynamic equilibrium state. On the contrary, engineering resilience, developed by Pimm and other authors (Pimm 1984 Bmneau et al. 2003) can be defined as the ability of a system to absorb an external shock and quickly return to the initial state. 

---