Dynamic equilibrium concentration

The fractional approach to the dynamic equilibrium concentration was defined as the SO2 concentration at a given time divided by the concentration at dynamic equilibrium. Representative results of the time dependence of the normalized SO2 concentration are shown in Figures 7 and 8. 

Dynamic equilibrium concentration of chain carriers (radicals), [R], generated by ionizing irradiation at the dose rate P, is defined by the second-order recombination kinetics ... 

Doi, M. and Edwards, S.F., 1978. Dynamics of concentrated polymer systems 1. Brownian motion in equilibrium state, 2. Molecular motion under flow, 3. Constitutive equation and 4. Rheological properties. J. Cheni. Soc., Faraday Trans. 2 74, 1789, 1802, 1818-18.32. 

All of us are familiar with the process of vaporization, in which a liquid is converted to a gas, commonly referred to as a vapor. In an open container, evaporation continues until all the liquid is gone. If the container is closed, the situation is quite different. At first, the movement of molecules is primarily in one direction, from liquid to vapor. Here, however, the vapor molecules cannot escape from the container. Some of them collide with the surface and reenter the liquid. As time passes and the concentration of molecules in the vapor increases, so does the rate of condensation. When the rate of condensation becomes equal to the rate of vaporization, the liquid and vapor are in a state of dynamic equilibrium ... 

The molar solubility of a substance is its molar concentration in a saturated solution. A saturated solution is one in which the dissolved and undissolved solute are in dynamic equilibrium with each other. 

Almost all aquatic organisms rely on the presence of dissolved oxygen for respiration. Although oxygen is nonpolar, it is very slightly soluble in water and the extent to which it dissolves depends on its pressure. We have already seen (in Section 4.2) that the pressure of a gas arises from the impacts of its molecules. When a gas is introduced into the same container as a liquid, the gas molecules can burrow into the liquid like meteorites plunging into the ocean. Because the number of impacts increases as the pressure of a gas increases, we should expect the solubility of the gas—its molar concentration when the dissolved gas is in dynamic equilibrium with the free gas—to increase as its pressure increases. If the gas above the liquid is a mixture (like air), then the solubility of each component depends on that component s partial pressure (Fig. 8.21). 

The diversity of these subcellular actin structures is remarkable and appears to be determined by the interactions of many actin-binding proteins (ABPs) as well as by changes in the concentrations of intracellular signaling molecules such as Ca and cAMP, by small GTP-binding proteins, and by signals arising from mechanical stress. Approximately 50% of the actin molecules in most animal cells are unpolymerized subunits in the cytosolic pool and exist in a state of dynamic equilibrium with labile F-actin filamentous structures (i.e., new structures are formed while existing structures are renewed) (Hall, 1994). 

Suppose that B is highly reactive. When formed, it rapidly reverts back to A or transforms into C. This implies kr > kf and ks kf. The quasi-steady hypothesis assumes that B is consumed as fast as it is formed so that its time rate of change is zero. More specifically, we assume that the concentration of B rises quickly and achieves a dynamic equilibrium with A, which is consumed at a much slower rate. To apply the quasi-steady h)rpothesis to component B, we set dbldt = 0. The ODE for B then gives... 

C02-0038. The photo shows a stoppered flask containing a highly concentrated salt solution with many salt crystals on the bottom. If the flask stands for a long time, some crystals become smaller while others grow in size, but the total mass of crystals remains constant. Explain what is happening at the molecular level in terms of a dynamic equilibrium. 

If the concentration of a solute is lower than its solubility, additional solute can dissolve, but once the concentration of solute reaches the solubility of that substance, no further net changes occur. Individual solute molecules still enter the solution, but the solubility process is balanced by precipitation, as Figure 12-6 illustrates. A saturated solution in contact with excess solute is in a state of dynamic equilibrium. For eveiy molecule or ion that enters the solution, another returns to the solid state. We represent d Tiamic equilibria by writing the equations using double arrows, showing that both processes occur simultaneously ... 

Several observations show that saturated solutions are at dynamic equilibrium. For example, if O2 gas enriched in the oxygen-18 isotope is introduced into the gas phase above water that is saturated with oxygen gas, the gas in the solution eventually also becomes enriched in the heavier isotope. As another example, if finely divided ciystalline salt is in contact with a saturated solution of the salt, the small crystals slowly disappear and are replaced by larger crystals. Each of these observations shows that molecules are moving between the two phases, yet the concentrations of the saturated solutions remain constant. 

Each gas establishes its own dynamic equilibrium with water. The concentration depends on the partial pressure of the gas in the atmosphere and on the value of its Henry s law constant at 25 °C. Recall from Chapter 5 that the partial pressure of any gas in a mixture is given by the mole fraction (X multiplied by total pressure. 

If a semipermeable membrane separates two identical solutions, solvent molecules move in both directions at the same rate, and there is no net osmosis. The two sides of the membrane are at dynamic equilibrium. The situation changes when the solutions on the two sides of the membrane are different. Consider the membrane in Figure 12-14a. which has pure water on one side and a solution of sugar in water on the other. The sugar molecules reduce the concentration of solvent molecules in the solution. Consequently, fewer solvent molecules pass through the membrane from the solution side than from the pure solvent side. Water flows from the side containing pure solvent to the side containing solution, so there is a net rate of osmosis. 

In the absence of other forces, osmosis continues until the concentration of solvent is the same on both sides of the membrane. However, pressure can be used to stop this process. An increase in pressure on the solution side pushes solvent molecules against the membrane and thereby increases the rate of transfer of water molecules from the solution side to the solvent side. Figure 12-14Z> shows that dynamic equilibrium can be established by increasing the pressure on the solution until the rate of solvent transfer is equal in both directions. 

The situation changes when there is a concentration imbalance. Figure 12-15 shows red blood cells immersed in solutions of different concentrations. When the fluid outside the cell has a higher solute concentration, the result is slower movement of water through the membrane into the cell. The net result is that water leaves the cell, causing it to shrink. When the fluid outside the cell has a lower concentration, movement of water into the cell increases. The extra water in the cell causes an increase in internal pressure. Eventually, the internal pressure of the cell matches the osmotic pressure, and water transport reaches dynamic equilibrium. Unfortunately, osmotic pressures are so large that cells can burst under the increased pressure before they reach equilibrium. 

The second part of Figure 14-1 shows a molecular view of what happens in the two bulbs. Recall from Chapter 5 that the molecules of a gas are in continual motion. The NO2 molecules in the filled bulb are always moving, undergoing countless collisions with one another and with the walls of their container. When the valve between the two bulbs is opened, some molecules move into the empty bulb, and eventually the concentration of molecules in each bulb is the same. At this point, the gas molecules are in a state of dynamic equilibrium. Molecules still move back and forth between the two bulbs, but the concentration of molecules in each bulb remains the same. 

Collisions between NO2 molecules produce N2 O4 and consume NO2. At the same time, fragmentation of N2 O4 produces NO2 and consumes N2 O4. When the concentration of N2 O4 is veiy low, the first reaction occurs more often than the second. As the N2 O4 concentration increases, however, the rate of fragmentation increases. Eventually, the rate of N2 O4 production equals the rate of its decomposition. Even though individual molecules continue to combine and decompose, the rate of one reaction exactly balances the rate of the other. This is a dynamic equilibrium. At dynamic equilibrium, the rates of the forward and reverse reactions are equal. The system is dynamic because individual molecules react continuously. It is at equilibrium because there is no net change in the system. 

Vapor pressure provides a simple illustration of why adding a pure liquid or solid does not change equilibrium concentrations. Recall from Chapter H that any liquid establishes a dynamic equilibrium with its vapor, and the partial pressure of the vapor at equilibrium is the vapor pressure. The vapor pressure is independent of the amount of liquid present. Figure 16-8 illustrates that the vapor pressure of water above a small puddle is the same as the vapor pressure above a large pond at the same temperature. More molecules escape from the larger surface of the pond, but more molecules are captured, too. The balance between captures and escapes is the same for both puddle and pond. 

When a zinc strip is dipped into the solution, the initial rates of these two processes are different. The different rates of reaction lead to a charge imbalance across the metal-solution interface. If the concentration of zinc ions in solution is low enough, the initial rate of oxidation is more rapid than the initial rate of reduction. Under these conditions, excess electrons accumulate in the metal, and excess cationic charges accumulate in the solution. As excess charge builds, however, the rates of reaction change until the rate of reduction is balanced by the rate of oxidation. When this balance is reached, the system is at dynamic equilibrium. Oxidation and reduction continue, but the net rate of exchange is zero Zn (.S ) Zn (aq) + 2 e (me t a i)... 

Given that, under the defined conditions, there is no interfacial kinetic barrier to transfer from phase 2 to phase 1, the concentrations immediately adjacent to each side of the interface may be considered to be in dynamic equilibrium throughout the course of a chronoamperometric measurement. For high values of Kg the target species in phase 2 is in considerable excess, so that the concentration in phase 1 at the target interface is maintained at a value close to the initial bulk value, with minimal depletion of Red in phase 2. Under these conditions, the response of the tip (Fig. 11, case (a)] is in agreement with that predicted for other SECM diffusion-controlled processes with no interfacial kinetic barrier, such as induced dissolution [12,14—16] and positive feedback [42,43]. A feature of this response is that the current rapidly attains a steady state, the value of which increases... 

Chemical reactions that are reversible are said to be in dynamic equilibrium because opposite reactions take place simultaneously at the same rate. A system that is at equilibrium can be shifted toward either reactants or products if the system is subjected to a stress. Changes in concentration, temperature, or pressure are examples of stresses. 

Chemical equilibria being of a dynamic type, equilibrium states are altered by changes in the variables controlling them. The effect of such changes can be interpreted qualitatively on the basis of a principle which was enunciated independently by Le Chatelier in 1885 and by Braun one year later. It states that when a system in a state of dynamic equilibrium is subjected to a stress imposed by variation in anyone of the variables controlling the equilibrium state, the system will tend to adjust itself in such a way as to minimize the effect of the stress. The variables of interest in this connection are temperature of the system, pressure on the system, and concentrations for the reactants and products taken individually. 

This study has shown that typical coating biocides can be encapsulated within modified silica frameworks. These porous frameworks offer a means to inhibit the aqueous extraction of the biocide. In such combinations the biocides retain their anti-microbial properties, while controlled delivery facilitates a dynamic equilibrium to maintain a minimum inhibitory concentration at the coating interface, over an extended time period. There is evidence that biocide housed in such frameworks has a longer effective activity for a given initial concentration, since it is to some extent protected from the usual environmental degradation processes. 

A catalyst used for the u-regioselective hydroformylation of internal olefins has to combine a set of properties, which include high olefin isomerization activity, see reaction b in Scheme 1 outlined for 4-octene. Thus the olefin migratory insertion step into the rhodium hydride bond must be highly reversible, a feature which is undesired in the hydroformylation of 1-alkenes. Additionally, p-hydride elimination should be favoured over migratory insertion of carbon monoxide of the secondary alkyl rhodium, otherwise Ao-aldehydes are formed (reactions a, c). Then, the fast regioselective terminal hydroformylation of the 1-olefin present in a low equilibrium concentration only, will lead to enhanced formation of n-aldehyde (reaction d) as result of a dynamic kinetic control. 

Most chemical reactions do not progress completely from reactants to products. Instead, the net reaction stops in the forward direction when equilibrium is established. Analysis of the contents of the reaction vessel would show a constant concentration of monomers and polymer once equilibrium is reached. This situation is actually a dynamic equilibrium, where the monomers are forming polymers at the same rate as the polymers depolymerize to monomer. Therefore, at equilibrium, the net concentrations of any one species remains constant. The amount of monomer converted into polymer will be defined by the equilibrium constant, K. This constant is the ratio of the concentration of the products to the reactants, with each concentration raised to the stoichiometric coefficients in the balanced equation. For Eq. 3.5 ... 

Polychalcogenides form chain fragments E2- that are in dynamic equilibrium with one another both in solution and in molten alkali metal fluxes. Longer chains (n = 3-6) can exist in significant concentrations at the relatively low temperatures employed for mild solvothermal syntheses (120-200°C), but are unstable with respect to disproportionation reactions of type (2) at higher temperatures. 

Instead, this concentration marks a steady state (or dynamic equilibrium, a term that persists despite being an oxymoron) at which the rate of cristobalite dissolution... 

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