Systems at Equilibrium

Two subsystems a. and p, in each of which the potentials T,p, and all the p-s are unifonn, are pennitted to interact and come to equilibrium. At equilibrium all infinitesimal processes are reversible, so for the overall system (a + P), which may be regarded as isolated, the quantities conserved include not only energy, volume and numbers of moles, but also entropy, i.e. there is no entropy creation in a system at equilibrium. One now... 

One of the fundamental equations of thermo dynamics concerns systems at equilibrium and relates the equilibrium constant K to the dif ference in standard free energy (A6°) between the products and the reactants... 

According to Le Chatelier s principle, a system at equilibrium adjusts so as to mini mize any stress applied to it When the concentration of water is increased the system responds by consuming water This means that proportionally more alkene is converted to alcohol the position of equilibrium shifts to the right Thus when we wish to pre pare an alcohol from an alkene we employ a reaction medium m which the molar con centration of water is high—dilute sulfuric acid for example... 

Although a system at equilibrium appears static on a macroscopic level, it is important to remember that the forward and reverse reactions still occur. A reaction at equilibrium exists in a steady state, in which the rate at which any species forms equals the rate at which it is consumed. 

The sign of AG can be used to predict the direction in which a reaction moves to reach its equilibrium position. A reaction is always thermodynamically favored when enthalpy decreases and entropy increases. Substituting the inequalities AH < 0 and AS > 0 into equation 6.2 shows that AG is negative when a reaction is thermodynamically favored. When AG is positive, the reaction is unfavorable as written (although the reverse reaction is favorable). Systems at equilibrium have a AG of zero. 

The observation that a system at equilibrium responds to a stress by reequilibrating in a manner that diminishes the stress, is formalized as Le Chatelier s principle. One of the most common stresses that we can apply to a reaction at equilibrium is to change the concentration of a reactant or product. We already have seen, in the case of sodium acetate and acetic acid, that adding a product to a reaction mixture at equilibrium converts a portion of the products to reactants. In this instance, we disturb the equilibrium by adding a product, and the stress is diminished by partially reacting the excess product. Adding acetic acid has the opposite effect, partially converting the excess acetic acid to acetate. 

Le Chatelier s principle provides a means for predicting how systems at equilibrium respond to a change in conditions. When a stress is applied to an equilibrium by adding a reactant or product, by adding a reagent that reacts with one of the reactants or products, or by changing the volume, the system responds by moving in the direction that relieves the stress. 

You should be able to describe a system at equilibrium both qualitatively and quantitatively. Rigorous solutions to equilibrium problems can be developed by combining equilibrium constant expressions with appropriate mass balance and charge balance equations. Using this systematic approach, you can solve some quite complicated equilibrium problems. When a less rigorous an-... 

To describe the state of a two-component system at equilibrium, we must specify the number of moles nj and na of each component, as well as—ordinarily- the pressure p and the absolute temperature T. It is the Gibbs free energy that provides the most familiar access to a discussion of equilibrium. The increment in G associated with increments in the independent variables mentioned above is given by the equation... 

The phase rule permits only two variables to be specified arbitrarily in a binaiy two-phase system at equilibrium. Consequently, the cui ves in Fig. 13-27 can be plotted at either constant temperature or constant pressure but not both. The latter is more common, and data in Table 13-1 are for that case. The y-x diagram can be plotted in either mole, weight, or volume frac tions. The units used later for the phase flow rates must, of course, agree with those used for the equilibrium data. Mole fractious, which are almost always used, are appfied here. 

The properties of a system at equilibrium do not change with time, and time therefore is not a thermodynamic variable. An unconstrained system not in its equilibrium state spontaneously changes with time, so experimental and theoretical studies of these changes involve time as a variable. The presence of time as a factor in chemical kinetics adds both interest and difficulty to this branch of chemistry. 

K-factors for vapor-liquid equilibrium ratios are usually associated with various hydrocarbons and some common impurities as nitrogen, carbon dioxide, and hydrogen sulfide [48]. The K-factor is the equilibrium ratio of the mole fraction of a component in the vapor phase divided by the mole fraction of the same component in the liquid phase. K is generally considered a function of the mixture composition in which a specific component occurs, plus the temperature and pressure of the system at equilibrium. 

For a system such as discussed here, the Gibb s Phase Rule [59] applies and establishes the degrees of freedom for control and operation of the system at equilibrium. The number of independent variables that can be defined for a system are ... 

The characteristics just described are typical of all systems at equilibrium. First, the forward and reverse reactions are taking place at the same rate. This explains why die concentrations of species present remain constant with time. Moreover, these concentrations are independent of the direction from which equilibrium is approached. 

Click Coached Problems for a self-study module on systems at equilibrium. 

If a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, the system will, if possible, shift to partially counteract the change. 

According to Le Chatelier s principle, if a chemical system at equilibrium is disturbed by adding a gaseous species (reactant or product), the reaction will proceed in such a direction as to consume part of the added species. Conversely, if a gaseous species is removed, die... 

We should emphasize that adding a pure liquid or solid has no effect on a system at equilibrium. The rule is a simple one For a species to shift the position of an equilibrium, it must appear in the expression for K. 

N02(p) system at equilibrium. The immediate effect (middle cylinder) is to crowd the same number of moles of gas into a smaller volume and so increase the total pressure. This is partially compensated for by the conversion of some of the N02 to N204, thereby reducing the total number of moles of gas. 

Effect of tamperature on the N2O4-NO2 system at equilibrium. At 0°C (tube at right. N2O4, which is colorless, predominates. At 50°C Itube at left), some of the N204 has disassociated to give the deep brown color of NO2. 

Le Chatelier s principle A relation stating that when a system at equilibrium is disturbed it responds in such a way as to partially counteract that change, 337-338 buffers and, 385 compression effects, 339-340 expansion effects, 339-340 precipitation equilibrium, 442 reaction conditions, 348q temperature changes, 340 Lead, 2,501 Leclanch cell, 500 Leucine, 622t... 

Though a system at equilibrium is constant in properties, constancy is not the only requirement. Consider a laboratory burner flame. There is a well-defined structure to the flame—an inner cone surrounded by a luminous region whose appearance does not change. A temperature measurement made at a particular place in the flame shows that the temperature at that spot is constant. At another place in the flame the temperature might be different but, again, it would be constant, not changing with time. A measurement of the gas flow rate shows a constant movement of gas into the flame. Yet a laboratory burner flame is not at equilibrium be-... 

Figure 9-1C shows a system at equilibrium. Solid iodine has dissolved in an alcohol-water mixture until the solution is saturated. Then no more solid dissolves and the color of the solution remains constant. 

Catalysts increase the rate of reactions. It is found experimentally that addition of a catalyst to a system at equilibrium does not alter the equilibrium state. Hence it must be true that any catalyst has the same effect on the rates of the forward and reverse reactions. You will recall that the effect of a catalyst on reaction rates can be discussed in terms of lowering the activation energy. This lowering is effective in increasing the rate in both directions, forward and reverse. Thus, a catalyst produces no net change in the equilibrium concentrations even though the system may reach equilibrium much more rapidly than it did without the catalyst. 

This distinction between the conditions in a chemical system at equilibrium and the rate at which these conditions are attained is very important in chemistry. By arguments that we shall consider a chemist can decide with confidence whether equilibrium favors reactants or products or neither. He cannot predict, however, how rapidly the system will approach the equilibrium conditions. That is a matter of reaction rates, and the chemist must perform separate experiments to learn whether a given rate is rapid or not. 

Colorimetric analysis based on visual estimation is not very exact. Some more accurate data on the H2, I2, HI system at equilibrium are shown in Table 9-1. The reaction is... 

For this system at equilibrium, the reaction is I2(solid) = I2(alcohol solution) (5)... 

Holder and Maass34 found that the lower critical end point was at 44.85°C, that is, 12.5°C above the critical temperature of pure ethane. They did not measure the pressure and their claim of having detected different solubilities in different parts of the fluid at temperatures above this point probably does not apply to a system at equilibrium in the absence of a gravitational field.66... 

This fundamentally important equation links thermodynamic quantities—which are widely available from tables of thermodynamic data—and the composition of a system at equilibrium. 

Experiment gives K = 3.4 X 10-21 at 800. K. The very small value of K tells us that the reactants N2 and 02 are the dominant species in the system at equilibrium. 

Example 9.4 deals with a system at equilibrium, but suppose the reaction mixture has arbitrary concentrations. How can we tell whether it will have a tendency to form more products or to decompose into reactants To answer this question, we first need the equilibrium constant. We may have to determine it experimentally or calculate it from standard Gibbs free energy data. Then we calculate the reaction quotient, Q, from the actual composition of the reaction mixture, as described in Section 9.3. To predict whether a particular mixture of reactants and products will rend to produce more products or more reactants, we compare Q with K ... 

SOLUTION (a) The addition of N2 (a product) to the equilibrium mixture causes the reaction to shift toward reactant formation, which increases the concentrations of NH, and 02 while decreasing the concentration of H2G. The concentration of N2 remains slightly higher than its original equilibrium value but lower than its concentration immediately after the additional N2 was supplied, (b) When NH, is removed from the system at equilibrium, the reaction shifts to form more reactants. Therefore, the concentration of 02 will increase and the concentrations of N2 and H2C) will decrease. The concentration of NH3 will he somewhat lower than its original equilibrium value but... 

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