Equilibrium equality

A At chemical equilibrium, equal amounts of products and reactants are present. 

In the first step, set the rate in the forward direction for the equilibrium equal to the rate in the reverse direction. Then solve for [Cl]2. 

Another type of biphase partition comprises equilibration of a crown ether-containing solution with a sparingly soluble solid salt. Assuming that the amount of free salt [M+.X in (1)] at equilibrium equals the solubility—which can be determined separately—one can calculate the association constant ATlp from the amount of solubilized salt. Reinhoudt et al. (1977) applied this technique using Zeise s salts. 

At equilibrium, equality of chemical potentials of a component in two liquid phases Li and L2 leads to... 

The result reached is in agreement with the equations (V-4) and (V-7), according to which the difference between the free energy of products and that of reactants at equilibrium equals zero ... 

It is worthwhile to appreciate that there is a definite free energy change associated with racemization (defined as conversion of either 100% R or 100% S to 50% R, 50% S). Since at equilibrium, equal amounts must be present the equilibrium constant is 1. Hence the standard free energy change (AG°) is 0. This, however, refers to the conversion of 1 mole R to 1 mole S in other words, to inversion not racemization. 

When two bodies have thermal equilibrium (equality of temperature) with a third body, they in turn, have thermal equilibrium (equality of temperature) with each other (Rock 1969). 

If red blood corpuscles are placed in pure water they swell, become round, and finally burst. This is the result of the fact that the cell wall is permeable to water but nOt to some of the solutes of the cell solution (mainly hemoglobin the red protein in red cells) in the effort to reach a condition of equilibrium (equality of water vapor pressure) between the two liquids water enters the cell. If the cell wall were sufficiently strong, equilibrium would be reached when the hydrostatic pressure in the cell had reached a certain value, at which the water vapor pressure of the solution equals the vapor pressure of the pure w ter outside... 

Consider a given species i distributed between two phases and " at equilibrium. Equality of the chemical potential leads to the expression... 

If a semiconductor is brought into contact with an electrolyte containing one or more redox couples, charge transfer between the two phases occurs until electrostatic equilibrium (equality of the free energies of the electron in both phases) is attained. 

Most of the atoms of Th that are produced from decay readily attach to particles and are removed from solution. In the surface ocean there are enough particles formed to create a deficiency in Th activity from that to be expected at secular equilibrium with At steady state, the depth-integrated deficiency of the activity concentrations of Th in the euphotic zone is equal to its flux from the surface ocean on particles. If one then knows the Th C ratio in the particles, the flux of particulate carbon can be calculated. An example of Th measurements in the surface waters of the subtropical Pacific (see Fig. 6.11) indicates that difference in Th activity from that expected at secular equilibrium (equal to the activity of U) is small but readily measurable. 

In liquid-liquid equilibrium, equality of fugacity applies as it does in vapor-liquid equilibrium. Therefore, Eq. (15) applies to liquid-liquid equilibrium where a and P apply to the two liquid phases. Therefore,... 

The second peculiarity results from the reciprocity of composition and thus from the equilibrium between AX, BY and AY, BX. The Gibbs energy of this equilibrium equals the sum of the standard Gibbs energies of formation of the components for the metathetical reaction... 

It is important to remember that though the partial pressure of a gas in a liquid may be low, the content of gas in the solution may be high. Comroe (1974) has pointed out that It is possible. .. to have more millilitres of a very soluble gas in 1 litre of liquid than in 1 litre of a gas mixture on top of it at equilibrium (equal partial pressures) . 

Adsorption occurs because it lowers the free energy of the system. According to Gibbs, the chemical potential of the adsorbate is at equilibrium equal in the solution and at the surface. Fie further postulated an infinitely thin dividing plane between the two phases and then derived the equation... 

As you have probably already guessed, this system can never reach equilibrium (equal concentrations inside and outside the bag) because regardless of how much water diffuses into the bag, diluting the glucose solution, the concentration of glucose will always be higher inside the bag (and the accompan)dng free water concentration will always be lower). 

Suppose you start a reaction with a mixture of reactants and products and you know the equilibrium constant at the temperature of the reaction. Because the value of Q can change, depending on the initial concentrations, Q can be smaller than K, larger than K, or, when the system reaches equilibrium, equal to K. By comparing the value of Q at a particular time with the known K, you can tell whether the reaction has attained equilibrium or, if not, in which direction it is progressing. With product terms in the numerator of Q and reactant terms in the denominator, more product makes Q larger, and more reactant makes Q smaller. 

In the steady state of radioactive equilibrium equal numbers of a-particles are emitted by each of the four species radium, radon, radium A, and radium C. Rutherford and Geiger (Proc. Roy. Soc. A. 1908, 81, 141) isolated a concentrated source consisting of a mixture of radium A, radium B, radium C, and radium C. After a quarter of an hour the radiation due to radium A has become negligible and all the a-activity is then due to the radium C in radioactive equilibrium with the radium C. Furthermore, of the species mentioned, radium C alone emits penetrating y-rays and so measurement of the intensity of this... 

For a reversible sorption/desorption isotherm for both media, food and polymer, the thermodynamic equilibrium (equal chemical potentials for both media) imposes ... 

By definition, the pole flows are positive quantities, so the exchange reversibility is also always positive. It ranges from zero, meaning total irreversibility in the j direction, to infinite, meaning total irreversibility in the opposite direction. The peculiar value one corresponds to an exchange in dynamic equilibrium (equal flows in both directions) and a tolerance around this value delimitates a reversible regime (or quasireversible when the tolerance is large). 

Simultaneously, conditions of thermal (equality of temperatures), mechanical (equality of pressures) and phase equilibrium (equality of chemical potentials of both components in both phases) must be satisfied. The constraints are defined by a set of equations nonlinear both in model parameters and in fliermodynamic quantities. When correlating vapor-liquid equilibrium data at low and moderate pressures, liquid phase is described in terms of a G -model and vapor phase is either considered as an ideal gas or its nonideality is expressed by an equation of state, e. g. the virial expansion limited to the second virial coefficient (Chap. 1.6). 

Vapor pressure is independent of surface area because an increase in surface area at equilibrium equally affects the rate of evaporation and the rate of condensation. 

Figure 7.4 shows that at thermal equilibrium, equality of temperatures Ta and Tb is not the same as equality of energies or entropies. We interpret temperature in more detail in Chapter 12. 

This is an empirical equation which accounts for the fact that for ideal chains, i.e. vanishing excluded volume interactions, the coil size in thermal equilibrium equals Rq j3 is a dimensionless coefficient of order unity. The first term gives the repulsion experienced on squeezing a polymer chain, the second term represents the retracting force built up on a coil expansion. As only the second term appears relevant for the case under discussion we ignore the first term and write... 

Equilibrium is reached at the point where the concentration of free reactive receptors becomes low enough to produce inactivated receptors only at the rate of reactivation. The maximal effect at equilibrium equals the maximal possible... 

However, unlike in homopolymerization systems, the concentrations of macrocydes are not at equilibrium equal (or approximately equal for not infinitely long linear chains) to the macrocydization equilibrium constants. It stems from the fact that various compositions and microstractures of chains can usually be obtained depending on the initial monomer feed and copolymerization equilibrium constants (of homo- and crosspropagations). The only exceptions are alternating copolymers for which macrocyde concentrations conespond to macrocydization equilibrium constants like in homopolymetization systems. 

The saturation of water refers to the solubility product of a compound. By definition, the ion-activity product (lAP) of reactants—i.e., Oca2+ and 00032- when CaCOs is the sealant—is, at equilibrium, equal to K,p-. 

To obtain a quantitative measure, the surface tension of a liquid may be defined in the following way. Make a cut in a plane liquid surface, extending only a short way into the liquid. If the liquid surface is to remain in equilibrium, equal and opposite forces, which are in the plane of the surface, must be applied to the faces of the cut. The force, per unit length of the cut, applied to one face of the cut, is the surface tensile stress that existed across the line of the cut and is known as the surface tension of the liquid, units N m". It follows from this definition that surface tension in liquids may be studied by determining the force exerted on some solid object either placed in, or terminating, a liquid surface. 

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