Composition at equilibrium

Ladder diagrams are a useful tool for evaluating chemical reactivity, usually providing a reasonable approximation of a chemical system s composition at equilibrium. When we need a more exact quantitative description of the equilibrium condition, a ladder diagram may not be sufficient. In this case we can find an algebraic solution. Perhaps you recall solving equilibrium problems in your earlier coursework in chemistry. In this section we will learn how to set up and solve equilibrium problems. We will start with a simple problem and work toward more complex ones. 

As shown in Fig. 18-57, the mutual solubility of two salts can be plotted on the X and Y axes with temperatures as isotherm hues. In the example shown, all the solution compositions corresponding to 100°C with solid-phase sodium chloride present are shown on the Tine DE, All the solution compositions at equihbrium with solid-phase KCl at 100°C are shown by the line EE If both sohd-phase KCl and NaCl are present, the solution composition at equilibrium can only be represented by point E, which is the invariant point (at constant pressure). Connecting all the invariant points results in the mixed-salt hne. The locus of this line is an important consideration in making phase separations. 

Nonpolarizable interfaces correspond to interfaces on which a reversible reaction takes place. An Ag wire in a solution containing Ag+ions is a classic example of a nonpolarizable interface. As the metal is immersed in solution, the following phenomena occur3 (1) solvent molecules at the metal surface are reoriented and polarized (2) the electron cloud of the metal surface is redistributed (retreats or spills over) (3) Ag+ ions cross the phase boundary (the net direction depends on the solution composition). At equilibrium, an electric potential drop occurs so that the following electrochemical equilibrium is established ... 

A catalyst is a substance that increases the rate of a chemical reaction without being consumed itself. We shall see a lot more of catalysts later, when we consider reaction rates in Chapter 13. However, it is important to be aware at this stage that a catalyst has no effect on the equilibrium composition of a reaction mixture. A catalyst can speed up the rate at which a reaction reaches equilibrium, but it does not affect the composition at equilibrium. It acts by providing a faster route to the same destination. 

These four equations are perfectly adequate for equilibrium calculations although they are nonsense with respect to mechanism. Table 7.2 has the data needed to calculate the four equilibrium constants at the standard state of 298.15 K and 1 bar. Table 7.1 has the necessary data to correct for temperature. The composition at equilibrium can be found using the reaction coordinate method or the method of false transients. The four chemical equations are not unique since various members of the set can be combined algebraically without reducing the dimensionality, M=4. Various equivalent sets can be derived, but none can even approximate a plausible mechanism since one of the starting materials, oxygen, has been assumed to be absent at equilibrium. Thermodynamics provides the destination but not the route. 

Kt Ratio of vapor to liquid composition at equilibrium for Component i (-)... 

When the standard states for the solid and liquid species correspond to the pure species at 1 atm pressure or at a low equilibrium vapor pressure of the condensed phase, the activities of the pure species at equilibrium are taken as unity at all moderate pressures. Consequently, the gas phase composition at equilibrium will not be... 

As a consequence of the determination of the composition at equilibrium of the products of expln reaction, it has been shown that a good approximation to the composition is afforded by the following conventional scheme ... 

Every chemical reaction tends toward a state of dynamic equilibrium, and the composition at equilibrium determines how much product we can expect. We need to understand equilibrium and its relation to thermodynamics in order to manipulate the outcome of a reaction by controlling conditions such as the temperature and pressure. These features have considerable economic and biological significance the control of chemical equilibrium affects the yields of products in industrial processes, and living cells struggle to avoid sinking into equilibrium. The importance of chemical equilibria can be appreciated by noticing that it is the basis of this and the next three chapters. This chapter lays the foundation for the next three. 

He showed that positive dX give d that reduce Gibbs free energy. This method is analogous to that of steepest descent, a first-order method for minimization of Gibbs free energy. Ma and Ship-man (11) used Naphtali s method to estimate compositions at equilibrium and the Newton-Raphson method to achieve convergence. 

The composition at equilibrium can be determined from the equilibrium constant based on molar fractions Kx = Ka/Kr This is, in turn, calculated from the equilibrium-constant-based activities IQ and activity coefficients Kr Figure 8.3 shows the variation over the range 350-475 K [1, 2], IQ takes values between 10 and 50, but the correction by IQ is important bringing IQ between 2 and 10. Above 430 K equilibrium conversion over 80% should be expected. If the water is continuously removed by distillation, then full conversion may be achieved. 

The X-value is a function of temperature, pressure, and composition. At equilibrium, whenever two of these three variables are fixed, so is the third, The JC-value can therefore be regarded as a function of pressure and composition, or temperature and composition or temperature and pressuie),... 

Table 1. Acetylacetone Variation of composition at equilibrium with solvent and the chemical shift of the enol proton, d(OHO)...

The work of this laboratory extends the defect treatment to intermetallie compounds. The experiments measure simultaneously both the cadmium vapor pressure and the composition at equilibrium for a series of only slightly different alloy compositions. The precision and the relative accuracy of the measurements are high the absolute values suffer from any starting composition uncertainty and from errors in the absolute vapor pressure of cadmium as determined by other techniques. The experimental method is described elsewhere in this symposium (6). It has proved possible to infer the concentration and identity of lattice defects by analyzing the experimental data following the analytical techniques described below. 

Likewise, combining systems 2 and 3 into a composite at equilibrium, we obtain... 

The equilibrium constant K is a function of temperature only. However, Eq. (13.25) relates K to fugacities of the reacting species as tliey exist in the real equilibrium mixture. These fugacities reflect the nonidealities of the equilibrium mixture and are functions of temperature, pressure, and composition. Tliis means that for a fixed temperature the composition at equilibrium must change with pressure in such a way that W ifilP ") remains constant. 

If a mixture forms an azeotropic composition, the vapor and liquid compositions at equilibrium are identical to each other. The following equations define this situation ... 

Sotr. For accurate work exact analysis of both the resin and external phases is undertaken, and accemnt taken of co-ion uptake and changes in resin water content. For this approximate experiment, the actual solution phase composition at equilibrium may be determined by separately preparing a calibration of conductivity against (H — A ) composition <>r by analysis for the ions ce ncerned. 

When several reversible reactions occur simultaneously, each reaction ty is characterized by its equilibrium constant K. When the are known, the composition at equilibrium can be calculated from a set of equations such as Eq. (7-15) for each reaction. 

The equilibrium constant (based on volumetric concentrations) is defined as the ratio of the forward and reverse rate constants and is related to the composition at equilibrium as follows ... 

The solution of such equations is now rather more complicated but it can be proved that there is a unique solution giving the composition at equilibrium. 

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