Equilibrium expressions

In thermodynamics courses, you have learned that chemical reaction equilibrium is determined by the equilibrium constant, which is defined in terms of the change of Gibbs free energy. 

The Gibbs free energy is tabulated at 298 K for pure components, and it is possible to extend the Gibbs free energy for a reaction to any temperature using the van t Hoff equation  

In the gas phase, the activity is the fugacity, since the activity is the fugacity divided by the fugacity of the standard state, which is one atmosphere. In turn, you can write the fugacity as the product of the fugacity coefficient (providing a correction from ideal gas behavior) times the total pressure times the mole fraction in the vapor phase  

The fugacity coefficient can be calculated using the equation of state (Denbigh, 1971, p. 126)  

When the pressure is less than 10 atm, the gas is usually ideal. From the formula it is clear that for an ideal gas the integral vanishes. Then In = 0 or (f = 1. You can use that assumption and combine all the terms in Eq. (4.7) into Eq. (4.10)  

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It should be noted that, whatever the fonu of Henry s law (i.e. in whatever composition units), Raoult s law must necessarily be expressed in mole fraction. This says nothing about the appropriateness of mole fractions in condensed systems, e.g. in equilibrium expressions it arises simply from the fact that it is a statement about... 

The equilibrium expressed by the preceding equation lies overwhelmingly to the side of the zwittenon... 

This last result describes the Donnan equilibrium condition as it applies to the system under consideration. Like other ionic equilibrium expressions, it requires the equality of ion products in equilibrium solutions. 

Tables 13-1, 13-2, and 13-4 include data on formic acid and acetic acid, two substances that tend to dimerize in the vapor phase according to the chemical-equilibrium expression...

Substituting for [PhCOCH2 ] from the equilibrium expression for step 1 gives... 

Many organic reactions involve acid concentrations considerably higher than can be accurately measured on the pH scale, which applies to relatively dilute aqueous solutions. It is not difficult to prepare solutions in which the formal proton concentration is 10 M or more, but these formal concentrations are not a suitable measure of the activity of protons in such solutions. For this reason, it has been necessaiy to develop acidity functions to measure the proton-donating strength of concentrated acidic solutions. The activity of the hydrogen ion (solvated proton) can be related to the extent of protonation of a series of bases by the equilibrium expression for the protonation reaction. 

Some chemical reactions are reversible and, no matter how fast a reaction takes place, it cannot proceed beyond the point of chemical equilibrium in the reaction mixture at the specified temperature and pressure. Thus, for any given conditions, the principle of chemical equilibrium expressed as the equilibrium constant, K, determines how far the reaction can proceed if adequate time is allowed for equilibrium to be attained. Alternatively, the principle of chemical kinetics determines at what rate the reaction will proceed towards attaining the maximum. If the equilibrium constant K is very large, for all practical purposes the reaction is irreversible. In the case where a reaction is irreversible, it is unnecessary to calculate the equilibrium constant and check the position of equilibrium when high conversions are needed. 

Derive an equilibrium expression for the reactive absorption of HiS in diethanolamine DEA . The molarity of DEA is 2 kmol/m. The following reaction takes place ... 

The problem can be solved using the equilibrium expression for the adenylate kinase reaction ... 

In the dilute aqueous solution normally used for measuring acidity, the concentration of water, H20], remains nearly constant at approximately 55.4 M at 25 °C. We can therefore rewrite the equilibrium expression using a new quantity called the acidity constant, Ka. The acidity constant for any acid HA is simply the equilibrium constant for the acid dissociation multiplied by the molar concentration of pure water. 

This equilibrium constant is often given the symbol Kp to emphasize that it involves partial pressures. Other equilibrium expressions for gases are sometimes used, including Kc ... 

Equilibrium expression, 19 Equimolar potency ratios, 200-201 Etodolac, 154f Evaporation rate, 10, 12 Exemestane, 163f Experiment(s)... 

In bulb B we approached equilibrium from a higher temperature (which favors NOj) then redaction (5) predominated at first. Using the same sort of argument we applied to bulb A, we see jthat as time progresses, reaction (4) becomes more and more rapid (as N204 is produced) and reaction (5) becomes slower (as N02 is used up). Finally, when the rates become equal, equilibrium is reached and the equilibrium expression (6) is applicable in bulb B. 

Now look at the numerical values of the equilibrium constants. The K s listed range from 10+1 to 10 16, so we see there is a wide variation. We want to acquire a sense of the relation between the size of the equilibrium constant and the state of equilibrium. A large value of K must mean that at equilibrium there are much larger concentrations present of products than of reactants. Remember that the numerator of our equilibrium expression contains the concentrations of the products of the reaction. The value of 2 X 10,s for the K for reaction (19) certainly indicates that if a reaction is initiated by placing metallic copper in a solution containing Ag+ (for example, in silver nitrate solution), when equilibrium is finally reached, the concentration of Cu+2 ion, [Cu+2], is very much greater than the square of the silver ion concentration, [Ag+]2. 

The simple form of the equilibrium expression (4) follows directly from the dynamic nature of the solubility equilibrium. There must be a dynamic balance between the rate that iodine molecules leave the ciystal and the rate that iodine molecules return to the crystal. To understand this dynamic balance, we must consider the factors that determine these two rates. 

Just as in expression (4), the concentration of the solid (silver chloride) does not appear in the equilibrium expression (20) it does not vary. 

From this equation, we can write the equilibrium expression ... 

Substituting (II) into the equilibrium expression, we can calculate the concentrations of the two types of ions ... 

Again Le Chatelier s Principle tells us qualitatively what will occur and the equilibrium expression tells us quantitatively. If we add OH-(ag), a change will take place that tends to counteract partially the resulting increase in [OH-]. This occurs through the reaction between OY (aq) and H+(aq), consuming both ions and reducing the value of [H+] X [OH-]. Reaction continues until this product reaches the equilibrium value, K = 1.00 X 10-14. 

Returning to our original 0.100 liter of 1.00 M HQ, let us now consider the addition of 0.101 mole of solid NaOH. Again we have added both H+(aqJ and OH (aq) to the same solution, and the concentrations immediately after mixing do not satisfy the equilibrium expression ... 

At equilibrium, the concentrations must be in accord with the equilibrium expression. That is,... 

Write the equilibrium expression relating the concentrations of reactants and products in reaction (26). Notice that the concentration of water must be included because it is not necessarily large enough to be considered constant. 

The above rate equation is in agreement with that reported by Madhav and Ching [3]. Tliis rapid equilibrium treatment is a simple approach that allows the transformations of all complexes in terms of [E, [5], Kls and Kjp, which only deal with equilibrium expressions for the binding of the substrate to the enzyme. In the absence of inhibition, the enzyme kinetics are reduced to the simplest Michaelis-Menten model, as shown in Figure 5.21. The rate equation for the Michaelis-Menten model is given in ordinary textbooks and is as follows 11... 

Write the equilibrium expression Kc for each of the following reactions ... 

We calculate the pH of solutions of weak bases in the same way as we calculate the pH of solutions of weak acids—by using an equilibrium table. The protonation equilibrium is given in Eq. 9. To calculate the pH of the solution, we first calculate the concentration of OH ions at equilibrium, express that concentration as pOH, and then calculate the pH at 25°C from the relation pH + pOH = 14.00. For very weak or very dilute bases, the autoprotolysis of water must be taken into consideration. 

A proponent of "reverse weathering" suggested that gibbsite, kaolinite, and quartz exist in equilibrium according to the following equation. In equilibrium expressions for these reactions, water will appear as the activity, rather than concentration. The activity can be approximated by the mole fraction of water. What is the activity of water if this equilibrium is maintained Could this equilibrium exist in seawater, where the mole fraction of water is about 0.98 AG values (kj/mol) gibbsite — 2320.4 kaolinite — 3700.7 quartz —805.0 water —228.4. 

Table 16-2 List of input components for the simplest case of the acid-base balance of unpolluted marine clouds. Also shown are the mass conservation statements, chemical equilibrium expressions and constants, and the requirement for charge balance...

Examining the equilibrium expressions in Table 16-2, the equations can be put into a logarithmic form, e.g., for the dissociation of a simple acid, HA,... 

To illustrate the generality of reversibility and the equilibrium expression, we extend our kinetic analysis to a chemical reaction that has a two-step mechanism. At elevated temperature NO2 decomposes into NO and O2 instead of forming N2 O4. The mechanism for the decomposition reaction, which appears in Chapter 15. 

If we multiply one of these equations by the other, the concentration of the intermediate, [NO3 ]g, cancels to produce an equilibrium expression entirely in terms of concentrations of reactants and products ... 

Each equilibrium expression described so far contains a ratio of concentrations of products and reactants. Moreover, each concentration is raised to a power equal to its stoichiometric coefficient in the balanced equation for the overall reaction. Concentration ratios always have products in the numerator and reactants in the... 

It is possible to carry out this type of kinetic analysis whether a mechanism is simple or elaborate. That is, we can always derive the equilibrium expression for a reaction by applying reversibility and setting forward and reverse rates equal to one another at equilibrium. It is unnecessary to go through this procedure for every chemical equilibrium. As our two examples suggest, inspection of the overall stoichiometry always gives the correct expression for the equilibrium constant. That is, a reaction of the form tjA + iBf ofD + eE has an... 

If the mechanism for this equilibrium were given, we could derive an equilibrium expression using the principle of reversibility, but Equation shows that we can write the equilibrium expression directly without knowing details of the mechanism. 

Both relationships include a constant and both involve concentrations raised to exponential powers. However, a rate law and an equilibrium expression describe fundamentally different aspects of a chemical reaction. A rate law describes how the rate of a reaction changes with concentration. As we describe in this chapter, an equilibrium expression describes the concentrations of reactants and products when the net rate of the reaction is zero. 

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