The Equilibrium Constant K

Notice that when the two countries reach dynamic equilibrium, their populations no longer change, because the number of people moving out of either country equals the number of people moving in. However, one country—because of its charm or the availability of good jobs or lower taxes, or for whatever other reason—may have a higher population than the other country, even when dynamic equilibrium is reached. 

Similarly, when a chemical reaction reaches dynamic equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the relative concentrations of reactants and products become constant. But the concentrations of reactants and products will not necessarily be equal at equilibrium, just as the populations of the two countries are not necessarily equal at equilibrium. 

FIGURE 14.3 A Population Analogy for Chemical Equilibrium Because Country A is initially overpopulated, people migrate from Country A to Conntry B. As the population of Conntry A falls and that of Country B rises, the rate of migration from Country A to Conntry B decreases and the rate of migration from Country B to Country A increases. Eventnally the two rates become eqnal. Eqnilibrium has been reached. 

We have just seen that the concentrations of reactants and products are not equal at equilibrium— rather, the rates of the forward and reverse reactions are equal. So what about the concentrations The equilibrium constant is a way to quantify the concentrations of the reactants and products at equilibrium. 

We distinguish between the equiiibrium constant (K) and the Ketvin unit of temperature (it) by itaiicizing the equiiibrium constant 

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Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

Na -f-OH -kCHjCOOH and the equilibrium constant, K, for this reaction is given by... 

The value of the standard free energy AG depends on the choice of reference state, as does the equilibrium constant. Thus it would be safer to write the equilibrium constant K for a gaseous reaction as... 

This important relation between the temperature derivative of the equilibrium constant K and the standard... 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

It is possible to detemiine the equilibrium constant, K, for the bimolecular reaction involving gas-phase ions and neutral molecules in the ion source of a mass spectrometer [18]. These measurements have generally focused on tln-ee properties, proton affinity (or gas-phase basicity) [19, 20], gas-phase acidity [H] and solvation enthalpies (and free energies) [22, 23] ... 

A connnon approach has been to measure the equilibrium constant, K, for these reactions as a fiinction of temperature with the use of a variable temperature high pressure ion source (see section (Bl.7.2)1. The ion concentrations are approximated by their abundance in the mass spectrum, while the neutral concentrations are known from the sample mlet pressure. A van t Hoff plot of In K versus /T should yield a straight Ime with slope equal to the reaction enthalpy (figure B1.7.11). Combining the PA with a value for basicityG at one temperature yields a value for A.S for the half-reaction involving addition of a proton to a species. While quadnipoles have been tire instruments of choice for many of these studies, other mass spectrometers can act as suitable detectors [19, 20]. 

In an earlier section, measurements were described in which the equilibrium constant, K, for bimolecular reactions involving gas-phase ions and neutral molecules were detennined. Another method for detemiining the proton or other affinity of a molecule is the bracketing method [ ]. The principle of this approach is quite straightforward. Let us again take the case of a proton affinity detemiination as an example. In a reaction... 

When AG = 0, the equilibrium constant K is unity. A large positive value of AG indicates that the reaction will not "go , being energetically unfavourable under the specific conditions to which AG refers. 

The logarithm of the equilibrium constant, K,. for the chemical equation shown in Figure 3-8a for a substituted benzoic acid can be related to the logarithm of the... 

The equilibrium constant K, the rate constants and and the dependences of all these quantities on temperature were determined. In the absence of added acetic acid, the conversion of nitric acid into acetyl nitrate is almost quantitative. Therefore, to obtain at equilibrium a concentration of free nitric acid sufficiently high for accurate analysis, media were studied which contained appreciable concentrations (c. 4 mol 1 ) of acetic acid. 

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... 

Furthermore, the value of AG is related to the equilibrium constant K for the reaction... 

Taking known values for the molar refractivities of water and methanol, and again assuming a range of values for the equilibrium constant (k) and the refractive index (ni) of the methanol/water associate, the actual values that fit the equation for these... 

It is seen that the three values for the equilibrium constant (k) range from 0.00443 to 0.00565 with an average value of 0.00504. The two values for the densities of the methanol/water associate are in reasonable agreement and have a magnitude that would be expected for the hydrogen bonded associate. 

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. 

Because the equilibrium constant K is given by CqIcaCb, we obtain... 

Equilibrium concentrations of reactants and products can be calculated from the equilibrium constant, K q, which is related to the free energy of reaction, AGrxn ... 

The Henry s Law constant, H, can be substituted for the equilibrium constant, K, when the system operates at or very close to atmospheric pressure ... 

Thus the equilibrium constant K can be evaluated from standard electrode potential or from the standard chemical potentials x . 

In a solution containing such particles, the conditions for equilibrium in all possible proton transfers must be satisfied simultaneously, In terms of these proton energy levels, we may say that this is made possible by the additivity of the J values. In Fig. 38 the values of J for the three proton transfers have been labeled J1, J2, and J3. From the relation J3 = Ji + Ji) we may obtain at once a relation between the values of Kx, and hence between the equilibrium constants K. In the proton transfer labeled Jt the number of solute particles remains unchanged, whereas in J4 and Jt the number of solute particles is increased by unity. 

Don t confuse the equilibrium constant K with the rate constant k. 

The form of the expression for Q, known as the reaction quotient, is the same as that for the equilibrium constant, K. The difference is that the partial pressures that appear in Q are those that apply at a particular moment, not necessarily when the system is at equilibrium. By comparing the numerical value of Q with that of K, it is possible to decide in which direction the system will move to achieve equilibrium. 

As pointed out earlier, the equilibrium constant of a system changes with temperature. The form of the equation relating K to T is a familiar one, similar to the Clausius-Clapeyron equation (Chapter 9) and the Arrhenius equation (Chapter 11). This one is called the van t Hoff equation, honoring Jacobus van t Hoff (1852-1911), who was the first to use the equilibrium constant, K. Coincidentally, van t Hoff was a good friend of Arrhenius. The equation is... 

The values of the equilibrium constant K listed in Table A are those obtained from data at low pressures, where the gases behave ideally. At higher pressures the mole percent of ammonia observed is generally larger than the calculated value. For example, at 400°C and 300 atm, the observed mole percent of NH3 is 47 the calculated value is only 41. 

The quantity Q that appears in this equation is the reaction quotient referred to in Chapter 12. It has the same mathematical form as the equilibrium constant, K the difference is that the terms that appear in Q are arbitrary, initial pressures or concentrations rather than equilibrium values. 

As pointed out previously, the value of the standard cell voltage, E°, is a measure of the spontaneity of a cell reaction. In Chapter 17, we showed that the standard free energy change, AG°, is a general criterion for reaction spontaneity. As you might suppose, these two quantities have a simple relation to one another and to the equilibrium constant, K, for the cell reaction. 

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