Equilibrium Constants K

We can write a reactant quotient at any point during the reaction, but the most meaningful point is when the reaction has reached equilibrium. At equilibrium, the reaction quotient becomes the equilibrium constant, Kc (or Kp if gas pressures are being used). We usually express this equilibrium constant simply as a number without units since it is a ratio of concentrations or pressures. In addition, 

The concentrations of pure solids and liquids do not appear in the equilibrium constant expression. 

If the partial pressures of the gases were used, then the Kp would be written in the following form  

A Be sure that your value of R is consistent with the units chosen for the partial pressures of the gases. 

The numerical value of the equilibrium constant gives an indication of the extent of the reaction after reaching equilibrium. If Kc is large, then that means the numerator is much larger than the denominator and the reaction has produced a relatively large amount of products (reaction lies far to the right). If Kc is small, then the numerator is much smaller than the denominator and not much product has been formed (reaction lies far to the left). 

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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... 

The solubilization of diverse solutes in micelles is most often examined in tenns of partitioning equilibria, where an equilibrium constant K defines the ratio of the mole fraction of solute in the micelle (X and the mole fraction of solute in the aqueous pseudophase. This ratio serves to define the free energy of solubilization -RT In K). 

Suppose now that the sites are not independent, but that addition of a second (and subsequent) ligand next to a previously bound one (characterized by an equilibrium constant K ) is easier than the addition of the first ligand. In the case of a linear receptor B, the problem is fonnally equivalent to the one-dimensional Ising model of ferromagnetism, and neglecting end effects, one has [M] ... 

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... 

Ionic polymers may exist as undissociated, unsolvated ion pairs undissociated ion pairs solvated to some extent solvated ions dissociated to some extent or some combination of these. The propagation rate constant kp and the dissociation equilibrium constant K of the lithium salt of anionic... 

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... 

Data Source Equilibrium Constant (k) Mol.Vol. of Associate Density of Associate Molar Refractivity of Associate Refractive Index of Associate... 

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. 

Equilibrium Constants (K dr) and Relative Rates of Hydration of Some Aldehydes and Ketones... 

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

The following equation is used to calculate tlie chemical reaction equilibrium constant K at a temperature T. 

Many equilibrium calculations are accomplished using tlie plrase equilibrium constant K,. Tliis constant has been referred to in industry as a coiiiponential split factor, since it provides the ratio of the mole fractions of a component in two equilibrium pluises. The defining equation is... 

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 ... 

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