Equilibrium Constants and Units

You may wonder why equilibrium constants are reported without units. The equilibrium constant is related to the kinetics of a reaction as well as to the thermodynamics. (We explore this latter connection in Chapter 19.) Equilibrium constants derived from thermodynamic measurements are defined in terms of activities rather than concentrations or partial pressures. 

The activity of any substance in an ideal mixture is the ratio of the concentration or pressure of the substance either to a reference concentration (1 M) or to a reference pressure (1 atm). For example, if the concentration of a substance in an equilibrium mixture is 0.010 M, its activity is 0.010 M/1 M = 0.010. The units of such ratios always cancel and, consequently, activities have no units. Furthermore, the numerical value of the activity equals the concentration. For pure solids and pure liquids, the situation is even simpler because the activities then merely equal 1 (again with no units). 

In real systems, activities are also ratios that have no units. Even though these activities may not be exactly numerically equal to concentrations, we will ignore the differences. All we need to know at this point is that activities have no units. As a result, the thermodynamic equilibrium constants derived from them also have no units. It is therefore common practice to write all types of equilibrium constants without units, a practice that we adhere to in this text. In more advanced chemistry courses, you may make more rigorous distinctions between concentrations and activities. 

If the concentration of N2O4 in an equilibrium mixture is 0.00140 M, what is its activity (Assume the solution Is ideal.) 

Before doing calculations with equilibrium constants, it is valuable to understand what the magnitude of an equilibrium constant can tell us about the relative concentrations of reactants and products in an equilibrium mixture. It is also useful to consider how the magnitude of any equilibrium constant depends on how the chemical equation is expressed. 

---

Homogeneous Equilibria Equilibrium Constants and Units Heterogeneous Equilibria The Form of K and the Equilibrium Equation Summary of Rules for Writing Equilibrium Constant Expressions... 

We use capital K% to denote thermodynamic equilibrium constants, and we use square brackets to denote concentrations, say, in moles per unit volume. 

Here Ca is the number of adsorbed molecules A per unit volume, Q is the maximum loading of A, Ka is the adsorption equilibrium constant and Pa is the partial pressure of A. During adsorption there could be several energetically and topologically inequivalent adsorption sites and, in that case, total adsorption may simply become the sum of multiple Langmuir isotherms with contributions from different adsorption sites. The latter and several other isotherms that model... 

At 298 K, k TIh 6 X 10 s and when multiplied by which is an association equilibrium constant (with units of molarity ), the units M s of k correspond to those of a bimolecular rate constant. 

Phyiscal Constants and Units Physicochemical Properties of Organic Compounds Temperature Dependence of Equilibrium and Kinetic Constants Properties of the Earth... 

In this model the unimolecular constants are relative to the turnover number and the bimolecular constants are chosen to yield equilibrium constants in units of millimolar. The model is primarily based on dead-end inhibition by CrATP, the Michaelis constant for ATP in the ATPase reaction, the isotope partitioning experiments of Rose et al. (65), and various binding and kinetic constants found in the literature. The final model was based on a computer simulation study attempting to discover what combination of rate constants would lit the isotope partition data and the observed kinetic and binding constants. 

All the partial pressures calculated from the equilibrium constants assume unit activity for the condensed-phase components. This assumption is good when they are solid. Above the melting points of the salts, however, continued decomposition of the salt will result in a solution containing dissolved oxide and the partial pressures will depend on the melt composition, and will therefore change as the decomposition proceeds. Because of the form of Kt, the partial pressure calculation will be worst for small oxide concentrations. An examination of the various tables shows that 02 and NO are the major products of nitrate decomposition, the concentration of N02 being rather minor. This results from the fact that the equilibrium 2 N02 = 2 NO + 02 lies to the right for low pressures. 

After sufficient time, the system reaches an equilibrium where the monomer concentrations remain constant at M, and M2 oo. The initial concentrations, /M, o and IM2 0, are selected at will for each kind of system, but the corresponding equilibrium concentrations IMXj00 and /M2 oo are determined by the pertinent equilibrium constants and by M, 0 and M2 0 i. e. by the initial monomer concentrations, including those monomeric units which have been incorporated in IM 0 and /M 0. 

It is very important to distinguish between the solubility of a given solid and its solubility product. The solubility product is an equilibrium constant and thus has only one value for a given solid at a given temperature. Solubility, on the other hand, is an equilibrium position and has an infinite number of possible values at a given temperature, depending on the other conditions (such as the presence of a common ion). The Ksp values at 25°C for many common ionic solids are listed in Table 8.5. The units are customarily omitted. 

Equilibrium constants and rate coefficients used in computation of hydrogen—nitrogen—oxygen flames [155] (Constants are expressed as AT exp (—C/T) in 1.mole.sec units)... 

Equilibrium constants and solubility product constants have no units. 

Here a is the equilibrium or Henry constant at infinite dilution, a is also equal to the initial slope of the adsorption isotherm. The coefficient b is the equilibrium constant per unit of surface area, and hence this coefficient is related to the adsorption energy. C is the mobile phase concentration of the analyte in equilibrium with q, the concentration of the analyte in the stationary phase. The monolayer capacity, qs (qs = alb) is the upper limit of concentration in the stationary phase (sometimes called specific saturation capacity of the stationary phase). The Langmuir equation can also be written as ... 

It is very important to distinguish between solubility of a solid specie and the product of solubility. Whereas the product of solubility is an equilibrium constant and thereby only has one value at a certain temperature, solubility is an equilibrium position which has an infinity of possible values at a given temperature depending on other factors such as the presence on foreign ions and more. The solubility product and the solubility of ions do also have different units which is why they cannot be readily compared. 

Figure 4. The calculated values of the equilibrium constant (%) in units of k = zlFs/RT, the surface free energy change due to the conformational change, superimposed upon the dashed curve of the Bohr effect in units of log P0 5, the oxygen pressure for half saturation of hemoglobin. The sets of values are made to coincide at pH 6.3 and are in the same units over the same pH range. (Reproduced with permission from reference 8. Copyright 1975.)...

Titration curves are generated by computation of Eq. (5) by means of a FORTRAN program running on an IBM 370/168 computer. Computations are made under various conditions. Plots of all curves are carried out on a Calcomp flat-bed plotter interfaced to the computer. The titration curves can be analysed by three different procedures. The equivalence point Is determined by a derivative method, an extrapolation method and a non-linear least-squares curve-fitting method, the last being the best. The precision and accuracy achieved with the system vary according to the level of noise. If a titration with a large equilibrium constant and less than 0.004 units of noise is performed, the equivalence point can be determined to within a few tenths of a... 

The units of the rate are mol/time-area. The rate expressions follow directly from the reaction mechanism because the reactions are treated as elementary steps. When the adsorption-desorption reactions are in equilibrium, the amount of adsorbed CO is related to the gas-phase partial pressure of CO, an equilibrium constant, and the total number of surface sites. Equating the adsorption and desorption rates at equilibrium gives... 

Remember that a rate constant is the rate of reaction when the substances in the rate expression are at unit concentration, i.e. lmoldm (see page 251). The above equation shows that the size of the equilibrium constant depends simply upon how much faster the forward reaction is (at unit concentrations) than the back reaction (at unit concentrations) at that temperature. We need only to know the equilibrium constant and one of the rate constants in order to calculate the remaining rate constant. For example, for the reaction... 

Extension material to support this unit is available on our website. More advanced calculations involving equilibrium constants, and an introduction to free energy changes (AG) are to be found in Appendix 15 on the website. 

---