Equilibrium constant concentration units

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. 

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 ... 

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. 

Substitute these values into the equilibrium expression for catalytic methanation. (The expression was obtained in Example 15.2.) Although until now we have consistently carried units along with numbers in calculations, it is the usual practice to write equilibrium constants without units. We will follow that practice here. Substitution of concentrations into the equilibrium-constant expression gives... 

Think About It When putting the equilibrium concentrations into the equilibrium expression, we leave out the units. It is common practice to express equilibrium constants without units. We wUl examine the reason why in Section 15.5. 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

Equilibrium constants for protein-small molecule association usually are easily measured with good accuracy it is normal for standard free energies to be known to within 0.5 kcal/mol. Standard conditions define temperature, pressure and unit concentration of each of the three reacting species. It is to be expected that the standard free energy difference depends on temperature, pressure and solvent composition AA°a also depends on an arbitrary choice of standard unit concentrations. 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

A first-order rate constant has the dimension time, but all other rate constants include a concentration unit. It follows that a change of concentration scale results in a change in the magnitude of such a rate constant. From the equilibrium assumption of transition state theory we developed these equations in Chapter 5 ... 

By custom, the units of concentration are always included in the units of rate constants but are customarily omitted for equilibrium constants. Problem 7-15 provides further insights. 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

Equilibrium constants are dimensionless numbers, yet the concentrations used in an equilibrium constant expression have units. To understand this, we need to explore the reaction quotient Q, introduced in Chapter 14. In Section 16-1 we explore in detail the link between Q and Keq. Here we use Q to address the issue of concentration units and the equilibrium constant. 

Chemical equilibria often involve pure liquids and solids in addition to gases and solutes. The concentration of a pure liquid or solid does not vary significantly. Figure 16-4 shows that although the amount of a solid or liquid can vary, the number of moles per unit volume remains fixed. In other words, the concentrations of pure liquids or solids are always equal to their standard concentrations. Thus, division by standard concentration results in a value of 1 for any pure liquid or solid. This allows us to omit pure liquids and solids from equilibrium constant expressions. For a general reaction (2A + iBt= C D-l-. S where S is a pure solid or liquid ... 

Write the equilibrium constant expression for the reaction of iron metal with strong aqueous acid, and indicate the concentration units for each reagent ... 

The law of mass action states that the rate of a reaction is proportional to the product of the concentrations of the reactants. Thus the rate of the forward reaction is proportional to [A][R] = k+i[A][R], where k+ is the association rate constant (with units of M s ). Likewise, the rate of the backward reaction is proportional to [AR] = k i[AR], where k- is the dissociation rate constant (with units of s ). At equilibrium, the rates of the forward and backward reactions will be equal so... 

The kinetic factor is proportional to the energetic state of the system and (for heterogeneous catalytic systems) the number of active sites per unit volume (mass) of catalyst. The driving-force group includes the influence of concentration and distance from chemical equilibrium on the reaction rate, and the hindering group describes the hindering effect of components of the reaction mixture on the reaction rate. The kinetic factor is expressed as the rate constant, possibly multiplied by an equilibrium constant(s) as will be shown later. 

Because of uncertainties of equilibrium constants, ES, pH, temperature, /02 and other parameters (activity coefficient, ionic strength, activity of water, pressure), the estimated values of concentrations may have uncertainties of 1 in logarithmic unit. However, it can be concluded from the thermochemical calculations and fluid inclusion data that the Kuroko ore fluids have the following chemical features. 

Because for now we are concerned only with equilibrium conditions and not with the rate at which equilibrium is reached, we can combine k and k x to form a new constant, KA = MM which has the unit of concentration. KA is a dissociation equilibrium constant (see Appendix 1.2A [Section 1.2.4.1]), though this is often abbreviated to either equilibrium constant or dissociation constant. Replacing k and k gives ... 

For a binding reaction we can pick whether we show the reaction as favorable or unfavorable by picking the substrate concentration we use. Association constants have concentration units (M-1)- The equilibrium position of the reaction (how much ES is present) depends on what concentration we pick for the substrate. At a concentration of the substrate that is much less than the dissociation constant for the interaction, most of the enzyme will not have substrate bound, the ratio[ES]/[E] will be small, and the apparent equilibrium constant will also be small. This all means that at a substrate concentration much less than the dissociation constant, the binding of substrate is unfavorable. At substrate concentrations higher than the dissociation constant, most of the enzyme will have substrate bound and the reaction will be shown as favorable (downhill). (See also the discussion of saturation behavior in Chap. 8.)... 

Stability comparisons between siderophore complexes with different binding stoichiometries are complicated by the fact that the units for the concentration equilibrium constants are different. Also, since the Fe3+ binding moieties have different pKa values competition for binding with H+ differs, which will not be reflected in the pH-independent / mlh values. Therefore, it is important to have a scale for iron-siderophore complex... 

Equilibrium constants do not have units because in the strict thermodynamic definition of the equilibrium constant, the activity of a component is used, not its concentration. The activity of a species in an ideal mixture is the ratio of its concentration or partial pressure to a standard concentration (1 M) or pressure (1 atm). Because activity is a ratio, it is unitless and the equilibrium constant involving activities is also unitless. 

In the case of a bidentate ligand the ratio KMLJKWL)i has units of concentration in mol 1 1. If one assumes that the equilibrium constants for formation of the monoco-ordinated complexes ML and ML L are equal,2 combination of the equilibrium constants for (26) and (27) shows that the ratio... 

The solubility of a compound refers to the concentration of that compound in solution, either as a molarity or as a mass per unit volume. The solubility product constant is the equilibrium constant in terms of concentrations of ions, for the dissolution equilibrium, raised to their appropriate coefficients. 

The ratio k 1/k1 is effectively the dissociation equilibrium constant3 for ES in step (1), and is usually designated by Km (Michaelis constant, with units of concentration). The rate of formation of the product, P, is determined from step (2) 4... 

A statement such as K = 0.4 moldirT3 is wrong, although we find examples in a great number of references and textbooks. We ought, rather, to say K = 0.4 when the equilibrium constant is formulated (i) in terms of concentrations, and (ii) where each concentration is expressed in the reference units of mol dirT3. Equilibrium constants such as Kc or Kv are mere numbers. 

H30+. This reaction has an equilibrium constant K of about 2 x 10 5 at room temperature (298 K) when formulated in the usual units of concentration (mol dm 3). What is the associated change in Gibbs function of this reaction ... 

The value of Kw is 1.04 x 10-14 at 298 K when expressed in concentration units of mol dm-3. Like all equilibrium constants, its value depends on the temperature. Table 6.2 lists a few values of Kw as a function of temperature. Note how Kw increases slightly as the temperature increases. 

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,... 

Sigma (a) bonds Sigma bonds have the orbital overlap on a line drawn between the two nuclei, simple cubic unit cell The simple cubic unit cell has particles located at the corners of a simple cube, single displacement (replacement) reactions Single displacement reactions are reactions in which atoms of an element replace the atoms of another element in a compound, solid A solid is a state of matter that has both a definite shape and a definite volume, solubility product constant (/ p) The solubility product constant is the equilibrium constant associated with sparingly soluble salts and is the product of the ionic concentrations, each one raised to the power of the coefficient in the balanced chemical equation, solute The solute is the component of the solution that is there in smallest amount, solution A solution is defined as a homogeneous mixture composed of solvent and one or more solutes. 

It assumes that there are no significant solute-solute interactions and no strong solute-solvent interactions which would influence the distribution process. Concentrations are expressed as mass/unit volume, and usually C1 refers to an aqueous phase and C2 to a non-aqueous phase. The equilibrium constant (P or K) defining this system is referred to as the partition coefficient or distribution ratio. The thermodynamic partition coefficient (P ) is given by the ratio of the respective mole fractions as follows ... 

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