Equilibrium constant pressure 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. 

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.)...

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 phase rule permits only two variables to be specified arbitrarily in a binaiy two-phase system at equilibrium. Consequently, the cui ves in Fig. 13-27 can be plotted at either constant temperature or constant pressure but not both. The latter is more common, and data in Table 13-1 are for that case. The y-x diagram can be plotted in either mole, weight, or volume frac tions. The units used later for the phase flow rates must, of course, agree with those used for the equilibrium data. Mole fractious, which are almost always used, are appfied here. 

You may wonder why the equilibrium constant, 11, has no units. The reason is that each term in the reaction quotient represents the ratio of the measured pressure of the gas to the thermodynamic standard state of one atmosphere. Thus the quotient (f3No2)2/f>N2o4 in Experiment 1 becomes... 

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... 

SOLUTION First convert the units of partial pressures to bars using 1 bar = 105 Pa P i7 = 4.2 X 10 8 bar, Pcli = 8.3 X 10 8 bar. Write the expression for the equilibrium constant from the chemical equation given. 

We will see functions like the one occurring under the logarithm operator quite often. For efficiency, this is generally written as In(Products)/(Reactants), where (Products) and (Reactants) denote the partial pressures of the species relative to the standard state pressure raised to a power that is equal to the stoichiometric coefficients. Kp is the equilibrium constant in terms of pressures. Since all pressures are in the same units, Rp is dimensionless. Note that in some literature there may be a combination of some power of P with Kp to obtain an equilibrium constant with pressure units. In this case. 

Here Q(t) denotes the heat input per unit volume accumulated up to time t, Cp is the specific heat per unit mass at constant pressure, Cv the specific heat per unit mass at constant volume, c is the sound velocity, oCp the coefficient of isobaric thermal expansion, and pg the equilibrium density. (4) The heat input Q(t) is the laser energy released by the absorbing molecule per unit volume. If the excitation is in the visible spectral range, the evolution of Q(t) follows the rhythm of the different chemically driven relaxation processes through which energy is... 

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. 

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 first row the relative dielectric constant for the compound is given. In the second row the valency of the unit is given. The other rows give the values for the various FH parameters. Remaining parameters the characteristic size of a lattice site 0.3 nm the equilibrium constant for water association K — 100 the energy difference for a local gauche conformation with respect to a local trans energy it/ 8 — 0.8 A T the volume fraction in the bulk (pressure control) of free volume was fixed to (pbv = 0.042575... 

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 form of the equilibrium constant in Equation (10.21) is different from that presented in introductory courses. It has the advantages that 1) it is explicit that Kp is a dimensionless quantity 2) it is explicit that the numerical value of Kp depends on the choice of standard state but not on the units used to describe the standard state pressure the equilibrium constant has the same value whether P° is expressed as 750.062 Torr, 0.98692 atm, 0.1 MPa, or 1 bar. 

Equilibrium constants are also dependent on temperature and pressure. The temperature functionality can be predicted from a reaction s enthalpy and entropy changes. The effect of pressure can be significant when comparing speciation at the sea surface to that in the deep sea. Empirical equations are used to adapt equilibrium constants measured at 1 atm for high-pressure conditions. Equilibrium constants can be formulated from solute concentrations in units of molarity, molality, or even moles per kilogram of seawater. 

Table 15.1 Solubility as (S = 35) Stoichiometric Equilibrium Constants (-logKip) for a Function of Temperature and Pressure Where K p Calcite and Aragonite Has Units of (mol/kg) ...

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... 

Of course, the equilibrium constant Km the latter equation does not have the same value as the ATin the equilibrium equation for ammonia. The numerical value of ATdepends on the particular reaction, the temperature, and the units used to describe concentration. For liquid solutions, the concentrations are usually expressed as molarity. For a mixture of gases, the concentration of each molecular species is commonly given either as molarity or as pressure in atmospheres. 

Adsorption experiments are conducted at constant temperature, and an empirical or theoretical representation of the amount adsorbed as a function of the equilibrium gas pressure is called an adsorption isotherm. Adsorption isotherms are studied for a variety of reasons, some of which focus on the adsorbate while others are more concerned with the solid adsorbent. In Chapter 7 we saw that adsorbed molecules can be described as existing in an assortment of two-dimensional states. Although the discussion in that chapter was concerned with adsorption at liquid surfaces, there is no reason to doubt that similar two-dimensional states describe adsorption at solid surfaces also. Adsorption also provides some information about solid surfaces. The total area accessible to adsorption for a unit mass of solid —the specific area Asp — is the most widely encountered result determined from adsorption studies. The energy of adsorbate-adsorbent interaction is also of considerable interest, as we see below. 

The subscript p on the left-hand side indicates that the equilibrium constant of Eq. 9.42 is in terms of the pressures of the constituents of the reactions. In the next section the equilibrium constant in concentration units, Kc, will also be used. 

The equilibrium constant in pressure units was previously encountered in Eq. 9.42. It can be written, using the conventions introduced in this section, as... 

The equilibrium constant in pressure units can be obtained from the reaction thermochemistry via Eq. 9.44,... 

By Eq. 9.91, the equilibrium constant in concentration units can be related to the equilibrium constant in pressure units... 

Although Kcj is given in concentration units, the equilibrium constants are more easily determined from the thermodynamic properties in pressure units, Kpj. They are related by... 

The exact definition of the equilibrium constant given by IUPAC requires it to be defined in terms of fugacity coefficients or activity coefficients, in which case it carries no units. This convention is widely used in popular physical chemistry texts, but it is also common to find the equilibrium constant specified in terms of molar concentrations, pressure or molality, in which cases the equilibrium constant will carry appropriate units. 

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