Equilibrium constant temperature/pressure dependence

Hence, the reaction order is seen to depend both on the equilibrium constant K2, which depends on temperature, and the actual partial pressure p2- We shall later see that the latter term for a catalyst is related to the extent that the surface is covered by a reactant. 

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. 

The dependence of the equilibrium constant on pressure for a chemical reaction is easily determined from Equation (11.4) with the aid of Equation (4.38), which gives the change of the Gibbs energy with pressure at constant temperature and constant number of moles. Thus, we have... 

At a constant temperature, the dependence of the equilibrium constant on pressure P) is given by Eq. 27. 

In practice, many reactions do not go to completion but rather approach a state or position of equilibrium. This equilibrium position, at which the reaction apparently comes to an end, is a mixture of products and unconsumed reactants present in fixed relative amounts. Once equilibrium has been achieved, there is no further net conversion of reactants to products unless the experimental conditions of the reaction (temperature and pressure) are changed. The equilibrium state is characterized by the equilibrium constant, which has a unique value for each reaction. Knowing the equilibrium constant and the initial amounts of reactants and products, we can calculate the composition of the equilibrium reaction mixture. Knowing the equilibrium constant and its dependence on experimental conditions, we can manipulate conditions to maximize the practical yield of that reaction. Calculating the equilibrium composition for a particular reaction and its dependence on experimental conditions is therefore a practical skill of enormous importance in chemistry. 

The maximum solubility of the solvent is limited by the maximum rate of the reaction at equilibrium. According to the Van t-Hoff relationships, the equilibrium constant K i depends on pressure and temperature. Generally, chemisorption processes are more effective at lower temperature and higher pressure. 

The equilibrium constant Ky therefore depends on the pressure as well as on the temperature, and for this reason is less useful than... 

The dependence on pressure can be derived in much the same way as the dependence on temperature. The pressure dependence X(p) reflects a volume change. The slope of the equilibrium constant with pressure is... 

A remarkable achievement of statistical mechanics is the accurate prediction of gas-phase chemical reaction equilibria from atomic structures. From atomic masses, moments of inertia, bond lengths, and bond strengths, you can calculate partition functions. You can then calculate equilibrium constants and their dependence on temperature and pressure. In Chapter 19, we will apply these ideas to chemical kinetics, which pertains to the rates of reactions. Reactions can be affected by the medium they are in. Next we will develop models of liquids and other condensed phases. 

Figure B2.5.7 shows the absorption traces of the methyl radical absorption as a fiinction of tune. At the time resolution considered, the appearance of CFt is practically instantaneous. Subsequently, CFl disappears by recombination (equation B2.5.28). At temperatures below 1500 K, the equilibrium concentration of CFt is negligible compared witli (left-hand trace) the recombination is complete. At temperatures above 1500 K (right-hand trace) the equilibrium concentration of CFt is appreciable, and thus the teclmique allows the detennination of botli the equilibrium constant and the recombination rate [54, M]. This experiment resolved a famous controversy on the temperature dependence of the recombination rate of methyl radicals. Wliile standard RRKM theories [, ] predicted an increase of the high-pressure recombination rate coefficient /r (7) by a factor of 10-30 between 300 K and 1400 K, the statistical-adiabatic-chaunel model predicts a...

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. 

As discussed in Sec. 4, the icomplex function of temperature, pressure, and equilibrium vapor- and hquid-phase compositions. However, for mixtures of compounds of similar molecular structure and size, the K value depends mainly on temperature and pressure. For example, several major graphical ilight-hydrocarbon systems. The easiest to use are the DePriester charts [Chem. Eng. Prog. Symp. Ser 7, 49, 1 (1953)], which cover 12 hydrocarbons (methane, ethylene, ethane, propylene, propane, isobutane, isobutylene, /i-butane, isopentane, /1-pentane, /i-hexane, and /i-heptane). These charts are a simplification of the Kellogg charts [Liquid-Vapor Equilibiia in Mixtures of Light Hydrocarbons, MWK Equilibnum Con.stants, Polyco Data, (1950)] and include additional experimental data. The Kellogg charts, and hence the DePriester charts, are based primarily on the Benedict-Webb-Rubin equation of state [Chem. Eng. Prog., 47,419 (1951) 47, 449 (1951)], which can represent both the liquid and the vapor phases and can predict K values quite accurately when the equation constants are available for the components in question. 

These data can be used to obtain the value of the equilibrium constant at any temperature and this in turn can be used to calculate the degree of dissociation through the equation for the conceiiuation dependence of the constant on the two species for a single element, die monomer and the dimer, which coexist. Considering one mole of the diatomic species which dissociates to produce 2x moles of the monatomic gas, leaving (1 — jc) moles of the diatomic gas and producing a resultant total number of moles of (1 +jc) at a total pressure of P atmos, the equation for the equilibrium constant in terms of these conceiiU ations is... 

Once equilibrium between liquid and vapor is reached, the number of molecules per unit volume in the vapor does not change with time. This means that the pressure exerted by the vapor over the liquid remains constant The pressure of vapor in equilibrium with a liquid is called the vapor pressure. This quantity is a characteristic property of a given liquid at a particular temperature. It varies from one liquid to another, depending on the strength of the intermolecular forces. At 25°C, the vapor pressure of water is 24 mm Hg that of ether, in which intermolecular forces are weaker, is 537 mm Hg. 

Clausius-Clapeyron equation An equation expressing the temperature dependence of vapor pressure ln(P2/Pi) = AHvapCl/Tj - 1/T2)/R, 230,303-305 Claussen, Walter, 66 Cobalt, 410-411 Cobalt (II) chloride, 66 Coefficient A number preceding a formula in a chemical equation, 61 Coefficient rule Rule which states that when the coefficients of a chemical equation are multiplied by a number n, the equilibrium constant is raised to the nth power, 327... 

Given any two of the four quantities EC, Aik, pH, Pco,/ the other two can always be calculated provided appropriate equilibrium constants are available (the equilibrium constants depend on temperature, salinity and pressure). Hydrogen ion concentration, for example, be calculated from Aik and EC with the equation... 

As previously noted, the equilibrium constant is independent of pressure as is AG. Equation (7.33) applies to ideal solutions of incompressible materials and has no pressure dependence. Equation (7.31) applies to ideal gas mixtures and has the explicit pressure dependence of the F/Fq term when there is a change in the number of moles upon reaction, v / 0. The temperature dependence of the thermodynamic equilibrium constant is given by... 

Solution A rigorous treatment of a reversible reaction with variable physical properties is fairly complicated. The present example involves just two ODEs one for composition and one for enthalpy. Pressure is a dependent variable. If the rate constants are accurate, the solution will give the actual reaction trajectory (temperature, pressure, and composition as a function of time). If ko and Tact are wrong, the long-time solution will still approach equilibrium. The solution is then an application of the method of false transients. 

In the deformed state, the variables in the Hamiltonian change from ( R , r ) to ( R , Ar ). However, the distribution p( r ) of finding the topology r depends solely on how the material is made instantaneously at thermal equilibrium (i.e., at constant temperature T, pressure p, etc.) i.e., p( r ) does not depend on the external deformation tensor A. Then, the final answer for the free energy of the deformed network is... 

All partitioning properties change with temperature. The partition coefficients, vapor pressure, KAW and KqA, are more sensitive to temperature variation because of the large enthalpy change associated with transfer to the vapor phase. The simplest general expression theoretically based temperature dependence correlation is derived from the integrated Clausius-Clapeyron equation, or van t Hoff form expressing the effect of temperature on an equilibrium constant Kp,... 

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