Equilibrium constant, pressure variation

Expected Range of pH Values. Changes in solution pH in rock-water systems may result from two primary causes. The first cause is due to changes in equilibrium constants with variation in temperature and pressure. For example, the neutral pH of pure water changes from 7.00 at 20°C to approximately 5.6 at 200°C and 300 bars pressure due to changes in the value of the dissociation constant for water. Precipitation, dissolution, oxidation, or reduction of phases with consumption or generation of hydrogen ion is the second primary cause of pH variation. 

Using AG = —RT In K, where K is the conventional thermodynamic equilibrium constant, the variation of K with pressure is obtained ... 

Heterogeneous physical equilibria, e.g., between a pure solid and its vapor or a pure liquid and its vapor, can be treated in a manner similar to that just described. If the total pressure of the system is 1 atm., the fugacity of the vapor is here also equivalent to the equilibrium constant. The variation of In/ with temperature is again given by equation (33.16), where MP is now the ideal molar heat of vaporization of the liquid (or of sublimation of the solid) at the temperature T and a pressure of 1 atm. If the total pressure is not 1 atm., but is maintained constant at some other value, the dependence of the fugacity on the temperature can be expressed by equation (29.22), since the solid or liquid is in the pure state thus,... 

From the third law of thermodynamics, the entiopy 5 = 0 at 0 K makes it possible to calculate S at any temperature from statistical thermodynamics within the hamionic oscillator approximation (Maczek, 1998). From this, A5 of formation can be found, leading to A/G and the equilibrium constant of any reaction at 298 K for which the algebraic sum of AyG for all of the constituents is known. A detailed knowledge of A5, which we already have, leads to /Gq at any temperature. Variation in pressure on a reacting system can also be handled by classical thermodynamic methods. 

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,... 

The variation of the equilibrium constant for a reaction with pressure (at constant temperature) takes the same form as for the variation of a rate constant... 

Experiments indicate that the smooth variations of thermodynamic properties (e.g., V, Ky, and the specific heat at constant pressure Cp) with temperature are intermpted by the kinetic process of glass formation, leading to cooling rate dependent kinks in these properties as a function of temperature. In our view, these kinks cannot be described by an equilibrium statistical mechanical theory, but rather are a challenge for a nonequilibrium theory of glass formation. Nonetheless, some insight into the origin of these kinks and the qualitative... 

From the above equation, the variation of equilibrium disjoining pressure and the radius of curvature of plateau border with position for a concentrated emulsion can be obtained. If the polarizabilities of the oil, water and the adsorbed protein layer (the effective Hamaker constants), the net charge of protein molecule, ionic strength, protein-solvent interaction and the thickness of the adsorbed protein layer are known, the disjoining pressure II(x/7) can be related to the film thickness using equations 9 -20. The variation of equilitnium film thickness with position in the emulsion can then be calculated. From the knowledge of r and Xp, the variation of cross sectional area of plateau border Qp and the continuous phase liquid holdup e with position can then be calculated using equations 7 and 21 respectively. The results of such calculations for different parameters are presented in the next session. 

We also account for density, heat capacity, and molecular weight variations due to temperature, pressure, and mole changes, along with temperature-induced variations in equilibrium constants, reaction rate constants, and heats of reaction. Axial variations of the fluid velocity arising from axial temperature changes and the change in the number of moles due to the reaction are accounted for by using the overall mass conservation or continuity equation. 

VAX T HOFF EQUATION. A relationship representing the variation with temperature (at constant pressure) of the equilibrium constant of a gaseous reaction in terms of the change in heat content, i.e., of the heat of reaction (at constant pressure). It has the form ... 

Cryoscopy. Souchay (40) has summarized the application of fused salt cryoscopy to ionic solutes. Obviously two limitations are inherent in this method. Under ordinary pressures, measurements are possible at only one temperature—namely that of the transition point (e.g., ca. 32.38°C. in the case of Na2S04 10 H20). Secondly, the solute is being examined in solutions of high ionic strength only. Isopiestic vapor pressure measurements have been used as a variation, which, in principle, eliminate both limitations. However, it does not appear that it is as yet possible to analyze such data to yield equilibrium constants (33). Furthermore, Tobias has cast doubt upon the inherent accuracy of the method when the polyions contain more than 3 or 4 metal ions (41). 

Thermodynamics is used to predict whether reactants have a spontaneous tendency to change into products. This tendency is associated with a decrease in the free energy or Gibbs energy of the system (G) to a minimum. As a consequence, the thermodynamic criterion for spontaneous change at constant temperature and pressure is AG < 0. Under standard conditions (concentrations = 1 M, and P = 1 atm), the standard Gibbs energy variation (AG°) is related with the equilibrium constant (A) by equation 11 ... 

The usual environmental variables are temperature and pressure. However, one can imagine a system in which equilibrium is affected by some other variable (e.g., a magnetic field). Pressure is not considered to be a variable when equilibrium is described at a fixed total pressure (e.g., atmospheric). In general the number of environmental variables is designated as E. Most phase diagrams are at constant pressure so the only environmental variable is temperature. In this case E = 1. (If both variations in both temperature and pressure are considered, E = 2). 

Equation (5) represents the variation of equilibrium constant with temperature at constant pressure. This equation is referred to as van t Hoff reaction isochore (Greek isochore = equal space), as it was first derived by van t Hoff for a constant volume system. Since AH is the heat of reaction at constant pressure, the name isochore is thus misleading. Therefore, equation (S) is also called as van s Hoff equation. 

Variation of Equilibrium Constant, K, With Overall Total Pressure, P... 

The separation is at constant pressure. This assumption is usually good unless the column operates under vacuum. For vacuum systems, the equilibrium curve needs adjustment for pressure variations,... 

Recent measurements of the melt-water from high-altitude snow in Greenland and the Himalayas have given pH values of 5.15 instead of the expected value. Some of this difference can be explained by the variation of the equilibrium constants as a function of temperature, (a) Please calculate the pH of water at 0°C in equilibrium with C02 at its current partial pressure, (b) What would the partial pressure (in ppm) of C02 have to be in order to get precipitation of pH = 5.15 at this temperature (c) What do you conclude Note that at 0°C p/s(H = l.ll, pKai = 6.57, and pK = 10.62. 

The vertical portions of the isotherms for the 25 weight % alloy, representing hydrogen uptake at constant pressure, show no variation of pressure with composition, indicating that in this slower hydrogen absorption, equilibrium of three solid phases has been reached. 

---