Equilibrium constant Gibbs-Helmholtz equation

The Van t Hoff isotherm establishes the relationship between the standard free energy change and the equilibrium constant. It is of interest to know how the equilibrium constant of a reaction varies with temperature. The Varft Hoff isochore allows one to calculate the effect of temperature on the equilibrium constant. It can be readily obtained by combining the Gibbs-Helmholtz equation with the Varft Hoffisotherm. The relationship that is obtained is... 

The effect of temperature on the equilibrium constant can be related to the Gibbs-Helmholtz equation ... 

Both K and AGq depend on temperature. The relationship between the equilibrium constant K and temperature is given by the Gibbs-Helmholtz equation, the integrated version of which is... 

There are other forms of the Gibbs-Helmholtz equation which are more frequently employed these deal with changes in the free energy, heat content, etc., accompanying an appreciable process. The process may be chemical or physical in nature the only restriction is that it takes place in a closed system, i.e., one of constant mass, which is in equilibrium with the external pressure. For the initial and final states, indicated by the subscripts 1 and 2, respectively, of an isothermal process, equation (25.8) becomes... 

Using the Gibbs-Helmholtz equation, we can calculate the equilibrium constant of a reaction at any temperature T from a knowledge of the equilibrium constant at one temperature Tq and the AH° of the reaction. For convenience we rewrite Eq. (11.60) ... 

The enthalpy (A//) and entropy (AS) of the complexation can be determined based on the temperature dependence of the equilibrium constant using the classical Gibbs-Helmholtz equation [33], [50], [51] ... 

Integrating (10.3.19) allows us to use a value for an equilibrium constant at one temperature to compute its value at another temperature T2. The result is the integrated form of the Gibbs-Helmholtz equation given in 3.3.2,... 

Temperature Dependence of Equilibrium Constant If we apply the Gibbs-Helmholtz Equation 5.76 on AG, we obtain... 

The molar standard-state free-energy change of a reaction (AG°) is a function of the equilibrium constant K) and is related to changes in the molar standard-state enthalpy (AH°) and entropy (A5°), as described by the Gibbs-Helmholtz equation ... 

Despite their names, the numerical values of equilibrium constants can vary depending on conditions, usually with varying temperatures. The effects of temperature on equilibria are easy to model. In the last chapter, we derived the Gibbs-Helmholtz equation as... 

This is useful because it implies that a plot of In K versus 1/Thas a slope of — A H°)/R. Values of A H can be determined graphically by measuring equilibrium constants versus temperature. (Compare this with the analogous plot of the Gibbs-Helmholtz equation. What differences and similarities are there in the two plots ) Figure 5.5 shows an example of such a plot. 

Gibbs-Helmholtz equation (physchem) An expression for the influence of temperature upon the equilibrium constant of a chemical reaction, d In K /iJT)p = AfTVRT, where K is the equilibrium constant, AH the standard heat of the reaction at the absolute temperature T, and R the gas constant. gibz helm,holts i,kw5-zh3n )... 

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

For a vstem at constant pressure and temperature, we see that the Gibbs free energy is constant for a reversible process but decreases for an irreversible process, reaching aminimum value consistent with the pressure and temperature for the equilibrium state just as for a system at constant volume the Helmholtz free energy is constant for a reversible process but decreases for an irreversible process. As with A, we can get the equation of state and specific heat from the derivatives of <7, in equilibrium. We have... 

Most of the experimental investigations on elastomers have been done under conditions of constant pressure. The thermodynamic function which can be used to describe equilibrium under these conditions is the Gibbs free energy (Equation 4.1), but since elastomers tend to deform at constant volume it is possible to use the Helmholtz free energy, A in the consideration of equilibrium. It is defined as... 

Equation 6.38 indicates that a system at constant temperature and pressure is at equilibrium when its Gibbs free energy is minimum. We have seen that for isolated systems, it is the entropy that is maximum at equilibrium, and that for NVT systems the Helmholtz free energy is minimum at equilibrium. 

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