Effect of temperature on the equilibrium constant

If U h° is replaeed by the eonventional AH° when the moles represented by stoiehiometrie numbers reaet, then 

If a proeess involves ehemieal reaetions, heat effeets will invariably be present. The amount of heat produeed in a ehemieal reaetion 

The values for standard heats of reaetion may be found in the literature or ealeulated by thermodynamie methods. The physieal state of the reaetants and produets (e.g. gas, liquid, or solid) must also be speeified, if the reaetion eonditions are sueh that different states may eoexist. For example. 

In proeess design ealeulations, it is usually more eonvenient to express the heat of reaetion in terms of the enthalpy per mole of produet formed or reaetant eonsumed. Sinee enthalpy is a state funetion, standard heats of reaetion ean be used to estimate the AH at different temperatures by making a heat balanee over a hypothetieal proeess  

AHproaucts = enthalpy ehange to bring produets from the standard temperature baek to reaetion temperature T 

If uih° is replaced by the conventional AH0 when the moles represented by stoichiometric numbers react, then 

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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... 

In order to illustrate this principle, let the effect of temperature on the equilibrium constant of an exothermic reaction, involving the oxidation of a metal to its oxides, be considered. Upon increasing the temperature of this reaction some of the metal oxides will dissociate into the metal and oxygen and thereby reduce the amount of heat released. This qualitative conclusion based on Le Chatelier s principle can be substantiated quantitatively from the Varft Hoff isochore. 

Please realize that the effect of temperature on the equilibrium constant depends on which of the two opposing reactions is exothermic and on which is endothermic. You must have information on the heat of a reaction before you can apply Le Chateliers principle to judge how temperature alters the equilibrium. 

Equation (3.11) gives the effect of temperature on the equilibrium constant. Note that a plot of In K versus T should give a straight line of slope —AG /R. 

The effect of temperature on the equilibrium constant for the association reaction for water is interesting. This reaction has the value K = 1 /Kw, which at 298.15 K is 1.0 x 1014 so that log/if = 14. With increasing temperature, logAf (and hence, K) first decreases and then increases. The effect of temperature on K is given by... 

FIGURE 1.6 The effect of temperature on the equilibrium constants. [Graph reconstructed from data by W. Stumm and J. J. Morgan, Aquatic Chemistry An Introduction Emphasizing Chemical Equilibria in Natural Waters, Wiley Interscience, New York, 1981, p. 71.]... 

Finally, it is worth noting that, according to Car-berry [19], heat transfer effects are only of minor importance in reversible reactions, since the effect of temperature on the equilibrium constant compensates at least partly for the effect of temperature on the rate constants. As an example, the temperature rise towards the pellet center, which is observed for exothermic equilibrium reactions, leads to a decrease of the equilibrium constant, but in addition also to an increase of the forward rate constant [91]. 

According to Eq. (15.17), the effect of temperature on the equilibrium constant K is determined by the sign of AH°. Thus when AH° is positive, i.e., when the standard reaction is endothermic, an increase in T results in an increase in K. Equation (15.25) shows that an increase in K at constant P results in an increase in [] (yi)" this implies a shift of the reaction to the right and an increase in ec. Conversely, when AH° is negative, i.e., when the standard reaction is exothermic, an increase in T causes a decrease in K and a decrease in n (yi Y" constant P. This implies a shift of the reaction to the left and a decrease in ee. 

The rigorous development of the effect of temperature on the equilibrium constant is based on tlie definition of the Gibbs energy, writtenfor a chemical species in its standard state ... 

The endothermic nature of this exchange process on smectites has been verified from the effect of temperature on the equilibrium constant of exchange, Ke. The van t Hoff equation ... 

Qualitative experimental observations on the effect of temperature on the equilibrium constant, K... 

To study TSA systems with the solute movement analysis we must determine the effect of tenperature changes on the solute waves, the rate at which a tenperature wave moves in the column, and the effect of temperature changes on concentration. The first of these is easy. As tenperature increases the equilibrium constants, and K, both decrease, often following an Arrhenius type relationship as shown in Eq. fl8-7). If the effect of temperature on the equilibrium constants is known, new values of the equilibrium constants can be calculated and new solute velocities can be determined. 

To round out our discussion of this reaction, let s calculate the effect of temperature on the equilibrium constant in reaction (8.18). From Appendix B we find the following data ... 

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