Van t Hoff reactions

Here is the chemical potential of i in its standard state and a, is its molal activity. This equation can be recast in the form known as the van t Hoff reaction isotherm ... 

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. 

The ceiling temperature of some monomers is given in Table 12.1 [2], Further, the van t Hoff reaction isobar can be calculated as... 

The van t Hoff reaction equation expresses the free energy change for a chemical reaction in the form... 

Equation 42, known as the van t Hoff reaction isobar, deflnes the temperature coefficient of Ka in terms of the heat of reaction AH° and the temperature T ... 

The enthalpy changes due to dimerization are determined from the van t Hoff relation. For a dimerization reaction between species i and j... 

A connnon approach has been to measure the equilibrium constant, K, for these reactions as a fiinction of temperature with the use of a variable temperature high pressure ion source (see section (Bl.7.2)1. The ion concentrations are approximated by their abundance in the mass spectrum, while the neutral concentrations are known from the sample mlet pressure. A van t Hoff plot of In K versus /T should yield a straight Ime with slope equal to the reaction enthalpy (figure B1.7.11). Combining the PA with a value for basicityG at one temperature yields a value for A.S for the half-reaction involving addition of a proton to a species. While quadnipoles have been tire instruments of choice for many of these studies, other mass spectrometers can act as suitable detectors [19, 20]. 

The Van t Hoff isotherm identifies the free energy relationship for bulk chemical reactions. 

Combining equation 6 and 7 with the Van t Hoff isotherm the Nemst equation for electrochemicA reactions is obtained ... 

Later, in the 1890s, Arrhenius moved to quite different concerns, but it is intriguing that materials scientists today do not think of him in terms of the concept of ions (which are so familiar that few are concerned about who first thought up the concept), but rather venerate him for the Arrhenius equation for the rate of a chemical reaction (Arrhenius 1889), with its universally familiar exponential temperature dependence. That equation was in fact first proposed by van t HofT, but Arrhenius claimed that van t Hoff s derivation was not watertight and so it is now called after Arrhenius rather than van t Hoff" (who was in any case an almost pathologically modest and retiring man). 

Thermodynamic quantities for a system may be determined from the van t Hoff equation Eq.(3), which defines the equilibrium constant, K, in terms of the reaction enthalpy, AH and the temperature, T. 

The principle has been enunciated, more especially in connexion with chemical reactions, by van t Hoff, under the name of the Principle of Mobile Equilibrium, and by Le Chatelier, as the Principle of Reaction. 

Nernst, in his Theoretische Chemie, devoted a whole chapter to a critical examination of the rule of Thomsen and Berthelot, and he concluded that in many cases the heat of reaction certainly does correspond very closely with the maximum work, AT, which latter magnitude he took from van t Hoff as a measure of the chemical affinity. Whilst pointing out that it very often gives results wholly incompatible with experience, and cannot therefore be indiscriminately applied, Nernst showed that the rule nevertheless holds good in too many cases to be wholly false in an appropriate metaphor he claimed that it contains a genuine kernel of truth which has not yet been shelled from its enclosing hull. This labour of emancipation was partially effected in the newer work of the same author, Applications of Thermodynamics to Chemistry, 1907, which is an attempt to place the rule of Berthelot on a scientific basis, and to determine under what conditions its use is legitimate. He points out that the equation ... 

What does this equation tell us Suppose that the reaction is endothermic, then AH° is positive. If T2 > T, then 1/T2 < 1/T, and the term in braces is also positive. Therefore, In (K2/K,) is positive, which implies that K,/K, > 1 and therefore that K2 > K,. In other words, an increase in temperature favors the formation of product if the reaction is endothermic. We predict the opposite effect for an exothermic reaction because AHr° is then negative. Therefore, the van t Hoff equation accounts for Le Chatelier s principle for the effect of temperature on an equilibrium. 

One word of warning when using the van t Hoff equation for reactions involving gases, the equilibrium constants must be K, not K(.. If we want a new value for Kc for a gas-phase reaction, we convert from K(. into K at the initial temperature (by using Eq. 12), use the van t Hoff equation to calculate the value of K at the new temperature, and then convert that K into the new Kc by using Eq. 12 at the new temperature. 

Relation between standard reaction Gibbs free energy and equilibrium constant van t Hoff equation ... 

Here, the a s refer to the activities in the chosen arbitrary state. The concept of activity is presented separately in a later section. For the present, the activity of a species in a system may just be considered to be a function of its concentration in the system, and when the species is in a pure form (or in its standard state), its activity is taken to be unity. The activities ac, aD, aA, aB given above correspond to the actual conditions of the reaction, and these may or may not correspond to the state of equilibrium. Two special situations can be considered. In the first, the arbitrary states are taken to correspond to those for the system at equilibrium. Q would then become identical to the equilibrium constant K and, according to the Van t Hoff isotherm, AG would then be zero. In the second situation, all the reactants and the products are considered to be present as pure species or in their standard states, and aA, aB, ac, and aD are all equal to 1. Then (7=1 and the free energy change is given by... 

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