Van’t Hoff isotherm

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 ... 

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... 

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... 

From the Van t Hoff isotherm it follows that for the oxidation reaction considered, the standard free energy change at temperature T is given by... 

Considering the phosphorus oxidation reaction given earlier, and applying the Van t Hoff isotherm for nonequilibrium conditions,... 

The Gibbs function is a function of state, so values of AG obtained with the van t Hoff isotherm (see p. 162) and routes such as Hess s law cycles are identical. 

Q and K only have the same value when the reaction has reached equilibrium, i.e. when AGr = 0. At this extent of reaction, the relationship between and AG is given by the van t Hoff isotherm ... 

SAQ 4.8 Show that the van t Hoff isotherm is dimensionally self-consistent. 

Inserting values into the van t Hoff isotherm (Equation (4.55)) ... 

The correct use of the van t Hoff isotherm necessitates using the thermodynamic temperature (expressed in kelvin). 

And we see a further point the equilibrium constant K of a reaction is a direct function of A Gr according to the van t Hoff isotherm (Equation (4.55)). If the overall energy of reaction remains unaltered by the catalyst, then the position of equilibrium will also remain unaltered. 

Problem 4 Give the thermodynamic derivation of maximum work obtained from gaseous reactions or van t Hoff isotherm. 

So, van t Hoff isotherm gives the increase of free energy change accompanying the transfer of reactants at any arbitrary concentration (or partial pressure) to products at any arbitrary concentration (orpartied pressure). 

Equations (4) and (5) are other forms of van t Hoff isotherm. The maximum work obtained is also given by equations (3), (4) and (5), and often - AG is called the affinity of the reaction. 

Chemical equilibrium in homogeneous systems, from the thermodynamic standpoint—Gaseous systems—Deduction of the law of mass action—The van t Hoff isotherm—Principle of mobile equilibrium (Le Chateher and Braun)— Variation of the equilibrium constant with temperature—A special form of the equilibrium constant and its variation with pressure... 

The right-hand side is the complete expression for the equilibrium constant K in the case of a reaction between perfect gases In the case of a perfect gas, however, the internal energy and therefore C log T is independent of the volume and therefore of the pressure Hence K as defined above (m terms of volume concentrations) is independent of the pressure, a result which we have already obtained by a consideration of the van t Hoff isotherm K. is now seen to be explicitly a function of T If T be kept constant the terms on the right-hand side are constant, and hence for the system considered, the expression on the left is likewise constant, 1 e the equilibrium constant... 

U 0 represents the heat evolved by the reaction in the neighbourhood of the absolute zero At the actual zero the existence of a gaseous state is supposed to be impossible Now we have already seen that the affinity of a leaction such as the above occurring in a condensed system (liquid or solid) is given by a particular form of the van t Hoff isotherm, viz —... 

---