Van‘t Hoff isochore

This equation is sometimes called the van t Hoff isochore, to distinguish it from van t Hoff s osmotic pressure equation (Section 8.17). An isochore is the plot of an equation for a constant-volume process. 

Strategy. For convenience, we will call the higher temperature T> and the lower temperature T. (1) The van t Hoff isochore, Equation (4.78), is written in terms of a ratio, so we do not need the absolute values. In other words, in this example, we can employ the solubilities s without further manipulation. We can dispense with the units of. v for the same reason. (2) We convert the two temperatures to kelvin, for the van t Hoff isochore requires thermodynamic temperatures, so T2 = 343.9 K and 7) = 312.0 K. (3) We insert values into the van t Hoff isochore (Equation (4.78)) ... 

The isochore, Equation (4.81), was derived from the integrated form of the Gibbs-Helmholtz equation. It is readily shown that the van t Hoff isochore can be rewritten in a slightly different form, as ... 

We often talk about the isochore when we mean the van t Hoff isochore. ... 

Figure 4.8 The equilibrium constant K for the isomerization of 1-butene depends on the temperature van t Hoff isochore plot of In K (as y) against 1 7 (as x) from which a value of A//°...

Figure 5.17 The solubility s of a partially soluble salt is related to the equilibrium constant (partition) and obeys the van t Hoff isochore, so a plot of In s (as y ) against 1 IT (as x ) should be linear, with a slope of AF lution -t- R . Note how the temperature is expressed in kelvin a graph drawn with temperatures expressed in Celsius would have produced a curved plot. The label KIT on the x-axis comes from l/T -t- 1/K...

The strength of acid sites can be approximated by determining the heat of adsorption using the Van t Hoff isochore. In this method the pressures P required to give a fixed surface coverage at a series of temperatures T is determined. The derivative of In P with respect to T is related to the isosteric heat of adsorption. This technique is not used routinely. Nor is that of IR spectroscopy, where it is reported that Lewis and Bronsted sites can be differentiated by using substituted compounds. 

Problem 5 Give the thermodynamic derivation of van t Hoff isochore or van t Hoff equation. Mention its applications also. 

The van t Hoff Isochore or van t Hoff Equation (Equation (46.11), Frame 46) expressed the variation of the In Kp/po term with change in temperature, T in the form ... 

Some texts refer to this equation (46.12) as the van t Hoff Isochore (Frame 1) (but there is no constancy of volume involved). 

Having found in this manner the thermodynamic justification of the law of mass action for dissolved substances, we can apply the van t Hoff isochore, viz —... 

The effect of temperature on the rate constants and adsorption coefficients was assumed to be given by the Arrhenius equation and Van t Hoff isochore respectively, i.e.. 

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