Kirchhoff s equation

The nature of the assumptions entertained in the deduction of Kirchhoff s equation ensure the theoretical validity of the latter only at low temperatures. Notwithstanding this, Juliusburger (1900), from a review of existing data, found the equation to give results deviating by 3 per cent, at most from the observed values for 74 substances out of 80 examined. He considers that it may be regarded as an empirical formula with three constants, up to the critical point, and gives the values of A, B, C for a number of substances. 

For the dependence of the heat of reaction at constant volume, we have Kirchhoff s equation ( 58) ... 

To calculate P at any other temperature we integrate Kirchhoff s equation for the heat of dilution ... 

From equations such as (3.106) one can readily determine AHrxn(Ti) at the standard temperature 7) of thermochemical compilations. How can we find the value AHrxn(T2) at other temperatures 72 of interest This is the subject of Kirchhoff s equation, which we shall derive as a simple consequence of the first law. 

Differentiating (3.107) with respect to 7 (at constant P), we obtain Kirchhoff s equation in the form... 

Figure 3.14 Graphical depiction of Kirchhoff s equation (3.111), showing the direct path for reaction at Tx compared with the indirect path for reaction at T2, with heating of initial reactants (A//h) and cooling of final products (AHc) to complete the thermochemical cycle AH(Ti) = A Hh + A H(T2) + A//c.

A further equation (Frame 11) involving an integration is Kirchhoff s equation which relates the enthalpy changes, AH% and AHj for a chemical reaction taking place at temperatures, T and T2, to an integral involving the heat capacity difference, ACp, between the products and reactants in the reaction ... 

Kirchhoff s equation), where is the molar heat capacity at constant pressure for species i at temperature T. 

Kirchhoff s equation holds for the vapour pressure of steam for this Brunelli gave ... 

From Kirchhoff s equations and equations (2) and (9) we then obtain the relation between the heat capacity of activation and the other kinetic parameters as... 

These equations are called the Clausius equations although the second, which relates the heat capacity change to the temperature coefficient of the heat of reaction, is also called Kirchhoff s equation and the last equation, giving the effect of volume on the heat of reaction, was first derived by De Donder. 

From Kirchhoff s equation (2.32) we have first, (using the abbreviation =... 

To obtain a more accurate equation we must take account of the fact that both and depend upon the temperature. The variation of with temperature is given by Kirchhoff s equation (2.32) so that... 

To integrate this equation accurately we must take account of the variation of Afh with temperature, and this may be done by using Kirchhoff s equation (2.32), which in this case gives us... 

Kirchhoff s Equation for Heat of Reaction (which involves the Principle of the First Law of Thermodynamics)... 

This is Kirchhoff s equation Its great importance lies in the fact that it allows one to calculate the temperature coefficient of heat effects from measurements of the specific heats of the substances involved in a very much more accurate manner than could possibly be done by actually measuring Q or Qv at two different temperatures... 

It is also possible1 to find the specific heats of solutions by determining the heat of dilution at different temperatures and using Kirchhoff s equation ( 20.11). 

These equations are often known as Kirchhoff s Equations, after their first protagonist. Equation 3.4 is more widely used than equation 3.5, and our attention will be confined to it from now on. 

VARIATION OF HEAT OF REACTION WITH TEMPERATURE -KIRCHHOFF S EQUATION... 

The above equation is known as Kirchhoff s equation. Similarly, at constant volume. 

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