Heat capacity of reactants and products

In general, the heat capacity of any substance changes with change in temperature. Thus in a reaction, the heat capacities of reactants and products change with variation in temperature and this change results in change of AH values for reactions as the temperature varies. For example, in the generalized typical reaction shown below,... 

The last term in the above equation, AH, refers to the enthalpies of transformation that the reactants and/or products may undergo in the temperature interval 298 to T. Enthalpies of transformations are added (the sign is + ) if products transform and subtracted (the sign is if reactants transform. Molar heat capacities of reactants and products do vary... 

Heat capacities of reactants and products are equal and constant in each vessel. Catalyst heat capacity is also constant. 

If analytic equations for the heat capacities of reactants and products are unavailable, we still can carry out the integration required by Equation (4.78) by graphical or numerical methods. In essence, we replace Equation (4.79) by the expression... 

If the heat capacities of reactants and products are expressed by equations of the form... 

We saw in Chapter 4 that AH for a reaction at any temperature can be calculated from a value at one temperature and from the values of the heat capacities of reactants and products in the temperature range of interest. Similarly, AS can be calculated at... 

This equation is known as Kirchhoff s law in integral form. It enables us to calculate the heat of reaction at different temperatures by knowing die heat of reaction at one temperature, say, 298K, and heat capacities of reactants and products. 

When the heat capacity of reactants and products (i.e., AC°) is independent of temperature,... 

The original work extends the discussion to more complex reactions and the determination of activation energies and heats of reaction. However, the equations were developed for homogeneous reactions in solution and required twelve assumptions some of which are very difficult to satisfy when applied to dta studies of solid state reactions. These assumptions 2u e (/) the heat transfer coefficients and heat capacities of reactants and products are equal and constant, and (ii) that the temperature is uniform throughout the sample and reference material. Freeman and Carroll and Wendlandt have suggested simplifications in Borchardt and Daniels procedure. 

Prediction of reliable values at elevated temperatures (above 50 to 100 C) requires accurate data for the enthalpy and heat capacity of reactants and products. Such data have been published by Helge.son et al. (1978) and Shock and Helgeson (1988). Methods of calculating reaction equilibria at elevated temperatures and pressures arc described in these references and in Nordstrom and Munoz (1985) and Kharaka et al. (1988). 

If the Specific heat capacity of reactants and products is considered equal (which is acceptable for most enzyme-catalyzed reactions), AH and AS will be independent on temperature so that derivating Eq. 3.109 ... 

If the heat capacities of reactants and products are the same (i.e., ACp = 0) A5° and AH° are independent of temperature. Subject to the condition that the difference in the heat capacities between reactants and products is zero, differentiation of Eq. (1.47) with respect to temperature yields a more familiar form of the van t Hoff equation ... 

It should be noted that each reaction enthalpy, AH, depends on the average temperature of the experiment. If the change in heat capacity between reactants and products, ACpr, is significant, a temperature-dependent value of AH might be necessary. 

Problem Find the molar enthalpy of reaction for the standard state formation of ammonia from hydrogen and nitrogen at 298, 400, 600, and 800 K (1) assuming constant heat capacities for reactants and products and (2) using 29.75 + 0.025T - 150,000/7 for the heat capacity (J mol ) of ammonia. 

Suppose we wish to relate A,(AB) with the standard enthalpies of formation of the species involved at 298.15 K. First we have to correct the reaction enthalpy from T = 0 to T = 298.15 K, for example, by using the integrated heat capacities (see equation 2.14) of reactants and products ... 

The enthalpies of reactants and products increase with temperature. If the total enthalpy of the reactants increases more than that of the products, then the reaction enthalpy will decrease as the temperature is raised (Fig. 6.34). On the other hand, if the enthalpy of the products increases more with an increase in temperature than that of the reactants, then the reaction enthalpy will increase. The increase in enthalpy of a substance when the temperature is raised depends on its heat capacity at constant pressure (Eq. 20), so we ought to be able to predict the change in reaction enthalpy from the heat capacities of all the reactants and products. 

The first and second terms on the right-hand side of Equation (1.44), (dH/dT), are the total heat capacities of all the products and reactants at constant pressure, respectively. Equation (1.44) then becomes ... 

If it is assumed that the heat capacity of the TSC is a linear combination of those of reactants and products, the linear free energy relation results... 

The initial increase in the heat capacity signal corresponds to the reaction heat capacity or the change in heat capacity from reactants to products (see arrow in Rg. 2.112). A thermodynamic analysis of the epoxy-aromatic amine reaction revealed that the primary amine-epoxy reaction contributes less to the increase in reaction heat capacity than does the secondary epoxy-amine reaction (Swier and van Mele 2003b). Information specific to the different steps in the reaction mechanism can therefore be deduced from the heat capacity signal, in contrast to the global conversion evolution obtained from the total heat flow signal. 

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