Heat of reaction at constant pressure

VAX T HOFF EQUATION. A relationship representing the variation with temperature (at constant pressure) of the equilibrium constant of a gaseous reaction in terms of the change in heat content, i.e., of the heat of reaction (at constant pressure). It has the form ... 

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 coefficient hT p = (dHld )T is the differential of the amount of heat that must be added to or extracted from the system for unit change in the extent of reaction at constant p and T, and its integral from = 0 to = 1 is the heat of reaction at constant pressure and temperature ... 

Recalling d(dH dIf)/dT - d(0HldT)/d%, we have from Eq. 2.15 the heat of reaction at constant pressure as a function of the heat capacities, Cp, of all the reaction species. The temperature dependence of the heat of reaction at constant pressure is thus determined by the partial molar heat capacities, cp of the reaction species as shown in Eq. 2.29 ... 

Under the ideal assumptions discussed above the combustion temperature is determined by the heat of reaction at constant pressure per unit mass as follows ... 

Heats of reaction at constant pressure and at constant volume.— Imagine now that in a system sensibly in equilibrium a small mass pt passes, without change of tmperature, from the state represented by the first member of the chemical equation to the state represented by the second member of the same equar... 

Isentropic-isopiestic systems are of no great practical importance, and the chief value of the function H lies in its relationship to the heat of reaction at constant pressure, Qp, Suppose that we allow a chemical system to react at the atmospheric pressure, in such a manner that the only work don-e is that due to the change in the volume of the system. 

The heat of reaction at constant pressure is therefore equal to the change in the function H. For this reason H is called the heat content of the system, or the heat function for constant pressure. 

Qp is the heat of reaction (at constant pressure) at the temperature r, and can be calculated from the heat of reaction Qp at the temperature Tq (usually room temperature) by means of a linear formula Qp = Qp — Cp T—Tq). Hence we obtain... 

The maximum electrical w ork nE which the cell is capable of doing at constant pressure is equal to the change in the thermodynamic potential, produced by the interaction of 1 mol. of the current producing substances in the cell. Similarly the heat of reaction (at constant pressure) is equal to the corresponding change in the heat content H. We have therefore... 

Let us consider for this purpose a chemical reaction at the absolute zero. The heat of reaction at constant pressure Qj, is equal to the change in the heat content H of the system consequent on the reaction. The affinity A is equal to the change in the thermodynamic potentials f of the reacting substances, i.e. = -h 2 and = - 2 -h TIS. 

The symbols most characteristic of the De Donder school are r j, rrp y and Arp, denoting respectively the heats of reaction at constant pressure and constant volume (with the old thermochemical convention that heat evolved is positive), and the volume change of reaction at constant T and p. These symbols have been discarded and we employ... 

Heat of Reaction at Constant Pressure versus Constant Volume... 

From this expression the value of the heat of reaction at constant pressure can be calculated if that at constant volume is known, or vice versa. An important use of equation (12.3) is in the determination of the AH values for combustion reactions, since the actual thermochemical measurements are made in an explosion bomb at constant volume. 

If the reaction involves solids and liquids only, and no gases, the volume change AV is usually so small that the PAV term in (12.2) may he neglected. In cases of this kind the heats of reaction at constant pressure and constant... 

Since AH is the heat of reaction at constant pressure, adjusted to ideal behavior, it follows that AH = AH + PAF = AH + An(RT), so that equation (33.18) becomes... 

A coffee-cup calorimeter (Figure 15-3) is often used in laboratory classes to measure heats of reaction at constant pressure, q, in aqueous solutions. Reactions are chosen so that there are no gaseous reactants or products. Thus, all reactants and products remain in the vessel throughout the experiment. Such a calorimeter could be used to measure the amount of heat absorbed or released when a reaction takes place in aqueous solution. We can consider the reactants and products as the system and the calorimeter plus the solution (mostly water) as the surroundings. For an exothermic reaction, the amount of heat evolved by the reaction can be calculated from the amount by which it causes the temperature of the calorimeter and the solution to rise. The heat can be visualized as divided into two parts. 

When reactant R of an energetic material reacts to generate product P, heat is released (or absorbed). Since the chemical bond energy of R is different from that of P, the energy difference between R and P appears as heat. The rearrangement of the molecular structure of R changes the chemical potential. The heat of reaction at constant pressure, represented by Qp, is equal to the enthalpy change of the chemical reaction ... 

The enthalpy of reaction equals the heat of reaction at constant pressure. 

In the preceding discussion, we noted that the enthalpy change equals the heat of reaction at constant pressure. This will be sufficient for the purpose of this chapter, which is to introduce the concepts of heat of reaction and enthalpy change. Later we will look at thermodynamics in more detail. Still, it is useful at this point to note briefly the relationship of enthalpy to internal energy. 

As you can see, AU does not differ a great deal from AH. This is the case in most reactions, so that the heat of reaction at constant pressure is approximately equal to the change of internal energy. 

We introduced the thermodynamic property of enthalpy, H, in Chapter 6. There we noted that the change in enthalpy equals the heat of reaction at constant pressure. Now we want to look at this property again, but define it more precisely, in terms of the energy of the system. We begin by discussing the first law of thermodynamics. 

In Chapter 6, we defined enthalpy tentatively in terms of the relationship of AH to the heat of reaction at constant pressure, qp. We now define enthalpy, H, precisely as the quantity U + PV. Because U, P, and V are state functions, H is also a state function. This means that for a given temperature and pressure, a given amount of a substance has a definite enthalpy. Therefore, if you know the enthalpies of substances, you can calculate the change of enthalpy, AH, for a reaction. 

Recall that the heat of reaction at constant pressure, qp, equals the enthalpy change A//. The second law for a spontaneous reaction at constant temperature and pressure becomes... 

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