Enthalpy change, dependence

Because enthalpy is a state property, the enthalpy change depends on the initial and final states only, not on the path the process follows. As die sum of all the reactions in path 2 results in the same reaction as the one in path 1, the enthalpy change should be the same for both paths. 

The enthalpy of formation, which we have discussed in the previous section, offers an easy way to overcome this difficulty. We now introduce Hess s Law. Recall that enthalpy is a state function, and hence the enthalpy change depends on only the initial and fmal states. Hess s law is basically the same as stated above, but expressed in a different way Hess s law states that the enthalpy change for a chemical reaction is the same whether it takes place in one or several stages. Consider the combustion of methane again. ... 

When two infinitely dilute solutions containing ions are mixed without reacting there is essentially no enthalpy of mixing for this process. However, if an interaction does occur, such that a precipitate or more solvent, of some other compound is formed, a chemical reaction has occurred that is characterized by an enthalpy change for that process. In sufficiently dilute solution these enthalpy changes depend only on the ions that are involved in the process and not on the partner ions that remain behind. It then becomes possible to adopt another simplifying convention ... 

As it can be seen from the reaction (4.13), the enthalpy change depends also on the coefficients r, s, b, and c, thus on the given stoichiometry. For instance... 

Enthalpy changes depend somewhat on the temperature at which the process occurs. Standard thermodynamic data are commonly quoted for a temperature of 25.00° C (298.15 K), and this can be given as a subscript or in parentheses. Thus,-... 

The enthalpy change of a reaction is an extensive property. This means that the enthalpy change depends upon the amounts of reactants consumed, which, in turn, control the quantities of product made. In the absence of any other information, we always assume that the AH value for a reaction is produced when the number of moles of reactants that combine are those indicated by the chemical equation. So, when we write the thermochemical equation... 

The magnitude of any enthalpy change depends on the temperature, pressure, and state (gas, liquid, or solid crystaUine form) of the reactants and products. To compare enthalpies of different reactions, we must define a set of conditions, called a standard suite, at which most enthalpies are tabulated. The standard state of a substance is its pure form at atmospheric pressure (1 atm) and the temperature of interest, which we usually choose to be 298 K (25 °C). The standard enthalpy change of a reaction is defined as the enthalpy change when all reactants and products are in their standard states. We denote a standard enthalpy change as AH°, where the superscript ° indicates standard-state conditions. 

The enthalpy of fusion is a constant at 6 kj/mol, so the enthalpy change depends on the size of the sample. Because the molar mass of water is 18 g/mol, a sample that is 240 grams is a bit more than 10 moles. That means we should expect an answer that is a bit larger than 60 kj, which is consistent with our result. 

The magnitude of any enthalpy change depends on tire conditions of temperature, pressure, and state (gas, liquid, or solid, crystalline form) of the reactants and products. In order to compare the enthalpies of different reactions, we must define a set of conditions, called a standard state, at which most enthalpies are tabulated. 

The enthalpy change depends on the amounts of reactants used. If the coefficients of the thermochemical equation are multiplied or divided by a common factor, the value of the enthalpy change is changed by the same fector. For example ... 

When you write thermochemical equations, you must use the state symbols (g), ( ), (s), and (aq). The equation is meaningless without them because the size of the enthalpy change depends on the state of the reactants and products. If Equation 10.5 is written with water in the liquid state,... 

For experiments conducted at constant pressure, the second term ia equation 36 disappears. The expression for the temperature dependence is then obtained by performing an indefinite integration on the remainder of the equation after assuming that the enthalpy change of volatilization, (/i. — hp ), is constant with respect to temperature. The resulting equation is... 

Enthalpy changes of processes depend only on the end states. Normally the enthalpy change of reaction is known at some standard tem-... 

The sensitivity of the equilibrium constant to temperature, therefore, depends upon the enthalpy change AH . This is usually not a serious limitation, because most reaction enthalpies are sufficiently large and because we commonly require that the perturbation be a small one so that the linearization condition is valid. If AH is so small that the T-jump is ineffective, it may be possible to make use of an auxiliary reaction in the following way Suppose the reaction under study is an acid-base reaction with a small AH . We can add a buffer system having a large AH and apply the T-jump to the combined system. The T-jump will alter the Ka of the buffer reaction, resulting in a pH jump. The pH jump then acts as the forcing function on the reaction of interest. 

Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2). Alternatively, for any process B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant ... 

The modem process for manufacturing nitric acid depends on the catalytic oxidation of NH3 over heated Pt to give NO in preference to other thermodynamically more favour products (p. 423). The reaction was first systematically studied in 1901 by W. Ostwald (Nobel Prize 1909) and by 1908 a commercial plant near Bochum. Germany, was producing 3 tonnes/day. However, significant expansion in production depended on the economical availability of synthetic ammonia by the Haber-Bosch process (p. 421). The reactions occurring, and the enthalpy changes per mole of N atoms at 25 C are ... 

As already mentioned, the enthalpy change A//° involved in an elementary propagation step corresponds to the equilibrium constant S. The parameter a, however, is purely entropically influenced mainly due to the steric restrictions during the formation of a helical nucleus. The determination of a, since it is related to the same power (3n - 2) of s, requires the consideration of the dependence of the thermodynamic parameters on the chain length (Eq. (9 a)). 

The Arrhenius activation energy,3 obtained from the temperature dependence of the three-halves-order rate constant, is Ea = 201 kJ mol-1. This is considerably less than the standard enthalpy change for the homolysis of acetaldehyde, determined by the usual thermodynamic methods. That is, reaction (8-5) has AH = 345 kJ mol-1. At first glance, this disparity makes it seem as if dissociation of acetaldehyde could not be a predecessor step. Actually, however, the agreement is excellent when properly interpreted. 

Because enthalpy is a state function, the enthalpy change of a system depends only on its initial and final states. Therefore, we can carry out a reaction in one step or visualize it as the sum of several steps the reaction enthalpy is the same in each case. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

As shown in Section 16-1. varies with temperature in a way that can be understood using the principles of thermod namics. Temperature is the only variable that causes a change In the value of. eq. The effect of temperature on depends on the enthalpy change of the reaction, ZlH. An increase in temperature always shifts the equilibrium position in the endothermic direction, and a decrease in temperature always shifts the equilibrium position in the exothermic direction. 

The binding enthalpy change (AH) could be determined either from the plots of the temperature dependence of the binding constant according to the van t Hoff relationship ... 

The effect of pressure on AG° and AH0 depends on the choice of standard states employed. When the standard state of each component of the reaction system is taken at 1 atm pressure, whether the species in question is a gas, liquid, or solid, the values of AG° and AH0 refer to a process that starts and ends at 1 atm. For this choice of standard states, the values of AG° and AH0 are independent of the system pressure at which the reaction is actually carried out. It is important to note in this connection that we are calculating the enthalpy change for a hypothetical process, not for the actual process as it occurs in nature. This choice of standard states at 1 atm pressure is the convention that is customarily adopted in the analysis of chemical reaction equilibria. 

In addition to its constraints on the concentration dependent portions of the rate expression thermodynamics requires that the activation energies of the forward and reverse reactions be related to the enthalpy change accompanying reaction. In generalized logarithmic form equation 5.1.69 can be written as... 

The enthalpy of formation of a compound is a so-called thermodynamic state function, which means that the value depends only on the initial and final states of the system. When the formation of crystalline NaCl from the elements is considered, it is possible to consider the process as if it occurred in a series of steps that can be summarized in a thermochemical cycle known as a Born-Haber cycle. In this cycle, the overall heat change is the same regardless of the pathway that is followed between the initial and final states. Although the rate of a reaction depends on the pathway, the enthalpy change is a function of initial and final states only, not the pathway between them. The Born-Haber cycle for the formation of sodium chloride is shown as follows ... 

All partitioning properties change with temperature. The partition coefficients, vapor pressure, KAW and KqA, are more sensitive to temperature variation because of the large enthalpy change associated with transfer to the vapor phase. The simplest general expression theoretically based temperature dependence correlation is derived from the integrated Clausius-Clapeyron equation, or van t Hoff form expressing the effect of temperature on an equilibrium constant Kp,... 

Time resolution of the enthalpy changes is often possible and depends on a number of experimental parameters, such as the characteristics of the transducer (oscillation frequency and relaxation time) and the acoustic transit time of the system, za, which can be defined by ra = r0/ua where r0 is the radius of the irradiated sample, and va is the speed of sound in the liquid. The observed voltage response of the transducer, V (t) is given by the convolution of the time-dependent heat source, H (t) and the instrument response function,... 

The temperature dependence of reaction enthalpies can be determined from the heat capacity of the reactants and products. When a substance is heated from T to T2 at a particular pressurep, assuming no phase transition is taking place, its molar enthalpy change from AHm (T]) to AHm (T2) is... 

Enthalpy changes of processes depend only on the end states. Normally the enthalpy change of reaction is known at some standard temperature, Tb = 298 K for instance. The simplest formulation of the heat balance, accordingly, is to consider the reaction to occur at this temperature, to transfer whatever heat is required and to raise the enthalpy of the reaction products to their final values. 

Hess s law, or the law of constant heat summation, states that at constant pressure, the enthalpy change for a process is not dependent on the reaction pathway, but is dependent only upon the initial and final states of the system. The enthalpy changes of individual steps in a reaction can be added or subtracted to obtain the net enthalpy change for the overall reaction. 

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