Extensive property enthalpy change

It is thus seen that heat capacity at constant volume is the rate of change of internal energy with temperature, while heat capacity at constant pressure is the rate of change of enthalpy with temperature. Like internal energy, enthalpy and heat capacity are also extensive properties. The heat capacity values of substances are usually expressed per unit mass or mole. For instance, the specific heat which is the heat capacity per gram of the substance or the molar heat, which is the heat capacity per mole of the substance, are generally considered. The heat capacity of a substance increases with increase in temperature. This variation is usually represented by an empirical relationship such as... 

In the early part of this century, many types of solid electrolyte had already been reported. High conductivity was found in a number of metal halides. One of the first applications of solid electrolytes was to measure the thermodynamic properties of solid compounds at high temperatures. Katayama (1908) and Kiukkola and Wagner (1957) made extensive measurements of free enthalpy changes of chemical reactions at higher temperatures. Similar potentiometric measurements of solid electrolyte cells are still made in the context of electrochemical sensors which are one of the most important technical applications for solid electrolytes. 

At equilibrium, the extensive properties U, S, V, Nh and the linear combination of them are functions of state. Such combinations are the Helmholtz free energy, the Gibbs free energy, and enthalpy, and are called the thermodynamic potentials. Table 1.13 provides a summary of the thermodynamic potentials and their differential changes. The thermodynamic potentials are extensive properties, while the ordinary potentials are the derivative of the thermodynamic potentials and intensive properties. 

The differences in the hydration of a solnte in H2O and D2O have been extensively stndied by measnring their thermodynamic properties, the change of free energy (AG°t), enthalpy (A//°t), and entropy (AY°t) at the transfer of 1 mol of solnte from a highly dilute solution in H2O to the same concentration in D2O under reversible conditions (mostly 25 °C and atmospheric pressure). Greyson measured the electromotive force (emf) of electrochemical cells of several alkali halides containing heavy and normal water solutions. The cell potentials had been combined with available heat of solution data to determine the entropy of transfer of the salts between the isotopic solvents. The thermodynamic properties for the transfer from H2O to D2O and the solubilities of alkali halides at 25° in H2O and D2O are shown in Table 4. 

Enthalpy (H) An extensive property of a substance that can be used to obtain the heat absorbed or released by a chemical reaction or physical change at constant pressure. It is defined as the sum of the internal energy (U) and the product of the pressure and the volume of the system (PV) H = U + PV. 

The enthalpy change for a reaction is a state function and it is an extensive property. Explain. 

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... 

Formation of CO2. Equation 5.27 is the formation reaction for 3 mol of COaCg). Because enthalpy is an extensive property> the enthalpy change for this step is 3AHf [C02(g)]. 

This is called volume of mixing and it maybe positive (volume expansion upon mixing), negative (contraction) or zero (no change). Similar expressions can be written for all extensive properties.a An important property is the enthalpy of mixing. 

Every substance has a characteristic enthalpy. In a chemical process, the enthalpy of reaction is the enthalpy of the products minus flie enthalpy of the reactants rxn = H(products) — H(reactants). Enthalpies of reaction follow some simple rules (1) Enthalpy is an extensive property, so the entiialpy of reaction is proportional to the amount of reactant that reacts. (2) Reversing a reaction changes the sign of AH. (3) The enthalpy of reaction depends on flie physical states of tiie reactants and products. 

A molar transition quantity of a pure substance is the change of an extensive property divided by the amount transferred between the phases. For example, when an amount n in a liquid phase is allowed to vaporize to gas at constant T and p, the enthalpy change is... 

At the nominal melting point Tm there is a first-order phase transition from the crystal to the mesophase with the usual discontinuities in the extensive properties (e.g. volume and entropy). In Fig. 5.7, we schematically illustrate a hypothetical differential-scanning-calorimetry (DSC) trace and the variation in volume of the sample versus temperature for an ideal nematic. The values for the changes in enthalpy (AH 45 kJ mol" ) and volume (A V 10%) at are typical of those changes in extensive properties that occur on melting ordinary organic molecular crystals. However, if you continue to heat the opalescent-looking mesophase, there is a second transition to a transparent isotropic state above Td. Nematic melts... 

When multiples of a reaction are considered, the same multiple of the energy change must be used. This applies to fractional as well as whole-number multiples. This is a consequence of enthalpy being an extensive property. 

Various thermometric assessments have been in the center of retailored techniques used to detect a wide variety of heat effects and properties. The traditional operation aims to measure, for example, heat capacities, total enthalpy changes, transitions and phase change heats, heats of adsorption, solution, mixing, and chemical reactions. The measured data can be used in a variety of clever ways to determine other quantities. Special role was executed by methods associated with enough adequate temperature measurements, which reveals an extensive history coming back to the first use of the word calorimeter introduced by the work Wilcke and later used by Laplace, Lavoisier as already discussed in the previous Chapter 4. 

Is the change in enthalpy for a reaction an extensive property Explain the relationship between AH for a reaction and the amounts of reactants and products that undergo reaction. 

In thermodynamics it often is necessary to distinguish between extensive and intensive properties. The value of an extensive property changes with the amount of material in the system, whereas the value of an intensive property is independent of the amount of material. Examples of extensive properties are mass, volume, and total free energy, enthalpy and entropy, whereas intensive properties include pressure, temperature, density and molar free energy, enthalpy and entropy. Generally, systems at equilibrium are defined in terms of their intensive properties. 

Students often ask, What is enthalpy The answer is simple. Enthalpy is a mathematical function defined in terms of fundamental thermodynamic properties as H = U+pV. This combination occurs frequently in thermodynamic equations and it is convenient to write it as a single symbol. We will show later that it does have the useful property that in a constant pressure process in which only pressure-volume work is involved, the change in enthalpy AH is equal to the heat q that flows in or out of a system during a thermodynamic process. This equality is convenient since it provides a way to calculate q. Heat flow is not a state function and is often not easy to calculate. In the next chapter, we will make calculations that demonstrate this path dependence. On the other hand, since H is a function of extensive state variables it must also be an extensive state variable, and dH = 0. As a result, AH is the same regardless of the path or series of steps followed in getting from the initial to final state and... 

The inequalities of the previous paragraph are extremely important, but they are of little direct use to experimenters because there is no convenient way to hold U and S constant except in isolated systems and adiabatic processes. In both of these inequalities, the independent variables (the properties that are held constant) are all extensive variables. There is just one way to define thermodynamic properties that provide criteria of spontaneous change and equilibrium when intensive variables are held constant, and that is by the use of Legendre transforms. That can be illustrated here with equation 2.2-1, but a more complete discussion of Legendre transforms is given in Section 2.5. Since laboratory experiments are usually carried out at constant pressure, rather than constant volume, a new thermodynamic potential, the enthalpy H, can be defined by... 

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