Pressure dependence enthalpy change

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. 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

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... 

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. 

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,... 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

The enthalpy change of a chemical reaction is known as the enthalpy of reaction, AHrxn- The enthalpy of reaction is dependent on conditions such as temperature and pressure. Therefore, chemists often talk about the standard enthalpy of reaction, AH°rxn - the enthalpy change of a chemical reaction that occurs at SATP (25 C and 100 kPa). Often, Alf n is written simply as AW°, The symbol is called nought. It refers to a property of a substance at a standard state or under standard conditions. You may see the enthalpy of reaction referred to as the heat of reaction in other chemistry books. 

The numerical values of cell potentials and half-cell potentials depend on various conditions, so tables of standard reduction potentials are true when ions and molecules are in their standard states. These standard states are the same as for tables of standard enthalpy changes. Aqueous molecules and ions have a standard concentration of 1 mol/L. Gases have a standard pressure of 101.3 kPa or 1 atm. The standard temperature... 

When Equation (10.24) is applied to the temperature dependence of In Kp, where Kp applies to an isothermal transformation, the A// that is used is the enthalpy change at zero pressure for gases and at infinite dilution for substances in solution (see Section 7.3). 

Because of this relationship between (TT — and p-j x.. the former quantity frequently is referred to as the Joule-Thomson enthalpy. The pressure coefficient of this Joule-Thomson enthalpy change can be calculated from the known values of the Joule-Thomson coefficient and the heat capacity of the gas. Similarly, as (H — is a derived function of the fugacity, knowledge of the temperature dependence of the latter can be used to calculate the Joule-Thomson coefficient. As the fugacity and the Joule-Thomson coefficient are both measures of the deviation of a gas from ideahty, it is not surprising that they are related. 

The enthalpies of formation of aqueous ions may be estimated in the manner described, but they are all dependent on the assumption of the reference zero that the enthalpy of formation of the hydrated proton is zero. In order to study the effects of the interactions between water and ions, it is helpful to estimate values for the enthalpies of hydration of individual ions, and to compare the results with ionic radii and ionic charges. The standard molar enthalpy of hydration of an ion is defined as the enthalpy change occurring when one mole of the gaseous ion at 100 kPa (1 bar) pressure is hydrated and forms a standard 1 mol dm-3 aqueous solution, i.e. the enthalpy changes for the reactions Mr + (g) — M + (aq) for cations, X (g) — Xr-(aq) for monatomic anions, and XOj (g) —< XO (aq) for oxoanions. M represents an atom of an electropositive element, e.g. Cs or Ca, and X represents an atom of an electronegative element, e.g. Cl or S. 

Clearly, this format takes more time to write, but consider the benefit to the student challenged to calculate an enthalpy change resulting from an isobaric and isoplethic heating. The expression itself tells the student what must be done, the initial and final temperatures must be known and an expression for a change in enthalpy depending only on temperature must be found because pressure and composition are constant. What does AH tell the student Push this example further. 

Since Enthalpy change (DH) depends on conditions of temperature, pressure, concentration of initial and final states, it is important to specify these. 

Since the enthalpy of an ideal gas depends on temperature only, a throttli process does not change the temperature of an ideal gas. For most real gases moderate conditions of temperature and pressure, a reduction in pressure constant enthalpy results in a decrease in temperature. For example, if stea at 1,000 kPa and 300°C is throttled to 101.325 kPa (atmospheric pressure),... 

Enthalpy change, A//, is equal to the heat involved in a process when the process is done under a constant pressure and involves no work except perhaps expansion (or contraction) against the atmosphere. When these conditions are not met. A// is a more fundamental quantity than heat. For example. A// is a state function, which means that the change in its value is independent of the path in going from the initial state to the final state. Another example of a state function is change in volume. For example, if a gas starts out occupying 2.5 L and finally occupies 4.5 L, AF = 2.0 L no matter if the gas is first expanded to 8.6 L, then contracted to 3.7 L, then expanded to 4.5 L, or if some other path were followed. (Heat, in contrast, does depend on the path, except when q = A//.) The A// value is important in both theoretical and practical terms in chemistry. 

The superscript zero on a thermodynamic function (for example, AH0) indicates that the corresponding process has been carried out under standard conditions. The standard state for a substance is a precisely defined reference state. Because thermodynamic functions often depend on the concentrations (or pressures) of the substances involved, we must use a common reference state to properly compare the thermodynamic properties of two substances. This is especially important because for most thermodynamic properties, we can measure only changes in that property. For example, we have no method for determining absolute values of enthalpy. We can measure only enthalpy changes (AH values) by performing heat flow experiments. 

In order to obtain —AH at conditions other than 1 atm and 25 C from equation (43) and tables of standard heats of formation, it is necessary to compute the enthalpy change of the reactant mixture and of the product mixture in going from 1 atm and 25°C to the given p and T additional tables are available to facilitate these computations for a number of materials [13], [15] [17], [26]-[28]. Usually the pressure dependence of —AH is negligible, and from equation (38) it follows that for ideal-gas reactions,... 

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