Pressure standard-state temperature

This method is invalid because the temperature in the denominator of the equation must be the temperature at which the liquid-vapor transition is at equilibrium. Liquid water and water vapor at 1 atm pressure (standard state, indicated by ) are in equilibrium only at 100° C = 373 K. 

In electrochemistry, the electron level of the normal hydrogen electrode is important, because it is used as the reference zero level of the electrode potential in aqueous solutions. The reaction of normal hydrogen electrode in the standard state (temperature 25°C, hydrogen pressure 1 atm, and unit activity of hydrated protons) is written in Eqn. 2-54 ... 

You may wonder how a reaction, such as combustion of methane, can occur at 25°. The fact is that the reaction can be carried out at any desired temperature. The important thing is that the AH° value we are talking about here is the heat liberated or absorbed when you start with the reactants at 25° and finish with the products at 25°. As long as AH0 is defined this way, it does not matter at what temperature the reaction actually occurs. Standard states for gases are 1 atm partial pressure. Standard states for liquids or solids usually are the pure liquid or solid at 1 atm external pressure. 

From the foregoing discussion, it follows that the standard exergy of one of the reactants can be estimated by use of the standard affinity of the reaction, provided that we know the values of the standard exergy of the other reactants and products. The numerical values of the molar exergy thus obtained of various chemical substances in the standard state (temperature T° = 298 K, pressure p° = 101.3 kPa, activity a° = 1) are tabulated as the standard chemical exergy of chemical substances in the literature on engineering thermodynamics [Ref. 9.]. 

Strictly, both T and K in Eq. 1.41 should be written T° and K° to denote the fact that they refer to the Standard States chosen for the reactants and products in a chemical reaction. As discussed in Special Topic 1, Standard states include a prescription of both temperature and applied pressure [usually T° = 298.15 K and P° = 0.1 MPa (1 bar) or 101.325 kPa (1 atm)], and it is under this condition lhat the chemical reaction described by K is investigated at equilibrium. The issue of temperature effects on K, then, is actually the problem of finding how K changes when the Standard-State temperature is changed at fixed Standard-Slate pressure. Evidently, according to Eqs. 1.41 and 1.42,... 

The chemical potential fn can be identified with the molar Gibbs energy Gi at the standard- ate temp aturc and pressure or with the molar Helmholtz energy Ai (= Gi-pVi Ui-TSi) at the standard-state temperature and molar volume. The first alternative is usual in thermodynamic tables it gives the relations... 

In considering the effect of pressure on activity, we must recall that the standard state pressure (P°) is not always the same as the system pressure (P), so that the differentiation with respect to pressure is not always completely analogous to differentiation with respect to temperature. First of all, for variable pressure standard states, those that do have P° = P, we have... 

For gases and supercritical fluids, fugacities are normally used, and the standard state is normally chosen as the ideal gas at the system temperature (T) and one bar, i.e., a fixed pressure standard state P° = 1 bar), so that normally... 

Normally of course the expression for the variation of K with P is simpler than this, perhaps because all three states of matter may not be present, but also because it is quite unusual to use a variable pressure standard state for constituents whose fugacities are known or sought, (because this adds complexities rather than simplifying matters), and the In Qig) term is therefore essentially never required. To take a real example, let s consider the brucite-periclase reaction again. We have discussed the variation of the equilibrium constant for the brucite-periclase-water reaction with temperature at one bar, and showed that the equilibrium temperature for the reaction at one bar is about 265°C. Calculation of the equilibrium temperature of dehydration reactions such as this one at higher pressures was discussed briefly in 13.2.2. Here we will discuss the reaction in different terms to demonstrate the relationships between activities, standard states and equilibrium constants. 

Standard state - A defined state (specified temperature, pressure, con-cenlration, e1e.)fortabulatingthermodynamic functions and carrying outthermodynamic calculations. The standard state pressure is usually taken as 100,000 Pa(l bar), but various standard state temperatures are used. [2]... 

Here f° is the pure-component value of the intensive quantity/at the standard-state temperature and pressure. A particular example of (10.4.14) appears in (10.3.11). For reaction equilibria, we are interested in situations for which/= g, ft, and Cp. We can consider many ways for obtaining values for the quantities so long as sufficient data are actually available. But here we consider one way that in which the / are computed from properties of formation. 

Let T° and P° be the standard-state temperature and pressure, and let P be the pure-f vapor pressure at T°. Then the difference between the vapor and liquid enthalpies of formation at P gives the latent heat of vaporization,... 

Standard temperature and pressure, or STP, is the standard condition most typically associated with gas law calculations. STP conditions are taken as room temperature (298.15 K) and atmospheric pressure. (Standard-state pressure is actually defined as 1 bar = 100 kPa. Atmospheric pressure is taken as 1 atm = 101.325 kPa. These slight differences are usually ignored.)... 

From Eq.l2.5.10and, since the G values are given at the standard state temperature of the reaction and pressure of 1 atm ... 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

The pressure at which standard-state fugacities are most conveniently evaluated is suggested by considerations based on the Gibbs-Duhem equation which says that at constant temperature and pressure... 

We find that the standard-state fugacity fV is the fugacity of pure liquid i at the temperature of the solution and at the reference pressure P. ... 

Correlations for standard-state fugacities at 2ero pressure, for the temperature range 200° to 600°K, were generated for pure fluids using the best available vapor-pressure data. 

At temperatures above those corresponding to the highest experimental pressures, data were generated using the Lyckman correlation all of these were assigned an uncertainty of 5% of the standard-state fugacity at zero pressure. Frequently, this uncertainty amounts to one half or more atmosphere for the lowest point, and to 1 to 5 atmospheres for the highest point. 

Standard-state fugacities at zero pressure are evaluated using the Equation (A-2) for both condensable and noncondensable components. The Rackett Equation (B-2) is evaluated to determine the liquid molar volumes as a function of temperature. Standard-state fugacities at system temperature and pressure are given by the product of the standard-state fugacity at zero pressure and the Poynting correction shown in Equation (4-1). Double precision is advisable. 

It is convenient to define a relative activity a. in tenns of the standard states of the reactants and products at the same temperature and pressure, where Aj = fi, =... 

All standard states, both for pure substances and for components in mixtures and solutions, are defined for a pressure of exactly 1 atmosphere. However the temperature must be specified. (There is some movement towards metricating this to a pressure of 1 bar = 100 kPa = 0.986 924 atm. This would make a significant difference only for gases at J= 298 K, this would decrease a p by 32.6 J moT )... 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

The values of fH° and Ay.G° that are given in the tables represent the change in the appropriate thermodynamic quantity when one mole of the substance in its standard state is formed, isothermally at the indicated temperature, from the elements, each in its appropriate standard reference state. The standard reference state at 25°C for each element has been chosen to be the standard state that is thermodynamically stable at 25°C and 1 atm pressure. The standard reference states are indicated in the tables by the fact that the values of fH° and Ay.G° are exactly zero. 

The first term, AG°, is the change in Gibb s free energy under standard-state conditions defined as a temperature of 298 K, all gases with partial pressures of 1 atm, all solids and liquids pure, and all solutes present with 1 M concentrations. The second term, which includes the reaction quotient, Q, accounts for nonstandard-state pressures or concentrations. Eor reaction 6.1 the reaction quotient is... 

From this equation, the temperature dependence of is known, and vice versa (21). The ideal-gas state at a pressure of 101.3 kPa (1 atm) is often regarded as a standard state, for which the heat capacities are denoted by CP and Real gases rarely depart significantly from ideaHty at near-ambient pressures (3) therefore, and usually represent good estimates of the heat capacities of real gases at low to moderate, eg, up to several hundred kPa, pressures. Otherwise thermodynamic excess functions are used to correct for deviations from ideal behavior when such situations occur (3). 

Energy balances differ from mass balances in that the total mass is known but the total energy of a component is difficult to express. Consequently, the heat energy of a material is usually expressed relative to its standard state at a given temperature. For example, the heat content, or enthalpy, of steam is expressed relative to liquid water at 273 K (0°C) at a pressure equal to its own vapor pressure. 

The equilibrium constant can be determined at any temperature from standard state information on reactants and product. Considering the synthesis of NH3, the equilibrium conversion can be determined for a stoichiometric feed of Hj and Nj, at the total pressure. These conversions are determined by the number of moles of each species against conversion X by taking as a basis, 1 mole of N2. 

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