Standard states fixed pressure

For species present as gases ia the actual reactive system, the standard state is the pure ideal gas at pressure F°. For Hquids and soHds, it is usually the state of pure real Hquid or soHd at F°. The standard-state pressure F° is fixed at 100 kPa. Note that the standard states may represent different physical states for different species any or all of the species may be gases, Hquids, or soHds. 

If we define the standard-state fugacity f° at a fixed pressure, then the second term on the left side of Eq. (50) vanishes and we obtain Eq. (42). However, if we define f° at the total pressure of the system, we obtain Eq. (43). 

From the definitions of standard states for components of solutions, it is clear that AGm is a function only of the temperature, because the standard state of each reactant and product is defined at a specific fixed pressure. Thus, AGm is a constant for a particular reaction at a fixed temperature. Hence, we can write... 

Although we have chosen to define the standard state at a fixed pressure, the vapor pressure of the pure solvent, the standard chemical potential is still a function of the pressure chosen, so that the first term on the right in Equation (16.32) is equal to Therefore,... 

EMF and vapour pressure measurements are dependent on the temperature, the number of phases involved and, importantly, the reference state of the component in question. The problem with the reference state is important as experimentally stated values of partial Gibbs energies will be dependent on this value. The standard states are fixed before optimisation and may actually have values different from those used by the original author. Therefore, as far as possible like should be compared with like. 

In this discussion the temperature and pressure of the reference state and of the standard state have been taken to be those of the solution this usage is consistent with the recommendations of the Commission on Symbols, Terminology, and Units of the Division of Physical Chemistry of the International Union of Pure and Applied Chemistry. For the standard state however, a fixed, arbitrary pressure (presumably 1 bar) might be chosen. If we define... 

The reference state of each component in a system may be defined in many other ways. As an example, we may choose the reference state of each component to be that at some composition with the condition that the composition of the reference state is the same at all temperatures and pressures of interest. For convenience and simplicity, we may choose a single solution of fixed composition to be the reference state for all components, and designate xf to be the mole fraction of the /cth component in this solution. If (Afikx) represents the values of the excess chemical potential based on this reference state, then (A/if x ) [T, P, x ] is zero at all temperatures and pressures at the composition of the reference state. That this definition determines the standard state is seen from Equation (8.71), for then... 

We find from this discussion that, when the reference state of a component in a multicomponent system is taken to be the pure component at all temperatures and pressures of interest, the properties of the standard state of the component are also those of the pure component. When the reference state of a component in a multicomponent system is taken at some fixed concentration of the system at all temperatures and pressures of interest, the system or systems that represent the standard state of the component are different for the chemical potential, the partial molar entropy, and for the partial molar enthalpy, volume, and heat capacity. There is no real state of the system whose properties are those of the standard state of a component. In such cases it may be better to speak of the standard state of a component for each of the thermodynamic quantities. 

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,... 

If the state of reaction components at a fixed constant pressure (generally at 1 atm) is considered as their standard state, the value of AO° depends only on tho temperature. Therofore the symbol of the change in standard free energy AO°t is marked by the suffix T contrary to the symbol of the change in froe energy AQj<.p, which depends op both, temperature and pressure. 

Included in this equation is the definition of K. Since G° is a property of pure species i in its standard state at fixed pressure, it depends only on temperature, It follows from Eq. (15.13) that K is also a function of temperature only. In spite of its dependence on temperature, K is called the equilibrium constant for the reaction. Equation (15.12) may now be written... 

The function A G° v,G° in Eq. (15.14) is the weighted difference (recall that the Vs are positive for products and negative for reactants) between the Gibbs energies of the products and reactants when each is in its standard state as a pure substance at the system temperature and at a fixed pressure. Thus the value of A G° is fixed for a given reaction once the temperature is established, and is independent of the equilibrium pressure and composition. Other standard property changes of reaction are similarly defined. Thus, for the general property M, we write... 

Since G° is a property of pure species i in its standard state at fixed pressure, it depends only on temperature. By Eq. (13.12)itfollowstliat AG° and hence K, are also functions of temperature onfy. 

Equation 2 must be satisfied at equilibrium whether the solution is initially supersaturated or undersaturated with respect to Si02, that is, whether H4Si04 initial > or H4Si04 initial < Ksq. The equilibrium activity in solution is independent of the amount of amoiphous Si02(s). The activity of pure Si02 (i.e., Xsi02 = 1) is a constant at fixed temperature and pressure under standard state conditions, we can choose Si02(s) to be unity. 

The third law of thermodynamics states that the entropy of any pure substance in equilibrium approaches zero at the absolute zero of temperature. Consequently, the entropy of every pure substance has a fixed value at each temperature and pressure, which can be calculated by starting with the low-temperature values and adding the results of all phase transitions that occur at intervening temperatures. This leads to tabulations of standard molar entropy S° at 298.15 K and 1 atm pressure, which can be used to calculate entropy changes for chemical reactions in which the reactants and products are in these standard states. 

The effect of temperature on the equilibrium constant follows from Eq. (4-41) written for pure speciesj in its standard state (wherein the pressure P° is fixed) ... 

In the cases discussed above, most of the standard states are chosen at a fixed reference pressure. Hence, neither Kg nor Ag° is a function pressure. Yet, if one or more of the standard states for any of the components were chosen to be at the system pressure, p, then both Kg and A would become... 

---