Standard state symbol

The standard-state symbol (shown as a degree sign) indicates that the variable has been measured with all the substances in their standard states. For example, when the enthalpy change of a reaction is measured at the standard state, it is the standard enthalpy of reaction, (also called standard heat of reaction). 

It should be noted that the right superscript, signifying the standard state of thermodynamic functions, is pertinent to the reference state considered, that is, rj =0 it should not be confused with the usual standard state symbols used in chemical thermodynamics (AS, AH , etc.), based on the SHE as the electrical reference state. 

For biochemical reactions in which hydrogen ions (H ) are consumed or produced, the usual definition of the standard state is awkward. Standard state for the ion is 1 M, which corresponds to pH 0. At this pH, nearly all enzymes would be denatured, and biological reactions could not occur. It makes more sense to use free energies and equilibrium constants determined at pH 7. Biochemists have thus adopted a modified standard state, designated with prime ( ) symbols, as in AG°, AH°, and so on. For values determined... 

IUPAC suggests fi for the activity coefficient with a Raoult s law standard state. We will use instead so as not to confuse the activity coefficient with the fugacity. which is also represented by the symbol f-... 

Figure 6.13 Standard states for CC14 in jrdQH O +. Y2CCI4 at T 308.15 K. The represents the Raoult s law standard state with f2 =./F = 23.26 kPa and the represents the Henry s law standard state with /2 — v = 19.23 kPa. The symbols represent the experimental results.

The quantity //, - H° is called the relative partial molar enthalpy and given the symbol L,. It is the difference between the partial molar enthalpy in the solution and the partial molar enthalpy in the standard state. That is,... 

Subscripts and superscripts of these symbols give reference to chemical species, charge, standard state, etc., of quantities concerned. Symbols that seldom occur have not been included in the above list, their meaning having been given in the text. 

Enthalpies of reaction can also be calculated from individual enthalpies of formation (or heats of formation), AHf, for the reactants and products. Because the temperature, pressure, and state of the substance will cause these enthalpies to vary, it is common to use a standard state convention. For gases, the standard state is 1 atm pressure. For a substance in an aqueous solution, the standard state is 1 molar concentration. And for a pure substance (compound or element), the standard state is the most stable form at 1 atm pressure and 25°C. A degree symbol to the right of the H indicates a standard state, AH°. The standard enthalpy of formation of a substance (AHf) is the change in enthalpy when 1 mol of the substance is formed from its elements when all substances are in their standard states. These values are then tabulated and can be used in determining A//°rxn. 

Redox half-reactions are often written for brevity as, for example, Li+ + e - Li. with the state symbols omitted. The electrode system represented by the half-reaction may also be written as Li+ /Li. The standard redox potentials for ion-ion redox systems can be determined by setting up the relevant half-cell and measuring the potential at 298 K relative to a standard hydrogen electrode. For example, the standard redox potential for the half-reactions... 

The superscript to the heat of formation symbol A// represents the standard state, and the subscript number represents the base or reference temperature. From the example for the Law of Heat Summation, it is apparent that the heat of formation of carbon monoxide from Eq. (1.8) is... 

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 standard reduction potentials used to calculate E ceii for the decomposition of water apply only to reactants and products in their standard states. However, in pure water at 25°C, the hydrogen ions and hydroxide ions each have concentrations of 1 x 10 mol/L. This is not the standard state value of 1 mol/L. The reduction potential values for the non-standard conditions in pure water are given below. The superscript zero is now omitted from the E symbol, because the values are no longer standard. 

E is the standard electrode potential, and represents a value of E measured (or calculated) when all activities are 1, when the applied pressure p is 1 atmosphere and with all redox materials participating in their standard states. As for E, E should be cited with subscripts to describe the precise composition of the redox couple indicated. Note that is often written as thus explaining why standard electrode potentials are commonly called nought . The symbol 0 implies standard conditions i.e. 298 K, p and unit activities throughout. 

The International Union of Puie and AppUed Chemistry now recommends a standard pressure of 0.1 MPa (1 bar) in place of the previously accepted standard of 101.325 kPa (1 atm). The difference in thermodynamic quantities is not significant for condensed phases, and differences in A// values are not significant even for gases, but the user of thermodynamic tables will have to note carefully the standard state chosen for any compilation of data. See Ref. 1, pp. 2—23 lUPAC Division of Physical Chemistry, Commission on Symbols, Terminology and Units, Manual of symbols and terminology for physico-chemical quantities and units, M. L. McGlashan, M. A. Paul, and D. N. Whiffen, eds., Pure andApp. Chem 51, 1 (1979), and Appendix IV, Pure and Applied Chem. 54, 1239 (1982). 

One could also interpret itself in terms of a similar process where the ligand is brought from a hypothetical standard state corresponding to C = 1. This interpretation is somewhat risky and should be avoided. Symbolically, we write the process as... 

Although this equation reduces to an identity whenever solute-solvent interactions are embodied in the definition of the Henry s law standard state (cf section 10.2), it must be noted that K[ is the molar ratio of trace element i in the two phases and not the weight concentration ratio usually adopted in trace element geochemistry. As we will see later in this section, this double conversion (from activity ratio to molar ratio, and from molar ratio to weight concentration ratio) complicates the interpretation of natural evidence in some cases. To avoid ambiguity, we define here as conventional partition coefficients (with the same symbol K ) all mass concentration ratios, to distinguish them from molar ratios and equilibrium constants. 

Chemists have found it possible to assign a numerical quantity for the entropy of each substance. When measured at 25° C and 1 atm, these are called standard entropies. Table l4-4 lists 12 such values, symbolized by S° where the superscript denotes the standard state. 

The standard enthalpy of formation of a substance (AfHx) is the enthalpy change involved at temperature T when one mole of the substance is formed in its standard state from its elements in their standard states. The symbol is used to denote standard state. It follows from the first law that the enthalpy change in the reaction... 

It may be more convenient to measure the volumetric feed rate at some standard state, especially when the reactor is to operate at a number of temperatures. If, for example, the material is gaseous when fed to the reactor at high temperature but is liquid at the standard state, care must be taken to specify precisely what state has been chosen. The relation between the space-velocity and space-time for actual feed conditions (unprimed symbols) and at standard conditions (designated by primes) is given by... 

Note that in the following analyses, we will drop the prime symbol. It should still be clear that deviation variables are being used. Then this linear representation can easily be separated into the standard state-space form of Eq. (72) for any particular control configuration. Numerical simulation of the behavior of the reactor using this linearized model is significantly simpler than using the full nonlinear model. The first step in the solution is to solve the full, nonlinear model for the steady-state profiles. The steady-state profiles are then used to calculate the matrices A and W. Due to the linearity of the system, an analytical solution of the differential equations is possible ... 

Using the same symbolism as the previous sub-section, Figure 2.7 shows a thermodynamic cycle for the formation of the cation of element M by treating the element in its standard state with an acid solution containing hydrated protons and producing the hydrated cation and an equivalent amount of dihydrogen ... 

In this equation the standard state corresponds to the state that results from letting fw - 1 and xw - 1, in which case = n°s w. Letting/ - 1 is equivalent to saying that the surfactant behaves ideally, and letting xw - 1 is equivalent to having pure surfactant possessing the kind of interactions it has when surrounded by water. Physically, this corresponds to an infinitely dilute solution of surfactant in water. Using the primed symbol to represent the chemical potential of surfactant in micelles per mole of micelles, we write... 

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