Standard slates

ACTIVITY COEFFICIENT. A fractional number which when multiplied by the molar concentration of a substance in solution yields the chemical activity. This term provides an approximation of how much interaction exists between molecules at higher concentrations. Activity coefficients and activities are most commonly obtained from measurements of vapor-pressure lowering, freezing-point depression, boiling-point elevation, solubility, and electromotive force. In certain cases, activity coefficients can be estimated theoretically. As commonly used, activity is a relative quantity having unit value in some chosen standard state. Thus, the standard state of unit activity for water, dty, in aqueous solutions of potassium chloride is pure liquid water at one atmosphere pressure and the given temperature. The standard slate for the activity of a solute like potassium chloride is often so defined as to make the ratio of the activity to the concentration of solute approach unity as Ihe concentration decreases to zero. 

For the convenience of tabulation and compulation of thermodynamic data, it is essential lo present them in a commonly accepted form relative to a single standard slate of reference. At all lemperatures, the standard stale for a pure liquid or solid is the condensed phase under a pressure of I atmosphere. The standard stale for a gas is the hypothetical ideal gas at anil fugarity (equivalent til a perfect gas" stale), in which state the enthalpy is that of the real gas at the same temperature when the pressure approaches aero. Values of thermodynamic quantities for standard-state conditions are identified by a superscriptQ. and Hn. for instance, is the enthalpy change of a reaction when reactants and products are in the standard state. 

The effect of temperature on a chemical reaction at equilibrium can be described quantitatively by considering the change in a thermodynamic equilibrium constant with temperature. As demonstrated in Special Topic 1 at the end of this chapter, the thermodynamic equilibrium constant is related formally to the Gibbs energy change lor a reaction, with all reactants and products in their Standard Slates ... 

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,... 

Enthftiply Reference ftmperalure Tr 2 g.tSK Standard Slate Pressure s p = 0.t MPa... 

We can. see that at equilibrium the [P /[S] ratio equals hence, AG — 0. To catalog and compare AG values for various reactions, chemists have agreed upon a "standard-state where all reactants and products are considered to be maintained at steady-staie concentrations of 1 M, The standard-Slate for gases is considered to be 1 atm partial pressure. Under this condition the log [P]/[S] term (regardless of the exponents) is zero. The AG under standard-state conditions is designated AG°. 

Hence, the anme activity coefficient for y,. The activity and the activity coefficient, like the fbgaciiy coefficient, are normalized fogacities. However, unlike the normalizing factor xfr in the normalizing factors in j end y, contain property information, for pure i (when ff = ff) or for the mixture of which i is a component (when ff = JCU). Moreover, the numerical valnea of d, and y , unlike those of are arbitrary to tha extent that the choice of standard slate is arbitrary. Activities are identically equal to mole fractions for ideal solutions. For a real solution, d, approuches V, in en appropriate composition limit. Thus, for a Raoult s Law standard stale. ... 

Activity coefficients are identically unity for ideal solutions. For a real solution, the value of y- approaches unity in en appropriate composition limit. For a Raouli s Law standard slate. ... 

Use or Eq. (1.5-17) requires an expression for a Henry s Law acliviry coefficient 7. Such expressions are usually developed from the conventional expressions for y, based on Raouh s Law standard slates. For a siagle-solute-single-solvent mixture the connection between the two is easily established, By Eqs. (1.2-52). (1.2-38), aed (1,4-5), we have... 

In this tabic wc have neglected the Poynting correction to the pure componem. standard slates. Ifu gu.seous or liquid mixture arc describablc by an eiiuaiioii-or-siitic wc have... 

The conventional thermodynamic standard state values of the Gibbs energy of formation and standard enthalpy of formation of elements in their standard slates are A -G = 0 and ArEf = 0. Conventional values of the standard molar Gibbs energy of formation and standard molar enthalpy of formation of the hydrated proton are ArC°(H, aq) = 0 and Ar/T (H, aq) = 0. In addition, the standard molar entropy of the hydrated proton is taken as zero S (H, aq) = 0. This convention produces negative standard entropies for some ions. 

The tensile standard uses the tensile dumbbells standardized in ISO 527-2 and requires that the load applied be maintained within I % of the desired load. The loading mt chan-ism must be designed both to apply the load smoothly and without overshoot and to do this consistently. In creep testing it is essential to avoid any shocks at any time during the test. The strain must be measured to an accuracy of 0.01mm, and the elapsed lime to 0.1 %. Contactless optical extensometers are recommended, e.spccially for creep rupture tests. The standard slates that strain gauges are only suitable w-here they can be attached by adhesive, and only when the adhesion quality is constant throughout the lest. 

Infinite dilution standard state whereby the standard slate value of fugacily or activity of a component at the temperature and pressure of the solution is given by the ratio of the fugacily or activity to the mole fiacUon" under conditions of infinite dilution... 

Standard slate a reference state for a specific substance defined according to a set of conventional definitions. (6.4)... 

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