Standard state molality

Standard half-cell potentials in aqueous solutions (T = 298 K, Standard state = 1 molal)... 

Standard state (1 molal) it then follows that on this basis the value for the Cl" 40.0 kcal moi Then, since the AH value for NaCl in aqueous solution is kcal mol" we have... 

Here, p and m are the standard chemical potential and concentration (molal scale) of the /-component (z = 1 for solvent, z = 2 for biopolymer) A2 is the second virial coefficient (in molal scale units of cm /mol, i.e., taking the polymer molar mass into account) and m° is the standard-state molality for the polymer. 

Any thermodynamic property 0 of a substance in its standard state Molal quantity Q... 

The relative activity of a solute is related to its molality by equation 6.7 where 7 is the activity coefficient of the solute, and mi and m° are the molality and standard state molality, respectively. Since the latter is defined as being unity, equation 6.7 reduces to equation 6.8. 

Activity coefficient (y) - Ratio of the activity of component B of a mixture to the concentration of that component. The value of y depends on the method of stating the composition. For mole fraction the relation is = y for molarity Cg, it is = y cjc , where c° is the standard state composition (typically chosen as 1 mol/L) for molality wi, it is = where m" is the standard state molality (typically 1 mol/kg). [2]... 

Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std. state or ss). In this state... 

ITlie free energy of solution of a given substance from its normal standard state as a sohd, liquid, or gas to the hyj)othetical one molal state in aqueous solution may he calculated in a manner similar to that described in footnote for calculating the heat of solution. 

It is a common practice to evaluate the molal volume ( V) of an ideal gas at a set of reference conditions known as the standard state. If the standard state is chosen to be... 

Units It should be noted that in the S.I. the activity of a solute is defined with reference to a standard state, i.e. an ideal solution of molality 1 mol kg". Thus the relative activity of a metal ion in solution is given by... 

However, as can be seen in Figure 6.15, which is a graph of the fugacity of HC1 against molality in dilute aqueous solutions of HC1 (near. i = 1), f2 approaches the m axis with zero slope. This behavior would lead to a Henry s law constant, kn.m = 0. given the treatment we have developed so far. Since the activity with a Henry s law standard state is defined as a —fi/kwnu this would yield infinite activities for all solutions. 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

The standard states are selected as m = 1 mol kg-1 and = 1 mol dm-3. In this convention, the ratio m./m is numerically identical with the actual molality (expressed in units of moles per kilogram). This is, however, the... 

It should be noted that the activity appearing in the dissociation constant K is the dimensionless relative activity, and constant K contains the dimensionless relative concentration or molality terms. Constants K and Kf are thus also dimensionless. However, their numerical values correspond to the units selected for the standard state, i.e. moles per cubic decimetre or moles per kilogram. 

At 900 °F the equilibrium constant for this reaction is 5.62 when the standard states for all species are taken as unit fugacity. If the reaction is carried out at 75 atm, what molal ratio of steam to carbon monoxide is required to produce a product mixture in which 90% of the inlet CO is converted to C02 ... 

The mole fraction X in the previous equation is replaced with a new unitless variable at, the species activity. The standard potentials pt° are defined at a new standard state a hypothetical one-molal solution of the species in which activity and molality are equal, and in which the species properties have been extrapolated to infinite dilution. 

This choice of a standard state seems like impossible mental gymnastics, but it allows activity to follow a molal scale, so that in dilute solutions activity and molality - despite the fact that activity is unitless - are equivalent numerically. A species molality m , the number of moles of the species per kilogram of solvent, is related to its activity by... 

Reference 170. The original values have been converted to a 1 molal ideal solution standard state (see reference 176)... 

The case of liquid solutions is more complicated because the conventions vary. These are always stated in introductory chapters of the thermochemical databases and deserve a careful reading. In most tables and in the present book, it is agreed that the standard state for the solvent is the pure solvent under the pressure of 1 bar (which corresponds to unit activity). For the solute, the standard state may refer to the substance in a hypothetical ideal solution at unit molality (the amount of substance of solute per kilogram of solvent) or at mole fraction x = 1. 

Debye-Huckel effects are significant in the dilute range and are not considered, and (2) the usual composition scale for the solute standard state is molality rather than mole fraction. Both of these problems have been overcome, and the more complex relationships are being presented elsewhere (17). However, for most purposes, the virial coefficient equations for electrolytes are more convenient and have been widely used. Hence our primary presentation will be in those terms. 

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