Activity coefficient of an ion

The Debye-Hiickel formula for the activity coefficient of an ion was developed by a consideration of ion atmosphere effects.10 It starts with an electrostatic expression for the free energy of interaction for one ion with one mole of others ... 

According to Deybe-Huckel limiting law, the activity coefficient/of an ion is related to the ionic strength as... 

The P-B equation is very similar to the B-G-S equation. The expression for the activity coefficient of an ion i of charge z, takes the form... 

An equation for estimating how the activity coefficient of an ion in dilute solutions is influenced by ionic strength. See Debye-Huckel treatment... 

In Equation 8-6, y is the activity coefficient of an ion of chaige z and size a (picomeiers, pm) in an aqueous solution of ionic strength p. The equation works fairly well for p 0.1 M. To find activity coefficients for ionic strengths above 0.1 M (up to molalities of 2-6 mol/kg for many salts), more complicated Pitzer equations are usually used.7... 

The relationship between the activity coefficient of an ion and the ionic strength of the solution is given by the Debye-Hiickel limiting law... 

Note that when a semicolon is put at the end of input, Mathematica does not print output. The effect of ionic strength on the activity coefficient of an ion is very sensitive to the charge number. At 298.15 K and 0.25 M ionic strength, the activity coefficients of ions with 1, 2, 3, and 4 charges are given by... 

Ionic strength measures the concentration of charges in solution. As the ionic strength of a solution increases, the activity coefficient of an ion decreases. The relationship between the ionic strength and the molarity of a solution of ionizable salt depends on the number of ions produced and their net charge, as sumniarized below. 

As we have already seen, the derivative of (1 - ) at the origin is finite in the case of a non-electrolyte, but infinite for an electrolyte. This behaviour of strong electrolytes is related to the long range electrostatic forces between the ions in the solution.J The statistical theory, in the form developed by Debye and Hiickel, leads to the following expression for the activity coefficient of an ion with a charge 2 , in a very dilute solution in which the ionic strength is I (cf. 27.38) ... 

Other methods are used to describe me behavior of ionic species (electrolytes). The activity coefficient of an ion in solution may be expressed in terms of modified Debye-Hiickel theory. A common expression suitable for low concentrations has the form... 

For a given ionic strength, the activity coefficient of an ion departs farther from unity as the charge carried by the species increases. This effect is shown in Figure 10-3. 

This expression assumes that the activity coefficients of an ion in the diffuse layer and in solution are the same. For low potentials, the Gouy-Chapman theory yields... 

Taking the above considerations into account, it turns out that reasonable agreement between theory and results is obtained if we express the free ion activity coefficient of an ion of valence z as... 

The calculated activity coefficient of an ion in a mixed electrolyte solution will be less accurate than in a single-electrolyte solution. ... 

When the standard environment is a highly dissociating solvent such as water, we know how the activity coefficient of an ion is... 

For aqueous solution at 2S°C, the activity coefficient of an ion,., is then given approximately by... 

It is possible to understand why solutions of electrolytes do not behave in an ideal manner in terms of both the coulombic attraction on ions which serves to constrain their movement and the thermal agitation which counteracts this restraint. Debye and Huckel developed a theory in which electrostatic forces shaping the behavior of the ions in solution as well as their finite radii formed a basis from which expressions for the activity coefficient of an ion could be derived. One of the simpler usable equations they developed, referred to as the Extended Limiting Law, gives the activity coefficient, y, of an ion i, having a charge Zj in a solution of ionic strength I. 

For the calculation of the activity coefficient of an ion j at the chosen standard state the equation... 

Despite the fact that the activity coefficient of an ion cannot be determined experimentally, their values can be reasonably approached, in all probability, by calculation, with the help of the Debye-Hiickel theory. They can be done for at least some ranges of ionic stfengths. 

The activity coefficient of an ion cannot be experimentally measured (as any other thermodynamic property of a single ion) but can be theoretically calculated for a dilute solution when 7 is less than about 0.05 mol kg . However, the activity coefficient of an electrolyte, y , can be experimentally measured, and such values are given in [Chapter 10, Tables 10.16 and 10.17]. is called the mean activity coefficient and is related to the activity coefficient of the cation, y+, and anion, y, as follows ... 

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