Activity coefficient Debye-Huckel theory

E. 7.2 Electrostatic Field due to Distributed Ions and Activity Coefficient Debye-HUckel Theory... 

If the activity coefficients are estimated from the Debye-Huckel theory in dilute regions of simple electrolyte systems, we have for aqueous solutions at 25 °C,... 

As a result of these electrostatic effects aqueous solutions of electrolytes behave in a way that is non-ideal. This non-ideality has been accounted for successfully in dilute solutions by application of the Debye-Huckel theory, which introduces the concept of ionic activity. The Debye-Huckel Umiting law states that the mean ionic activity coefficient y+ can be related to the charges on the ions, and z, by the equation... 

The question of the relationship between activity and concentration arises. Here the Debye-Huckel theory of activity coefficients, although valid only below 0.01 M, has proved to be most helpful, either for establishing an acid concentration from its H+ activity or for calculating H+ activity from its previously known acid concentration. 

Although it is not possible to measure an individual ionic activity coefficient,, it may be estimated from the following equation of the Debye-Huckel theory ... 

Stokes-Robinson Modification of Debye-Huckel Theory Effect of Ion-Solvent Interaction. Debye-Huckel theory explains the activity and activity coefficient data on the basis of ion-ion interaction for dilute solution. According to Eqs. (5.29) and (5.33), the activity coefficient is a decreasing function of concentration. 

The activity coefficient yt of an ion depends on the ionic strength (I = ( )Zzfc , where zi is the charge number) according to the Debye-Huckel theory in the limit of low ionic strengths. As discussed in Section 1.2, this equation can be extended... 

Activity coefficients of H4[SiWi204o] obtained in 0.0004 to 0.04 M concentrations in queous solutions have also been reported11S. The results obtained agree with the Debye-Huckel theory for 1—4 electrolytes. Osmotic coefficients of 12-tungsto-silicic acid have also been reported116. ... 

In a catholyte containing 100 g NaOH and 190 g NaCl per litre of solution there are 2.73 moles of NaOH and 3.55 moles of NaCl in 1000 grams of water (i. e. mNa+ = 6.28, wia- = 3.55 and moH- = 2.73). In order to calculate the activity coefficient of sodium hydroxide or of hydroxyl ions respectively the Debye-Huckel theory is applied according to this, the activity coefficient of... 

For solutions of electrolytes, yean be calculated using Debye-Huckel theory. The mean activity coefficient (y+) of positively and negatively charged ions in solution at 25°C is given by ... 

The first accurate calculation of the activity coefficient based on energetic effects of inter-ionic interactions in solvents was carried out by -> Debye and -> Huckel in 1923 by assuming that all the deviations from ideality at low concentrations of electrolyte were due to interionic interactions (- Debye-Huckel theory) with this it is possible to show that... 

It is a function expressing the effect of charge of the ions in a solution. It was introduced by -> Lewis and Randall [iii]. The factor 0.5 was applied for the sake of simplicity since for 1 1 electrolytes I = c (electrolyte). It is an important quantity in all electrostatic theories and calculations (e.g., - Debye-Huckel theory, - Debye-Htickel limiting law, - Debye-Huckel-Onsager theory) used for the estimation of -> activity coefficients, -> dissociation constants, -> solubility products, -> conductivity of -> electrolytes etc., when independently from the nature of ions only their charge is considered which depends on the total amount (concentration) of the ions and their charge number (zj). 

Electromotive force measurements of the cell Pt, H2 HBr(m), X% alcohol, Y% water AgBr-Ag were made at 25°, 35°, and 45°C in the following solvent systems (1) water, (2) water-ethanol (30%, 60%, 90%, 99% ethanol), (3) anhydrous ethanol, (4) water-tert-butanol (30%, 60%, 91% and 99% tert-butanol), and (5) anhydrous tert-butanol. Calculations of standard cell potential were made using the Debye-Huckel theory as extended by Gronwall, LaMer, and Sandved. Gibbs free energy, enthalpy, entropy changes, and mean ionic activity coefficients were calculated for each solvent mixture and temperature. Relationships of the stand-ard potentials and thermodynamic functons with respect to solvent compositions in the two mixed-solvent systems and the pure solvents were discussed. 

THE TRIUMPHS AND LIMITATIONS OF THE DEBYE-HUCKEL THEORY OF ACTIVITY COEFFICIENTS... 

Even before any detailed comparison with experiment, one can use an elementary spot check At infinite dilution, where the interionic forces are negligible, does the theory yield the activity coefficient that one would expect from experiment, i.e., unity At infinite dilution, cor/->0, which means that log J - Oor - l.The properties of an extremely dilute solution of ions should be the same as those of a solution containing nonelectrolyte particles. Thus, the Debye-Huckel theory ema-ges successfully from the infinite dilution test. 

Does Mayer s theory of calculating the viriai coefficients in equations such as Eq. (3.165) (which gives rise directly to the expression for the osmotic pressure of an ionic solution and less directly to those for activity coefficients) really improve on the second and third generations of the Debye-Huckel theory—those involving, respectively, an accounting for ion size and for the water removed into long-lived hydration shells ... 

Electrolytes for which the concentration is less than lO Mcan usually be dealt with by the Debye-Huckel limiting law. Utilize the Debye-Huckel theory extended by allowance for ion size and also for removal of some of the active solvent into the ion s primary solvation shell to calculate the activity coefficient of 5 M NaCland 1M LaClj solutions (neglecting ion association or complexing). Take the total hydration number at the 5 M solution as 3 and at the 1 M solution as 5. Take r,- as 320 pm. 

Since both sides have high electrolyte strength, the activity coefficient term can be assumed identical for a given species in the two solutions, in accordance with the correlation based on modified Debye-Huckel theory proposed by Davies [28]. Therefore, the concentration term can replace the activity coefficient term and the condition for Donnan equilibrium becomes... 

In addition to the short-range interactions between species in all solutions, long-range electrostatic interactions are found in electrolyte solutions. The deviation from ideal solution behavior caused by these electrostatic forces is usually calculated by some variation of the Debye-Huckel theory or the mean spherical approximation (MSA). These theories do not include terms for the short-range attractive and repulsive forces in the mixtures and are therefore usually combined with activity coefficient models or equations of state in order to describe the properties of electrolyte solutions. 

According to the Debye-Huckel theory, the activity coefficient of the i ion in a solution having an ionic strength of p is given by ... 

Another well-known example of a medium effect in solution kinetics is the effect of ionic strength on reactions between ions [38, 39]. This is normally treated using the extended Debye-Huckel theory to estimate the activity coefficients in equation (7.10.1). The activity coefficient for species i is given by... 

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