Activity coefficient 9 Concentration

Of course, in this simplified presentation, one assumes that by the time the concentration is so high that the activity coefficient-concentration relation turns upward (Fig. 2.18), the interionic interaction effects, although still there, have been overwhelmed by the effect of ions in reducing free waters. In reality, both this effect and the interionic effects that dominated at lower concentrations (below the minimum) should be taken into account. 

Basic equations for almost every subfield of electrochemistry from first principles, referring at all times to the soundest and most recent theories and results unusually useful as text or as reference. Covers coulometers and Faraday s Law, electrolytic conductance, the Debye-Hueckel method for the theoretical calculation of activity coefficients, concentration cells, standard electrode potentials, thermodynamic ionization constants, pH, potentiometric titrations, irreversible phenomena. Planck s equation, and much more, a indices. Appendix. 585-item bibliography. 197 figures. 94 tables, ii 4. 478pp. 5-% x 8. ... 

ACTIVITY AND ACTIVITY COEFFICIENTS—CONCENTRATION IS NOT THE WHOLE STORY... 

An iterative method is used for the calculation of activity coefficients. Concentrations of H+ and OH in aqueous solutions are usually very small numbers and therefore are difficult to be handled. Soren Sorensen proposed a more practical measure called pH, which indicates the acidity, neutrality, or alkalinity of an aqueous solution. Mathematically, for ions of H+, one obtains... 

Debye-Hiickel theory The activity coefficient of an electrolyte depends markedly upon concentration. Jn dilute solutions, due to the Coulombic forces of attraction and repulsion, the ions tend to surround themselves with an atmosphere of oppositely charged ions. Debye and Hiickel showed that it was possible to explain the abnormal activity coefficients at least for very dilute solutions of electrolytes. 

The thickness of the equivalent layer of pure water t on the surface of a 3Af sodium chloride solution is about 1 A. Calculate the surface tension of this solution assuming that the surface tension of salt solutions varies linearly with concentration. Neglect activity coefficient effects. 

Derive the equation of state, that is, the relationship between t and a, of the adsorbed film for the case of a surface active electrolyte. Assume that the activity coefficient for the electrolyte is unity, that the solution is dilute enough so that surface tension is a linear function of the concentration of the electrolyte, and that the electrolyte itself (and not some hydrolyzed form) is the surface-adsorbed species. Do this for the case of a strong 1 1 electrolyte and a strong 1 3 electrolyte. 

Just as increasing the pressure of a gas or a gas mixture introduces non-ideal corrections, so does increasing the concentration. As before, one can introduce an activity a- and an activity coefficient y and write a- = cr-[. and... 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

Figure A2.4.6. Mean activity coefFicient for NaCl solution at 25 °C as a function of the concentration full curve from ((A2A61 ) dashed curve from ((A2A63 ) dot-dashed curve from (A2.4.64). The crosses denote experimental data. From [2],...

A quite different approach was adopted by Robinson and Stokes [8], who emphasized, as above, that if the solute dissociated into ions, and a total of h molecules of water are required to solvate these ions, then the real concentration of the ions should be corrected to reflect only the bulk solvent. Robinson and Stokes derive, with these ideas, the following expression for the activity coefficient ... 

Investigations of the solubilities of aromatic compounds in concentrated and aqueous sulphuric acids showed the activity coefficients of nitrocompounds to behave unusually when the nitro-compound was dissolved in acid much more dilute than required to effect protonation. This behaviour is thought to arise from changes in the hydrogenbonding of the nitro group with the solvent. 

That the rate profiles are close to parallel shows that the variations in rates reflect the changing concentration of nitronium ions, rather than idiosyncrasies in the behaviour of the activity coefficients of the aromatic compounds. The acidity-dependences of the activity coefficients of / -nitrotoluene, o- and -chloronitrobenzene (fig. 2.2, 2.3.2), are fairly shallow in concentrations up to about 75 %, and seem to be parallel. In more concentrated solutions the coefficients change more rapidly and it... 

Unfortunately, insufficient data make it impossible to know whether the activity coefficients of all aromatic compounds vary slightly, or whether certain compounds, or groups of compounds, show unusual behaviour. However, it seems that slight variations in relative rates might arise from these differences, and that comparisons of reactivity are less sound in relatively concentrated solutions. 

Considering first pure nitric acid as the solvent, if the concentrations of nitronium ion in the absence and presence of a stoichiometric concentration x of dinitrogen tetroxide are yo and y respectively, these will also represent the concentrations of water in the two solutions, and the concentrations of nitrate ion will be y and x- y respectively. The equilibrium law, assuming that the variation of activity coefficients is negligible, then requires that ... 

Activity coefficient (referenced to Henry s law) Concentration basis 7c c,B ... 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

For gases, pure solids, pure liquids, and nonionic solutes, activity coefficients are approximately unity under most reasonable experimental conditions. For reactions involving only these species, differences between activity and concentration are negligible. Activity coefficients for ionic solutes, however, depend on the ionic composition of the solution. It is possible, using the extended Debye-Htickel theory, to calculate activity coefficients using equation 6.50... 

Several features of equation 6.50 deserve mention. First, as the ionic strength approaches zero, the activity coefficient approaches a value of one. Thus, in a solution where the ionic strength is zero, an ion s activity and concentration are identical. We can take advantage of this fact to determine a reaction s thermodynamic equilibrium constant. The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolated... 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

Equation 11.16 can be solved for the metal ion s concentration if its activity coefficient is known. This presents a serious complication since the activity coefficient may be difficult to determine. If, however, the standards and samples have an identical matrix, then yM + remains constant, and equation 11.16 simplifies to... 

In most quantitative analyses we are interested in determining the concentration, not the activity, of the analyte. As noted earlier, however, the electrode s response is a function of the analyte s activity. In the absence of interferents, a calibration curve of potential versus activity is a straight line. A plot of potential versus concentration, however, may be curved at higher concentrations of analyte due to changes in the analyte s activity coefficient. A curved calibration curve may still be used to determine the analyte s concentration if the standard s matrix matches that of the sample. When the exact composition of the sample matrix is unknown, which often is the case, matrix matching becomes impossible. 

Another approach to matrix matching, which does not rely on knowing the exact composition of the sample s matrix, is to add a high concentration of inert electrolyte to all samples and standards. If the concentration of added electrolyte is sufficient, any difference between the sample s matrix and that of the standards becomes trivial, and the activity coefficient remains essentially constant. The solution of inert electrolyte added to the sample and standards is called a total ionic strength adjustment buffer (TISAB). 

Quantitative Analysis Using the Method of Standard Additions Because of the difficulty of maintaining a constant matrix for samples and standards, many quantitative potentiometric methods use the method of standard additions. A sample of volume, Vx) and analyte concentration, Cx, is transferred to a sample cell, and the potential, (ficell)x) measured. A standard addition is made by adding a small volume, Vs) of a standard containing a known concentration of analyte, Cs, to the sample, and the potential, (ficell)s) measured. Provided that Vs is significantly smaller than Vx, the change in sample matrix is ignored, and the analyte s activity coefficient remains constant. Example 11.7 shows how a one-point standard addition can be used to determine the concentration of an analyte. 

---