Sodium chloride activity coefficient

The activity coefficient for the counterions was taken to be a constant value of 0.862. This value was derived from the experimental value of 0.745 for NaCJl, which was reported by Moore (20). The sodium ion activity coefficient was obtained as the square root of the sodium chloride activity coefficient. 

Mean sodium chloride activity coefficients have been determined [41] with a sodium ion-selective electrode and silver-silver chloride reference electrode system in mixed sodium chloride-calcium chloride solutions within the range of sodium chloride and calcium chloride levels (0.05-0.5 mol dm ) encountered in extracellular fluids. These show that at constant ionic strength, log /Naci varies linearly with the ionic strength of calcium chloride in the mixture in accordance with Harned s rule [45] ... 

Strong association of Na ion with the polystyrenesulfonate anion (or, of Cl ion with the polycation). The activity coefficient of sodium ion, is strongly decreased from its value in pure NaCl solutions of the same concentration as has been demon-stated by measurements with single-ion electrodes. [3, 25] These measurements indicate that the sodium ion activity coefficient is ca. 0.3 [3] or 0.435 [25] for solutions of sodium polyvinylsulfate or sodium polymethylstyrenesulfonate at m = 0.1, respectively. The smaller of these two 71 1 + values is almost the same as y+ for Trace concentrations of NaCl in the presence of 0.1 m NaPSS (Figure 11). This near equality would appear to require that the activity coefficient of chloride ion be approximately the same as that for Na" ion, or, marked disagreement... 

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. 

Finally, as an example of a highly soluble salt, we may take sodium chloride at 25° the concentration of the saturated solution is 6.16 molal. The activity coefficient of NaCl, like that of NaBr plotted in Fig. 72, passes through a minimum at a concentration between 1.0 and 1.5 molal and it has been estimated2 that in the saturated solution the activity coefficient has risen to a value very near unity. Writing y = 1.0, we find that the work required to take a pair of ions from the surface of NaCl into pure water at 25° has the rather small value... 

In the Phadebas TM amylase test (72) (Pharmacia Labs) the substrate was a water insoluble cross-TTnked blue starch in tablet form which also contains some inert ingredients, sodium and potassium phosphate buffer salts and sodium chloride. This polymer was hydrolyzed by amylase into water soluble blue starch fragments. After centrifugation the absorbance of the blue supernatant was proportional to the activity of amylase present in the test samples. The day to day variation on a quality control serum had a coefficient of variation of 2.7% based on 30 days of data in our laboratory. The method is simple, reproducible and uses microquantities of serum. 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

Fig. 9. Logarithm of the cation activity coefficient versus the square root of the concentration for the system of manganese ions and cation vacancies in sodium chloride at 500°C. Filled-in circles represent the association theory with Rq = 2a, and open circles the association theory with R = 6/2. Crosses represent the present theory with cycle diagrams plus diagrams of two vertices, and triangles represent the same but with triangle diagram contributions added.

Generally, mn+ estimated from Equation (20.8) by inserting an approximate value of K and neglecting the activity coefficients. Thus, it is possible to obtain tentative values of — (RT/S ) In fC and hence K at various concentrations of acetic acid, sodium acetate, and sodium chloride, respectively. The ionic strength / ... 

Substances typical of acids and bases are, respectively, HCl and NaOH. Hydrogen chloride dissolves in water with practically complete dissociation into hydrated protons and hydrated chloride ions. Sodium hydroxide dissolves in water to give a solution containing hydrated sodium ions and hydrated hydroxide ions. Table 3.6 gives values of the mean ionic activity coefficients, y , at different concentrations and indicates the pH values and those expected if the activity coefficients are assumed to be unity. 

Table II. Calculated and Observed Values of the Activity Coefficients of Potassium, Sodium, Lithium, and Hydrogen Chlorides ...

Even with activity coefficients, we are always limited by chemistry that we do not know. In the mixture of sodium hydrogen tartrate (Na+HT ), pyridinium chloride (PyH+Cl ), and KOH, several possible ion-pair equilibria are... 

D. 11 Include activity coefficients from the Davies equation to find the pH and concentrations of species in the mixture of sodium tartrate, pyridinium chloride, and KOH in Section 13-1. Consider only Reactions 13-1 through 13-4. 

This is a special form applicable to an electrolyte such as sodium chloride. j is the mean ionic activity coefficient on the mole-fraction scale which is equal to y at this dilution. The activity of water is linear with m in this region and hence accurate values are obtained merely by interpolation (9). For 50% recovery from a feed of 5000 p.p.m., the following values were calculated ... 

In Equation 4.21, the activity of pure water (a) is unity and the activity of the water with the inhibitor (a ) is the product of the water concentration (xw) and the activity coefficient (xw). The water concentration is known and the activity coefficient is easily obtained from colligative properties for the inhibitor, such as the freezing point depression. For instance the activity of water in aqueous sodium chloride solutions may be obtained from Robinson and Stokes (1959, p. 476) or from any of several handbooks of chemistry and physics. 

Equations used to calculate L and 4>CP are taken from K. S. Pitzer, Ion interaction approach theory and data correlation , Chapter 3 in Activity Coefficients in Electrolyte Solutions, 2nd Edition, K. S. Pitzer, Editor, CRC Press, Boca Raton, Florida, 1991. Equations for calculating L, L2, Ju and J2 are summarized in K. S. Pitzer, J. C. Peiper, and R. H. Busey, Thermodynamic properties of aqueous sodium chloride solutions , J. Phys. Chem. Ref Data, 13, 1-102 (1984). 

For the above reasons, the IFCC recommendations on activity coefficients [19] and the measurement of and conventions for reporting sodium and potassium [21] and chlorides [25] by ISEs were developed. At the core of these recommendations is the concept of the adjusted active substance concentration (mmol/L), as well as a traceable way to remove the discrepancy between direct and indirect determinations of these electrolytes in normal sera. Extensive studies of sodium and potassium binding to inorganic ligands and proteins, water binding to proteins, liquid-junction effects and the influence of ionic strength have demonstrated that the bias between sodium and potassium reports obtained from an average ISE-based commercial... 

It is worthwhile to discuss why the mass-action law on concentration basis (moles/litre) is plausible. It is beyond doubt that it is not always valid. The concentration 5.5 M of saturated aqueous sodium chloride indicates the solubility product 30 moles2/litre2. If an equal amount of such a solution is added to 12 M hydrochloric acid, the concentration of Na+ is 2.75 M and of Cl- (12 + 5.5)/2 = 8.75 M. Their product 24.06 M2 is distinctly below the solubility product, but nevertheless, more than 80 percent of the NaCl present crystallizes out. It would be to short-circuit this paradox to speak about the mass-action law on activity basis. The introduction of activity a as the product a =/Cof the activity coefficient/and the concentration is a tautological trick to keep the mass-action law valid, and it is more fruitful to try to explain why/varies more dramatically in some cases than in others. 

FIG. 2 Effect of solute molality (m) on the mean molal activity coefficient (y ) for sodium chloride (O), sodium acetate (O), and sodium propionate ( ) at 25°C, as extracted from Robinson and Stokes (2002). The continuous lines were calculated using Eq. 9 and the empirical coefficients At extracted from Fidaleo and Moresi (2005a,b, 2006). 

An anolyte containing 265 grams of NaCl per litre has 5.026 moles of NaCl in 1000 grams of water (i. e. mNa+ = Wei- = 5.026). In the Table 8 it will be seen that the mean activity coefficient of sodium chloride in this solution equals 0.877. This value will be further considered to coincide with th activity coefficient of chloride ions (ya-) in a solution of the same concentration. The potential of the chlorine electrode then equals ... 

Fig. 4 to Fig. 8 show the severe divergence for activity coefficients such as given here for calcium, chloride, sulfate, sodium and water ions, calculated with different equations. The activity coefficients were calculated applying Eq. 13 to Eq. 17 for the corresponding ion dissociation theories, whereas the values for the PITZER equations were gained using the program PHRQPITZ. The limit of validity of each theory is clearly shown. 

If activity coefficients are disregarded, and if it is assumed that the standard values g (NaCl) are same on both sides of the barrier, then this is equivalent to requiring that [[Na J[CI"]]Ie([ = [[Na+][Cl"]]Right The sodium ions are supplied by the polyelectrolyte as well as the added salt. Furthermore, if a sodium ion migrates through the membrane it has to be accompanied by chloride ion in order to maintain electrical neutrality on both sides of the membrane. It follows that, at equilibrium... 

In saline soils and soils contaminated with geothermal brines, the ionic strengths of the soil solution may exceed 0.5 M. This fact poses the necessity of using equations which have been developed to describe the activity coefficients of ions in concentrated, multicomponent electrolyte solutions. As part of a study on the chemistry of ore-forming fluids, Helgeson (50) has proposed that the true individual ion activity coefficients for ions present in small concentrations in multicomponent electrolyte solution having sodium chloride as the dominant component be approximated by a modified form of the Stokes-Robinson equation. The equation proposed is ... 

---