Activity of a solute

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... 

There are several different scales 011 which the activity of a solute may be defined.1 In thermodynamic expressions for a solute in a non-ideal solution the activity on the molality scale plays the same part that is played by the molality of a solute in an ideal solution. Since the activity is expressed in the same units as the molality, the ratio of the activity to the molality—the activity coefficient—is a pure number whose value is independent of these units it is also indopendont of the particular b.q.s. that has been adopted. Thus the numerical values of all activities and molalities would change in the same ratio, if at any time a new choice were made for the b.q.s. 

As we saw in Section 9.2, the activity of a solute J in a dilute solution is approximately equal to the molar concentration relative to the standard molar concentration, [JJ/c°, with c° = 1 mol-L, and so a practical form of this expression is... 

Lipophilicity is a molecular property expressing the relative affinity of solutes for an aqueous phase and an organic, water-immiscible solvent. As such, lipophilicity encodes most of the intermolecular forces that can take place between a solute and a solvent, and represents the affinity of a molecule for a lipophilic environment. This parameter is commonly measured by its distribution behavior in a biphasic system, described by the partition coefficient of the species X, P. Thermodynamically, is defined as a constant relating the activity of a solute in two immiscible phases at equilibrium [111,112]. By convention, P is given with the organic phase as numerator, so that a positive value for log P reflects a preference for the lipid phase ... 

The activity of a solution It is unwise to speak in broad terms of the activity of a solution because so many different situations may be considered. For example, consider the following two examples. 

The activity of a solute in a liquid solvent. The activity a and concentration c may be considered to be wholly identical if the concentration is tiny (to a maximum of about 10-3 mol dm-3), provided the solution contains no other solutes. Such a concentration is so tiny, however, as to imply slightly polluted distilled water, and is not particularly useful. 

PH The symbol relating the hydrogen ion (H+) concentration or activity of a solution to that... 

ACTIVITY OF A SOLUTE FROM DISTRIBUTION BETWEEN TWO IMMISCIBLE SOLVENTS... 

If the activity of a solute is known in one solvent, then its activity in another solvent immiscible with the hrst can be determined from the equilibrium distribution of the solute between the two solvents. As an example, let us consider an extreme situation, such as that illustrated in Figure 17.7, in which the shapes of the fugacity curves are different in two different solvents. The limiting behavior at inhnite dilution, Henry s law, is indicated for each solution. The graphs reveal that the standard states are different in the two solvents because the hypothetical l-moM solutions have different fiigacities. 

Concentration Effects The pH of a solution varies with the concentration of buffer ions or other salts in the solution. This is because the pH of a solution depends on the activity of an ionic species, not on the concentration. Activity, you may recall, is a thermodynamic term used to define species in a nonideal solution. At infinite dilution, the activity of a species is equivalent to its concentration. At finite dilutions, however, the activity of a solute and its concentration are not equal. 

ACTIVITY COEFFICIENT. A fractional number which when multiplied by the molar concentration of a substance in solution yields the chemical activity. This term provides an approximation of how much interaction exists between molecules at higher concentrations. Activity coefficients and activities are most commonly obtained from measurements of vapor-pressure lowering, freezing-point depression, boiling-point elevation, solubility, and electromotive force. In certain cases, activity coefficients can be estimated theoretically. As commonly used, activity is a relative quantity having unit value in some chosen standard state. Thus, the standard state of unit activity for water, dty, in aqueous solutions of potassium chloride is pure liquid water at one atmosphere pressure and the given temperature. The standard slate for the activity of a solute like potassium chloride is often so defined as to make the ratio of the activity to the concentration of solute approach unity as Ihe concentration decreases to zero. 

On the basis of the thermodynamic expression, the Gibb s free-energy change for mixing in solution can in turn be related to the activity of a solute at equilibrium as described by Equations 3.7 through 3.10 in Chapter 2 of this book, namely,... 

With the Raoultian standard state, it is found not infrequently that the activity of a solute in a dilute solution is very small. 

In this section a transition-state model has been explicitly assumed and it has been implicitly assumed that for equal solute concentrations the activity of a solute is the same in H20, D20, and isotopic mixtures. It was shown that these assumptions are consistent with the results. However, the results do not establish the model, which will be discussed at greater length in Section IIIB, and the assumption is only a fair approximation (Goodall and Long, 1968). 

Lewis and Randall give an example of calculating the activity of a solute from its vapour pressure. When a solution is in equilibrium with the vapour of the solute x2, we may measure the vapour pressure of x2 over a range of concentrations, and by knowing the fugacity of the vapour at each pressure we may obtain the activity of the solute in the solution. When we may assume that the vapour is a perfect gas, the activity a2 in the solution may be taken as proportional to p2, the vapour pressure of the solute. Hence, as we pass from the mole fraction N2 to an infinitely dilute solution of mole fraction Nx2... 

The activity of a solute is a measure of its observed chemical behaviour in (aqueous) solution. Interactions between the solute and other species in solution lead to deviations between solute activity i and concentration [i]. An activity coefficient, y , is therefore defined as a correction factor, which interrelates solute activity and concentration. 

Concentration and activity of a solute are only the same for very dilute solutions, i.e. yi approaches unity as the concentration of all solutes approaches zero. For non-dilute solutions, activity coefficients must be used in chemical expressions involving solute concentrations. Although freshwaters are sufficiently dilute to be potable (containing less than about 1000 mg total dissolved solids (TDS)), it cannot be assumed that activity coefficients are close to unity. 

Let the symbol H be read as the effective concentration or activity of H and the symbol [H ] be read as the concentration of H. The effective concentration H refers to the ions of H that actually participate in a reaction. This is different from the concentration [H ], which refers to the actual concentration of iG, but not all the actual concentration of this H participate in the chemical reaction. Effective concentration is also called activity. The effective concentration or activity of a solute is obtained from its actual concentration by multiplying the actual concentration by an activity coefficient,/(i.e., H =/[H ]). 

For the present purpose, equation (34), page 326, for the hydrogen ion activity of a solution of a dibasic acid, of initial concentration a moles per liter, to which has been added a concentration of b equiv. per liter of strong base, may be written as... 

For solutes the standard state and the activity usually must be defined in terms of behavior under conditions of infinite dilution, where by definition the activity of a solute is set equal to its concentration. Thus at infinite dilution the ratio of activity to concentration (in whatever units) is unity, and y, = 1. When the value of some physical property of a solution is plotted as a function of concentration, a curve like those in Figure 2-2 is obtained. If the asymptote passing through the origin on the concentration scale is extrapolated to higher concentrations, we obtain the standard state of unit activity for the property in question. This hypothetical solution, labeled S, of unit concentration exhibits the same type of behavior as the infinitely dilute solution. The extent to which the real value of the physical property measured differs from the hypothetical value at a specific concentration is expressed by the activity coefficient, a coefficient that is simply the ratio between two measurable quantities. In Figure 2-2 the activity coefficient yj is the ratio BC/AC and is defined by... 

If the activity of a solute or ion were ideal, it could be taken as equivalent to the molal concentration, of the i ion or solute. However, interactions with other ions and with the solvent water are strong enough to cause nonideal behavior and the characteristic property relating concentration to chemical potential is the activity coefficient, y, ... 

In dealing with quantitative aspects of chemical equilibrium, we inevitably are faced with the problem either of evaluating or maintaining constant the activities of the ions under consideration. G. N. Lewis (1907) defined the chemical activity of a solute A, A, and its relationship to chemical concentration of that solute, [A], by... 

The quantitative evaluation of the systematic relations that determine equilibrium concentrations (or activities) of a solution constitutes a purely mathematical problem, which is amenable to exact and systematic treatment. 

Although the phrase activity of a solution usually refers to the activity of the solute in the solution as in the preceding section, we also can refer to the activity of the solvent. Experimentally, solvent activity may be determined as the ratio of the vapour pressure Pi of the solvent in a solution to that of the pure solvent pf, that is... 

Equilibrium constants for empirical models are determined from measurements of the activity of a solute in water and the equilibrium adsorbed concentration. Experiments usually consist of a series of batch reactors where a solid phase is suspended in solutions that have a range of known solute concentrations. Equilibrium constants are then derived from various types of plots of the adsorbed and aqueous concentrations. These equilibrium constants are highly dependent on solution and solid composition. Eor example, values of Kl and Kp for As adsorption have been shown to be a function of pH, the concentration of competing ions, and the mineralogy of the adsorbent (Darland and Inskeep, 1997a Ghosh and Yuan, 1987 Kingston et al., 1971 Hsia et al., 1992 Pierce and Moore, 1982 Sakata, 1987). Therefore, empirical models are limited to the specific experimental conditions used to determine the Log K s. 

Let H be the protonic activity of a solution to be tested and E the electromotive force (emf) measured between the electrodes... 

The activity of a pure solid is I, and, for dilute solutions (sparingly soluble salts), the activity of a solute species can be replaced by its molarity. 

The significance of the foregoing definition of the activity of a solute may be seen by making use of the fact ( 31b) that the activity is proportional to the fugacity, the value of the proportionality constant depen ng on the chosen reference or standard state. Representing this constant by 1/k, it is seen that the activity at of the solute and its fugacity / may be related by... 

The concentration-based equilibrium constant embodied in Equation 9-7 on page 234 provides only an approximation to real laboratory measurements. In this chapter, we show how the approximate form of the equilibrium constant often leads to significant error. We explore the difference between the activity of a solute and its concentration, calculate activity coefficients, and use them to modify the approximate expression to compute species concentrations that more closely match real laboratory systems at chemical equilibrium. 

---