Activity of a species

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. 

Here, the a s refer to the activities in the chosen arbitrary state. The concept of activity is presented separately in a later section. For the present, the activity of a species in a system may just be considered to be a function of its concentration in the system, and when the species is in a pure form (or in its standard state), its activity is taken to be unity. The activities ac, aD, aA, aB given above correspond to the actual conditions of the reaction, and these may or may not correspond to the state of equilibrium. Two special situations can be considered. In the first, the arbitrary states are taken to correspond to those for the system at equilibrium. Q would then become identical to the equilibrium constant K and, according to the Van t Hoff isotherm, AG would then be zero. In the second situation, all the reactants and the products are considered to be present as pure species or in their standard states, and aA, aB, ac, and aD are all equal to 1. Then (7=1 and the free energy change is given by... 

Equilibrium constants do not have units because in the strict thermodynamic definition of the equilibrium constant, the activity of a component is used, not its concentration. The activity of a species in an ideal mixture is the ratio of its concentration or partial pressure to a standard concentration (1 M) or pressure (1 atm). Because activity is a ratio, it is unitless and the equilibrium constant involving activities is also unitless. 

The activities of a species such as H+, as would be determined by pH measurement, or the oxidation state given by an Eh determination. 

Figure 14-7 Cell used to measure the standard potential of the reaction Ag + e Ag(s). This cell is hypothetical because it is usually not possible to adjust the activity of a species to 1. 

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. 

Ion-selective electrodes belong to the group of potentiometric methods. Many electrode systems, partly well known, partly in development and under investigation, show a Nemstian relationship between the measured electrode potential and the activity of a species in solution. Important conditions to be fulfilled for the development of ion-selective electrodes are the affinity of a membrane surface for a typical ion or molecule and a minimum ion conductivity over the membrane. If possible, but not necessarily, these conditions should be fulfilled at room temperature. 

For the equilibrium constants defined above, the activity of the ions in question has been used. The activity of a species a, is related to the total concentration [Q] via the activity coefficient y which is expressed in the following equation ... 

To discuss equilibrium in a chemical reaction system, it is convenient to introduce the activity at of a species to replace the chemical potential of a species because a is more closely related to partial pressures and concentrations of species. The activity of a species is defined by... 

The activity of a species is unity when it is at the standard state. This is true, even though die choice of die standard state is arbitrary. Is this statement true ... 

The activity of a species is indicated as the symbol of the species enclosed in brackets. This quantity is equal to the concentration of the species times a mean activity coefficient ... 

Surface activity — is -> activity of a species i adsorbed (see -> adsorption) on the electrode or activity of species accumulated in the interfacial region between two immiscible liquids (see interface between two immiscible electrolyte solutions). Surface activity is related to the activity of species in the bulk of the solution as follows af = a exp where af and a is the activity of... 

To be more correct thermodynamically, activities (the activity of a species is its concentration multiplied by a number known as the activity coefficient) should be used instead of concentrations. However, in dilute solutions, the activity coefficients are usually taken to be 1 so concentrations are used instead. Table 5.1 shows the dissociation constants of several common acids, and a more complete list can be found in the CRC Handbook of Chemistry and Physics. Because the strength of an acid is... 

Remembering that the activity of a species in a pure phase, is... 

For mixtures, the relationship between the Gibbs free energy of a reaction and the composition of the system is obtained by substituting the expression for the chemical potential in terms of the activity of a species /... 

Instead of concentrations, one should strictly use activities in thermodynamical calculations. Most basic calculations assume that the system is ideal and activity of a reacting species equals its concentration. This is usually not valid. The difference is the activity coefficient, y. The activity of a species is therefore its concentration multiplied by the activity coefficient. 

The activity of a species is a measure of its effective concentration as determined by colligative properties (such as increasing the boiling point or decreasing the freezing point of water), by electrical conductivity, and by the mass action effect. 

The results of potentiometric determinations are the activities of analytes, in contrast to most analytical methods, which give the concentrations of analytes. Recall that the activity of a species Ux is related to the molar concentration of X by Equation 10-2... 

Acid salt A conjugate base that possesses an acidic hydrogen. Activity, a The effective concentration of a participant in a chemical equilibrium the activity of a species is given by the... 

Therefore, if the activity of a species in solution is ever greater than unity, a separate phase pure (or very concentrated) in that species will form and reduce the activity of the species in the other phases to unity. 

For most equilibrium constant measurements the amount of a reactant or product present is found as a concentration, e.g. spectrophotometric or conductance analyses. However, pH and some emf methods determine the activity of a species directly rather than a concentration, and so corrections for non-ideality for these species will not be necessary. But, there are also some situations where, although the basic experimental measurement is an activity, subsequent calculations involve stoichiometric relations given in concentrations. Unless care is taken, the final equilibrium constant could end up involving terms in activities and concentrations, i.e. is mixed. Here corrections for non-ideality will still have to be made. Specific cases will make this clearer. 

By definition, the activity coefficient a, indicates the deviation of the activity of a species from its measured concentration. If molar fi action is chosen as composition variable, we may write ... 

In this equation, yx i he activity coefficient of solute X, and the bracketed term is the molar concentration of X. In some of the examples, however, for convenience we will assume that the activity coefficient is unity so that the molar concentration and the activity of a species are identical. 

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