Activity quotient

R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday s constant, and Q is the activity quotient. The second form, involving the log Q, is the more useful form. If you know the cell reaction, the concentrations of ions, and the E°ell, then you can calculate the actual cell potential. Another useful application of the Nernst equation is in the calculation of the concentration of one of the reactants from cell potential measurements. Knowing the actual cell potential and the E°ell, allows you to calculate Q, the activity quotient. Knowing Q and all but one of the concentrations, allows you to calculate the unknown concentration. Another application of the Nernst equation is concentration cells. A concentration cell is an electrochemical cell in which the same chemical species are used in both cell compartments, but differing in concentration. Because the half reactions are the same, the E°ell = 0.00 V. Then simply substituting the appropriate concentrations into the activity quotient allows calculation of the actual cell potential. 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

The total energy of this adsorption reaction can be found experimentally from the microscopic activity quotient, and separated theoretically into the following components (1) transfer of the ion to be adsorbed from the bulk of solution to the oxide surface plane, at which the mean electrostatic potential is t/>q with respect to the bulk of solution (2) reaction of the adsorbate in the surface plane with a functional group at the surface (3) transfer of a fraction of the counter charge from solution into the solution part of the double layer by attraction of counter ions and (4) transfer of the remainder of the counter charge by expulsion of co-ions from the solution part of the double layer to the solution. 

Qis the activity quotient, products over reactants. This equation allows the calculation of A Gin those situations in which the concentrations or pressures are not 1. 

To obtain activity Quotients (AQ), enzyme activities (units per g liver) were divided by those in normal, adult liver. For further details see reference 5. 

Equation (17) is valid if interfacial charge-transfer equilibrium between the electrodes and both the reactants (A,B) and products (C,D) has been established. For illustration, consider two relevant special conditions If the underlying chemical reaction is at equilibrium, as characterized by the activity quotient of Equation (10), the driving force for the chemical, and thus for the electrochemical reaction, is zero - that is, AG (reaction) = -nFE - 0. On the other hand, if standard conditions prevail, then AG (reaction) = AG°(reaction) (i.e. E - E°). Equation (17) is valid for any combination of two electrodes making up a complete cell. 

In Equation (18b), the activity quotient is separated into the terms relating to the silver electrode and the hydrogen electrode. We assume that both electrodes (Ag+/Ag and H+/H2) operate under the standard condition (i.e. the H+/H2 electrode of our cell happens to constitute the SHE). This means that the equilibrium voltage of the cell of Figure 3.1.6 is identical with the half-cell equilibrium potential E°(Ag+l Ag) = 0.80 V. Furthermore, we note that the activity of the element silver is per definition unity. As the stoichiometric number of electrons transferred is one, the Nemst equation for the Ag+/Ag electrode can be formulated in the following convenient and standard way ... 

As shown in Equation (19), it is conventional for Nernst equations to represent the sum of E° and the logarithmic term, rather than the difference. Consequently, in the activity quotient, the activity of the oxidized form of the electroactive species has to be written as the numerator. Standard potentials of individual electrode reactions are conveniently available in textbooks of physical chemistry and electrochemistry, and in relevant handbooks. A small selection is presented in Table 3.1.3. 

When we look carefully at Equations 18-11 and 18-12, we see that the constant is the electrode potential whenever the concentration quotient (actually, the activity quotient) has a value of 1. This constant is by definition the standard electrode potential for the half-reaction. Note that the quotient is always equal to 1 when the activities of the reactants and products of a half-reaction are unity. 

Because of this the Donnan membrane theory states that the activity quotient inside the gel and outside the gel are equal at equilibrium. In mathematical terms then, the following equation is true ... 

This is the general reaction isotherm, also known as the van t Hoff isotherm it is of prime importance. The logarithmic ratio is sometimes known as the activity quotient, and is written Q. As before, AG is a measure of the affinity of the process actually occurring, where the logarithmic term makes adjustment for non-unit activities. This equation would apply for example when it was required to determine the feasibility of a reaction for which all starting activities are known. 

We must remember that the activities appear as they would in the activity quotient. As before, F is the Faraday constant, and n the number of moles of electrons involved in the process. If decadic logarithms are used, and the temperature is 298 K, a value of 0.05916 may be used for i 7 (2.303)/F. 

It is convenient to define the activity quotient Q such that... 

Equation 22-13 reveals that the constant is equal to the half-cell potential when the logarithmic term is zero. This condition occurs whenever the activity quotient is equal to unity, such as. for example, when the activities of all reactants and products are unity. Thus, the standard potential is often defined as the electrode potential of a half-cell reaction (versus SHE) when all reactants and products have unit activity. 

The stability constant can be expressed as a product of two terms, a concentration quotient and an activity quotient, Eq. 3 ... 

If the activity quotient can be regarded as a constant, a stability constant can be defined as a concentration quotient, Eq. 4 ... 

Another useful application of Equation 2-7 is for the prediction of the direction of reaction in a mixture of any initial composition. The activity quotient (the argument of the logarithmic term) in Equation 2-7 of the mixture is calculated on the basis of the initial composition and AG evaluated. The direction of the reaction is now readily obtained using the sign of the AG as criterion. A simpler corollary of this involves comparing the value of K for the reaction with the right-hand side of 2-8, using initial values of the aetivities of all the substances involved in the reaction, which is called the activity quotient. 

When K > activity quotient the reaction tends to proceed spontaneously (composition changes so as to increase activity quotient)... 

When K = activity quotient the reaction is at equilibrium (composition does not change with time)... 

The product H is called the reaction quotient or activity quotient, Qr... 

---