Activity coefficient, dimensionless

The difference on the left is the partial excess Gibbs energy G y the dimensionless mXio J on the right is called the activity coefficient of species i in solution, y. Thus, by definition. 

Y- Mean ionic activity coefficient of solute Dimensionless Dimensionless... 

Activity coefficients are dimensionless. With standard states selected as indicated above, activity coefficients will be unity in ideal systems. The degree of departure of a system from the ideal state is described by the departure of the activity coefficients from unity. 

Activity ax is termed the rational activity and coefficient yx is the rational activity coefficient This activity is not directly given by the ratio of the fugacities, as it is for gases, but appears nonetheless to be the best means from a thermodynamic point of view for description of the behaviour of real solutions. The rational activity corresponds to the mole fraction for ideal solutions (hence the subscript x). Both ax and yx are dimensionless numbers. 

The activity a and the activity coefficient y are both dimensionless quantities, which explains why we must include the additional c term, thereby ensuring that a also has no units. We say the value of ce is 1 mol dm-3 when c is expressed in the usual units of mol dm-3, and 1 molm-3 if c is expressed in the SI units of mol m-3, and so on. 

For all other situations, we employ the Debye-Hiickel laws (as below) to calculate the activity coefficient y. And, knowing the value of y, we then say that a = (c -y c°) x y (Equation (7.25)), remembering to remove the concentration units because a is dimensionless. 

The dimensionless partition coefficient K is based on mole fractions. v, or number of moles In the literature, partition coefficients are more often defined as concentration ratios. At low solute concentration and when the adsorbed amounts become very small, the activity coefficients approach zero and the surface potential also becomes insignificant (ZiF fj —> 0) ... 

In this section we establish the equation of the forward scan current potential curve in dimensionless form (equation 1.3), justify the construction of the reverse trace depicted in Figure 1.4, and derive the charge-potential forward and reverse curves, also in dimensionless form. Linear and semi-infinite diffusion is described by means of the one-dimensional first and second Fick s laws applied to the reactant concentrations. This does not imply necessarily that their activity coefficients are unity but merely that they are constant within the diffusion layer. In this case, the activity coefficient is integrated in the diffusion coefficient. The latter is assumed to be the same for A and B (D). 

The case of a real solution, shown by equation 2.62, is handled by introducing a dimensionless correction, called the activity coefficient (y ). In the high dilution limit (mi -> 0), Xi = 1, and equation 2.62 reduces to 2.61. The activity of species i is simply a, = ypnjma. 

When the solution is dilute enough to approximate the activity coefficients to 1 (reference state solute at infinite dilution), activities can then be replaced by molar fractions (dimensionless quantities), but in solution they are generally replaced by molar concentrations ... 

In Eq. 30, Uioo and Fi are the activity in solution and the surface excess of the zth component, respectively. The activity is related to the concentration in solution Cioo and the activity coefficient / by Uioo =fCioo. The activity coefficient is a function of the solution ionic strength I [39]. The surface excess Fi includes the adsorption Fi in the Stern layer and the contribution, f lCiix) - Cioo] dx, from the diffuse part of the electrical double layer. The Boltzmann distribution gives Ci(x) = Cioo exp - Zj0(x), where z, is the ion valence and 0(x) is the dimensionless potential (measured from the Stern layer) obtained by dividing the actual potential, fix), by the thermal potential, k Tje = 25.7 mV at 25 °C). Similarly, the ionic activity in solution and at the Stern layer is inter-related as Uioo = af exp(z0s)> where tps is the scaled surface potential. Given that the sum of /jz, is equal to zero due to the electrical... 

The dimensionless quantity yj is called the activity coefficient of the substance J (Fig. 9.4). More advanced techniques in chemistry enable us to relate the activity coefficient to the composition. For the dilute solutions that concern us, it will be sufficient to set yj = 1. However, we have to remember that our expressions are then valid only for ideal gases and very dilute solutions. 

Equation 4.7 invites comparison with Eq. 1.12, as does Eq. 4.8 with Eq. 1.26. (Note, however, that the rational activity coefficient f is dimensionless.)... 

Thus the activity coefficient of a species in solution becomes unity as the species becomes pure. At the other limit, where xf - 0 and species i becomes infinitely dilute, In y,- is seen to approach some finite limit, which we represent by In y In the limit as - 0, the dimensionless excess Gibbs energy GB/RT as given by Eq. (11.69) becomes... 

These quantities are not in general dimensionless. One can define in an analogous way an equilibrium constant in terms of fugacity Kf, etc. At low pressures Kp is approximately related to K by the equation K Kp/(p )lv, and similarly in dilute solutions Kc is approximately related to K by K Kc/(c )lv however, the exact relations involve fugacity coefficients or activity coefficients [24]. 

Here /A is the activity coefficient, a dimensionless quantity, which varies with concentration. For the simple equilibrium reaction, mentioned in Section 1.13... 

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