Transporters Gibbs free energy

Fig. 16. A. Plot of log iNa as a function of T 1 (°K) using the experimental values of the rate constants and the location of the binding sites in Eq. 4. The Gibbs free energy of activation is calculated from Eq. 3 the AS are taken to be zero, and the current is calculated by means of Eq. 4. The purpose is to demonstrate that multibarrier channel transport can be seen as single rate process with average values for the enthalpies of activation. Non-linearity of such a plot is then taken to arise form the dynamic nature of the channel.

This is but one possible expression for the Gibbs free energy. We could write an expression in terms of changes in other state variables, such as temperature and pressure. Furthermore, we must account for the possibility that a component may be distributed among or transported between several phases within the system (e.g., alloys). Alternatively, many reactions of interest to the materials... 

The dependence of the Gibbs free energy pathway on electrode potential (Figure 3.3.10A) manifests itself directly in the experimental current potential characteristic illustrated in Figure 3.3.10B. At 1.23 V, no ORR current is measureable, while with decreasing electrode potentials the ORR current increases exponentially until at +0.81 V, processes other than surface kinetics (e.g. mass transport) begin to limit the overall reaction rate. Figure 3.3.10B represents a typical performance characteristic of a Pt or Pt-alloy electrocatalyst for the ORR. 

Figure 3.3.10 (A) The electrode potential dependence of the Gibbs free energy reaction pathway of the ORR. While the overall reaction has elementary steps that are energetically uphill at +1.23 V (red pathway), all elementary steps become downhill at +0.81 V (yellow pathway) (i.e. at an overpotential of approximately -0.42 V. At this point, the reaction is not limited by kinetics anymore. (B) The experimentally observed current-potential (j-E) relation of the ORR is consistent with the computational conclusions from (A) between +1.23 V and +0.81 V the j-E curve shows an exponential behavior, while at electrode potentials below +0.81 V, the ORR reaction rate becomes oxygen mass-transport limited, which is reflected by a flat ( j-E) profile. Figure adapted with permission from [19]. 

Therefore there is no overall chemical reaction. Assuming that conditions such as pH and ionic strength are the same on both sides of the membrane, the equilibrium constant for the transport reaction is KGlut = 1 and the equilibrium Gibbs free energy is AG°glut = 0. 

Applying Equation (7.15) to isothermal isobaric transport, we have the following equation for the Gibbs free energy for the coupled chemical reaction and transport... 

From Equation (7.17), the Gibbs free energy for the transport reaction is... 

Gibbs free energy that is, F equals 96.49 kJ mol-1 V-1 (Appendix I see Table 6-2). ATP usually supplies at least 40 kJ mol-1 when hydrolyzed and can act as the Gibbs free energy source for the active transport of solutes across membranes toward regions of higher chemical potential (Tables 6-1 and 6-2). 

J is the number of nuclei formed per unit time per unit volume, No is the number of molecules of the crystallizing phase in a unit volume, v is the frequency of atomic or molecular transport at the nucleus-liquid interface, and AG is the maximum in the Gibbs free energy change for the formation of clusters at a certain critical size, 1. The nucleation rate was initially derived for condensation in vapors, where the preexponential factor is related to the gas kinetic collision frequency. In the case of nucleation from condensed phases, the frequency factor is related to the diffusion process. The value of 1 can be obtained by minimizing the free energy function with respect to the characteristic length. 

An example of using Gibbs free energy is to determine the suitable precursor for a given CVD process. Halides are the most common precursors in CVD processes and could be written in a general form as MXn. M is a metal element and X is the halogen element of F, Cl, Br or I. As discussed in Chapter 3, the precursor should be stable enough to be transported at relatively low temperatures. However, it must be able to react on the substrate surface at the deposition temperature, so the precursor must not be too stable. 

Many environmentally important chemicals are transported as complexes in natural waters. Complexes may increase or decrease the toxicity and/or bioavailability of elements. Complexation increases the solubility of minerals and may increase or decrease the adsorption of elements. The major monovalent and divalent cations and anions (especially > 10 m) form outer-sphere complexes or ion pairs, in which the bonding is chiefly long-range and electrostatic. Ion pairs are unimportant in dilute fresh waters, but become important in saline waters such as seawater. Minor and trace ions such as Cu, Fe +, Pb +, and Hg are usually complexed, and occur in inner-sphere complexes, which are usually much stronger complexes than the ion pairs. Written in terms of Gibbs free energy. 

Transport properties are studied off equilibrium, thus investigating the irreversible or the steady-state process. The flux (J) may be considered the time-dependent change of any nondifferentiated state variable (X) in the Gibbs free energy fnnction (Eqnation 8.84) divided by the cross sectional area through which the flow occurs. The flow is induced by the gradient of the conjngated differentiated state variable (T)- The flnx J is thns defined as... 

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