Differences in electrical potentials

A charge is always associated with matter in real systems. Therefore, the energy of a homogenous system is still expressed as a function of the entropy, volume, and mole numbers of the species, so 

Equation (12.2) is applicable to every phase in a heterogenous system. Because of the identity of this equation with Equation (4.12) with the exclusion of other work terms, the conditions of equilibrium must be the same as those developed in Chapter 5 in a heterogenous system without restrictions, the temperature of every phase must be the same, the pressure of every phase must be the same, and the chemical potential of a species must be the same in every phase in which the species exists. For phase equilibrium, then, 

1 Guggenheim [36] calls this the electrochemical potential. However, it is not distinct from the chemical potential, and we prefer to continue the use of the term chemical potential.  

We recognize from our previous experience that pt is a function of the entropy, volume, temperature, or pressure in appropriate combinations and the composition variables. The splitting of into these two terms is not an operational definition, but its justification is obtained from experiment. The quantity pt is the quantity that is measured experimentally, relative to some standard state, whereas the electrical potential of a phase cannot be determined. Neither can the difference between the electrical potentials of two phases alone at the same temperature and pressure generally be measured. Only if the two phases have identical composition can this be done. If the two phases are designated by primes, 

In order to clarify these concepts, we consider a length of copper wire along which there exists a potential gradient, such as a slidewire in a potentiometer. The potentials at two points a and b in the wire are designated as 0 and (j b, so that the potential difference between the two points is given by ( fib — If we attach a piece of copper wire at each point, the potential difference between the two pieces of wire is still ( pb — (j a). The only species that can transfer across the boundary at each junction is electrons, and these electrons are in equilibrium. We have, from Equation (12.3), 

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Anion A negatively charged ion in an electrolyte solution, attracted to the anode under the influence of a difference in electrical potential. Chloride is an anion. Anion exchange capacity Sum total of exchangeable anions that a soil can adsorb. Expressed as centimoles of negative charge per kilogram of soil. 

Electrode Potential (E) the difference in electrical potential between an electrode and the electrolyte with which it is in contact. It is best given with reference to the standard hydrogen electrode (S.H.E.), when it is equal in magnitude to the e.m.f. of a cell consisting of the electrode and the S.H.E. (with any liquid-junction potential eliminated). When in such a cell the electrode is the cathode, its electrode potential is positive when the electrode is the anode, its electrode potential is negative. When the species undergoing the reaction are in their standard states, E =, the stan-... 

We can determine an approximate value of the pH of an aqueous solution very quickly with a strip of universal indicator paper, which turns different colors at different pH values. More precise measurements are made with a pH meter (Fig. 10.11). This instrument consists of a voltmeter connected to two electrodes that dip into the solution. The difference in electrical potential between the electrodes is proportional to the hydronium ion activity (as will be explained in Section 12.10) so, once the scale on the meter has been calibrated, the pH can be read directly. 

When two electrodes contain different amounts of excess charge, there is a difference in electrical potential between them. Because it has more excess electrons, the zinc electrode is at a higher electrical potential than the copper electrode. In a galvanic cell, the difference in electrical potential causes electrons to flow from a region where the concentration of electrons is higher to a region where the concentration of electrons is lower. In this case, eiectrons flow from the zinc electrode toward the copper electrode, as shown at the molecular level in Figure 19-12. 

The difference in electrical potential between two electrodes is the cell potential, designated E and measured in volts (V). The magnitude of E increases as the amount of charge imbalance between the two electrodes increases. For any galvanic cell, the value of E and the direction of electron flow can be determined experimentally by inserting a voltmeter in the external circuit. 

The surface potential of a liquid solvent s, %, is defined as the difference in electrical potentials across the interface between this solvent and the gas phase, with the assumption that the outer potential of the solvent is zero. The potential arises from a preferred orientation of the solvent dipoles in the free surface zone. At the surface of the solution, the electric field responsible for the surface potential may arise from a preferred orientation of the solvent and solute dipoles, and from the ionic double layer. The potential as the difference in electrical potential across the interface between the phase and gas, is not measurable. However, the relative changes caused by the change in the solution s composition can be determined using the proper voltaic cells (see Sections XII-XV). 

The transport of toluene-4-sulfonate into Comamonas testosteroni has been examined (Locher et al. 1993), and rapid uptake required growth of the cells with toluene-4-sulfonate or 4-methylbenzoate. From the results of experiments with various inhibitors, it was concluded that a toluenesulfonate anion/proton symport system operates rather than transport driven by a difference in electrical potential (A (/), and uptake could not take place under anaerobic conditions unless an electron acceptor such as nitrate was present. 

Space-clamped (HH) equations relate the difference in electrical potential across the cell membrane (V) and gating variables (0 < m, n, h < 1), for ion channels to the stimulus intensity (7J and temperature (T), as follows ... 

The cell potential is the difference in electrical potential (inner potential) between the right-hand and left-hand mercury terminals ... 

AU mental activity is achieved by two types of cells, neurones and glial cells, and approximately 50 different chemicals that provide communication between the neurones. The neurones are specialised cells that generate differences in electrical potential that are transmitted along their surface to carry information. Within the brain, integration and coordination is brought about by around 10" neurones, com-... 

Thus, thioarylation may be facilitated electrochemically. The conventional nucleophilic substitution of the phenylthio gronp for bromine in 4-bromobenzophenone requires extremely rigid conditions. When a difference in electric potentials is set up, the reaction proceeds readily and gives products in a high yield (80%). It is sufficient to set up only the potential difference necessary to ensure the formation of the substrate anion-radical (with the potential and current strictly controlled). The chemical reaction takes place in the bulk of solution and yields 4-(phenylthio)benzophenone (Pinson and Saveant 1974) (Scheme 5.1). 

Corrosion is an electrochemical process that occurs when metal is immersed in water and a difference in electrical potential between different parts of the metal causes a current to pass through the metal between the region of lower potential (anode) and the region of higher potential (cathode). The migration of electrons from anode to cathode results in the oxidation of the metal at the anode and the dissolution of metal ions into the water. 

I = EIR where I is the current, E is the electromotive force, and R is the resistance. The SI units for each of these is amperes, volts, and ohms, respectively. Ohm s law is also expressed as / = AE/7 where AE is the difference in electric potential. The resistance is dependent upon the dimensions of the conductor. 

The SI unit for electric potential and for electromotive force (symbolized by V) equivalent to one joule per coulomb. It is the difference in electric potential needed for a one ampere current to flow through a resistance of one ohm. 

The ion specificity of systems such as shown in Fig. 2 may be studied by measuring the steady-state difference in electrical potential between solution 1 and solution 2 (both usually aqueous) in electrochemical cells of the type ... 

Ferrous metal corrosion can occur quite readily whenever a difference in electrical potential exists between iron and a corroding agent. Corrosion begins whenever electrons leave the iron surface at the anode and ferrous ions form ... 

Although the cell potential of a single electrode cannot be measured, two different electrodes can be connected to each other to measure the flow of electrons that occurs between them. Electrode potential is the difference in electrical potential between the metal strip and the solution in a half-cell. The larger the electrode potential, the greater the energy required to move an electron from the metal strip to the solution. 

The unit for measuring the difference in electrical potential is called the volt, and quantifies the potential difference between the two half-cells. Because this... 

The difference in electric potential, E, between two points is the work needed (or that can be done) when moving an electric charge from one point to the other. Potential difference is measured in volts (V). The greater the potential difference between two points, the stronger will be the push on a charged particle traveling between those points. 

The electrochemical interface is the site where electrode reactions take place. At equilibrium, differences of chemical potential in the electrode and electrolyte bring about differences in electrical potential across the interface. The structure and models of such an electrochemical interface will be discussed in Sect. 2.3. 

DIALYSIS. The process of separating compounds or materials by the difference in their rates of diffusion through a colloidal sentipermeahle membrane. Thus, sodium chloride diffuses eleven limes as last as tannin ami twemy-une times as fast as albumin. When the process is conducted under the influence of a difference in electrical potential, as from electrodes on opposite sides of the semipermeable membrane, it is called clectrodialysis. 

If the solute carries a net charge, there is an additional thermodynamic effect of moving the charge across any difference in electric potential that exists between the solutions on the two sides of the membrane. The free energy change then is... 

Figure 12 shows the response patterns to 8 different brands of beer among 36 brands measured [20]. The patterns were measured relative to a certain beer as a standard. Although the difference in electrical potential between different brands was a few mV or more, each beer was easily distinguished from the other by these patterns because of the high reproducibility and... 

Discontinuous systems. The membrane is regarded as a surface of discontinuity, hindering the movement of the different ions and molecules. The driving forces are in this case the differences in electrical potential, pressure and chemical potential (765, 166) [see equation (4)]. 

There is difference in electric potential across the membrane. So there is an electric field in the membrane, but there are no electric fields in the two bulk phases. The electrical work required to move charge dQ across the center of the membrane is (cj>B — charge transport because the potential difference is constant. Since dnCx = — dncp, equation 8.3-3 can be used to show that at phase equilibrium,... 

This looks like there are five intensive variables, but there are not because only the difference in electric potentials between the phases is important. We can take a = 0 and delete the electric work term in equation 8.3-6. Since there are four intensive variables and two equations, F = 2, in agreement with F = C — p + 2 = 2 — 2 + 2 = 2. Note that Qp is taken as a component. This leads to... 

Of course, these reactions may be very much more complicated. Since the pH is specified, H + is not included as a reactant, and a reactant may be a sum of species if the reactant has pKs in the pH region of interest. These biochemical reactions do balance atoms of elements other than hydrogen, but they do not balance electric charges. When the half-reactions occur in half-cells connected by a KC1 salt bridge, the difference in electric potential between the metallic electrodes... 

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