Nernst relation

As we have already seen, the standard potentials are relative to standard reference conditions—i.e., one-molal solutions at 2) = 25 °C and /) = 1 bar, in equilibrium with pure metals or pure gases. Applying the Nernst relation to a redox equilibrium such as reaction 8.163 and assuming unitary activity for the condensed phases (i.e., pure metals), we have... 

As is the pattern with other E-pH diagrams the area above the top dotted line shows the predominance of O2, the area below the lower dashed line shows the predominance of H2, and the area in between the dashed lines shows the predominance of HOH. In other words, at high potentials water decomposes into O2 and at low potentials water decomposes into H2. Values of E at H" " concentrations other than 1.00 M may be readily calculated by introducing the above equations and the appropriate E° values into the Nernst relation. 

The use of a sodium amalgam electrode [Na(Hg)/NaC104(s)] in DMF has been reported [205] and a similar lithium amalgam electrode has been employed in DMSO [207]. The potential of the cell, Li(Hg)/Li Cr (DMSO), has been measured for LiCl concentrations from 0.01 to 1.0 M and the Nernst relation was verified within 1 mV the Li(Hg) electrode obeys the Tafel equation with the transfer coefficient a = 0.5 over... 

Given the problems inherent to the electrode measurement of in soil solution, it would seem desirable to consider other methods of estimating Eh. Theoretically, one could analyze the soil solution for the reduced and oxidized species of a redox couple, say dissolved Fe " and Fe, and use the Nernst relation (equation 7.2) to calculate Eh. Usually, however, there are difficulties with this approach. In the case of the Fe couple, Fe solubility in all but very acid soil solutions is extremely low (below detection), so that an assumption must be made about the activity of the free Fe " ion. It might reasonably be assumed that the solubility product of Fe oxide limits this activity, but Fe oxides have a rather wide range of solubilities depending on oxide crystallinity, structure, and purity. A better approach to measuring E would be to use an indicator chemical that undergoes reversible electron transfer with natural redox couples in soil solution, that is,... 

The basic principle behind potentiometric measurements is the development of charge related to the analyte activity in the sample through the Nernst relation ... 

Using this result and the Nernst relation /" = D(Cq - c ) 8q, we estimate the diffusion layer thickness to be... 

Flow Past a Reacting Flat Plate 81 The diffusion layer thickness can be estimated from the Nernst relation... 

Figure 2.13. Measured and predicted redox potential variation with reaction quotient of measured spedes concentration in the Nernst relation (average potential shift 0.37 V) (Pamukcu, Weeks, and Wittle, 2004).

In an irreversible process, the potential is no longer given by a Nernst relation throughout the wave and only the forward current-potential term in Eq. (71) applies, especially at elevated potentials. Many electro-organic processes behave in the latter manner. 

All results apply to 1 F N(CHj)jCl and 20° unless otherwise stated. The titration of methanolic hydrochloric acid with lithiummethylate shows the expected Nernst relation between potential of the hydrogen electrode and total concentrations of H in all pertinent forms and that of methylate, respectively pK = -log [Htl tOR ] 16,60 pK 16,05, 1 F LiCl. This permits the definition of pH-scales based on molar concentrations. The titration curves or proton acids like acetic acid (pK = 8,9 ), acetylacetone (pK a 11,8), ammoniumion (pK = 11,2), oxalic acid (pKj = 8,4, pK = 5,lj) and pyrocatechol (pK 15,4, pK = 13,2) were as expected and permitted to check the measuring techniques. 

An eCMR is also an effective device for gas separation, enrichment, and pumping (Winnick, 1990). This is accomplished when a gas i (e.g., H2, O2, CI2, CO2) catalyt-ically reacts to form an ion (cation or anion) at one electrode, which is pumped across the electrolyte to the opposite electrode by applying an external potential, where the gas is released in the reverse catalytic reaction. In this case, if the polarization model, Eqn (15.20), were used, it is apparent that the standard anode and cathode electrodes are the same, so that V = 0, although the partial pressure term in the Nernst relation remains. Further, because the electrode reaction p is the same, just reverse at either electrode, Eqn (15.20) reduces to. 

One can see that the true value will be closer to the measured value using the Nernst relation when P- is very small and the reference pressure much bigger than P-. Taking P- as lO atm., real activity and measured activity for 0 in liquid steel have been calculated at l600 C (20) (Table) with air as reference ... 

In current practice, the reference electrode is either calomel or silver-silver chloride and the hydrogen electrode is replaced by antimony, quin-hydrone, or glass electrodes. The electrodes and pH-meter potentiometric circuit are calibrated against standard reference solutions. Under the assumption that liquid junction potential does not change if unknown solution is replaced by U2. the Nernst relation would be... 

In biological studies, we are normally interested in cationic determinations. The membrane-electrode potentials which are observed are described by the Nernst relation... 

The membrane serves as a phase separator, which is made selectively permeable to those ions for which a concentration value (activity) is to be determined. Using the Nernst relation, with necessary correction factors for temperature and nonideality of the membrane, the potential between the known and unknown concentration can be measured and the unknown ionic concentration thus determined. 

As we have pointed out previously, electrodes respond to ion activity rather than ion concentration. In addition, there is lack of linearity between theoretical (from the Nernst relation) and measured values of emf for a given spread of ion activities for a particular ion in aqueous solution. Figure 6.3 presents this situation. 

In the laboratory, a calibration curve is developed for each ion-selective electrode and the calibration is checked periodically to detect membrane degradation. From the Nernst relation, we can compute that the potential at the glass membrane changes by approximately 59 mV for each change by a factor of ten in ion concentration at 25°C. 

The OH " level in the filling solution which is detected by the sensing element, is directly proportional to the sample ammonia level. The electrode potential follows the approximate Nernst relation... 

To verify the accuracy of this equality, it is sufficient to write the equilibrium solution potential with two Nernst relations, one involving the couple and the other... 

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