Mercury surface, equation

As in direct metalation, the reaction occurs at the metal surface. An electron is transferred from the surface to the <7 antibonding orbital of the carbon-bromine bond to produce the anion radical in the rate-determining step " (equation 1). The anion radical can then dissociate at the surface to the 1-methyl-2,2-diphenylcyclopropyl radical (equation 2). At this point some racemization may occur and the radical can undergo a number of indistinguishable reactions. The radical may pick up another electron to yield the anion (equation 3) or since mercury is such an efficient radical trap, the radical may become adsorbed on the mercury surface (equation 4) from which it can either take another electron to yield the anion (equation 5) or combine with another adsorbed radical to produce a dicyclopropylmercury (equation 6). 

The original IlkoviC equation neglects the effect on the diffusion current of the curvature of the mercury surface. This may be allowed for by multiplying the right-hand side of the equation by (1 + ADl/2 t1/6 m 1/3), where A is a constant and has a value of 39. The correction is not large (the expression in parentheses usually has a value between 1.05 and 1.15) and account need only be taken of it in very accurate work. 

For the familiar dropping mercury electrode, the electrical potential 1J1 at the metal surface relative to the bulk region of the electrolyte is controlled by an external potential source - a constant voltage source. In this case, can be set to any value (within reasonable physical limits) as the mercury/electrolyte interface does not allow charge transfer or chemical reactions to occur (at least to a good approximation for the case of NaF). Therefore, we can say that the equation of state of the mercury surface is... 

Mo(VI) at the mercury surface [95]. The reduction of the Mo(VI) complex proceeds as a one-electron surface electrode process. Due to the complex molecular stracture of the deposited compound, attractive interactions emerge within the adsorbed film The quasireversible maxima have been measured for this system at three distinct accumulation times. The position of the maximum varies with the surface coverage according to the following equation ... 

Equation 1.7 for the reduction of protons at a mercury surface in dilute sulphuric add is followed with a high degree of accuracy over the range -9 Tafel plot i.s shown in Figure 1.5. At large values of the overpotential, one reaction dominates and the polarization curve shows linear behaviour. At low values of the overpotential, both the forward and back reactions are important in determining the overall current density and the polarization curve is no longer linear. 

The vapours are evidently adsorbed on to the mercury surface and the amount adsorbed can be calculated with the aid of the Gibbs equation... 

In the case of the adsorption of benzene vapour by mercury examined by Iredale (p. 67) at a pressure of 12-5 mm. at 300° K., 0-564 of the surface is covered with benzene and 0-436 is bare. From the Herz-Knudsen equation it can be calculated that 0 902 x 10 gm. mols of benzene hit this bare surface per second, whilst on the covered surface 0 443 x 10 gm. mols are present. Thus the life of a benzene molecule on the mercury surface is 4 9 x 10 seconds. Over a free benzene surface, if the orientation of the molecules be similar to that on mercury, 1 666 x 10 gm. molecules evaporated per second or the life of a benzene molecule on a benzene surface is 4 7 X 10 seconds. 

It thus appears that the surface concentration calculated with the aid of Gibbs equation is equal on the one hand to minus the surface charge found by Lippmann s equation from the slope of the electro-capillary curve and on the other hand to minus the number of grm. equivalents of mercurous ions taken up by an expanding mercury surface or thrown off a contracting one in the course of the N emst ionic transfer. 

The mercury surface is probably the best characterized surface with respect to its electric properties. The explanation is that mercury is one of the few metals that is liquid at room temperature. Since it is a metal a voltage can easily be applied. Since it is a liquid the surface tension can be measured simply and precisely. Then the surface charge can be calculated with the help of the Lippmann equation. Additionally, a fresh surface free of contamination can be continuously produced. 

The formation of the dicyclopropylmercury alone or in combination with the adsorbed radical type intermediates accounts for the observation that the substrate disappears at a faster rate than the reduction product appears The dicyclopropylmercury can then accept an electron to produce the anion and a cyclopropylmercury radical which in combination with the mercury surface becomes an adsorbed radical (equation 7) which can be recycled through the pathway of equation 5 or equation 6. The anions formed in equation 3, equation 5, and equation 7 react at the surface with acetonitrile solvent (equation 8) to yield the hydrocarbon. When deuterated acetonitrile was used the hydrocarbon isolated contained 76% deuterium The anion can also react with the electrolyte, tetraethylammonium bromide, in an elimination reaction (equation 9) to produce hydrocarbon, ethylene and triethylamine, all of which have been identified in the reaction mixture ... 

Figure 9.3. Data on the adsorption of caprylic acid on a hydrophobic (mercury) surface in terms of a double logarithmic plot of equation 16. (a) Comparison of the experimental values with a theoretical Langmuir isotherm, using the same values for the adsorption constant B for both curves, (b) The adsorption process can be described by introducing the parameter a, which accounts for lateral interaction in the adsorption layer. Equation 16 postulates a linear relation between the ordinate [= log[0/l )] - 2a d/( n 10)] and the abscissa (log c). If the correct value for a is inserted, a straight line results. For caprylic acid at pH 4, a value of a = 1.5 gives the best fit. (From Ulrich et al., 1988.)...

Mercury porosimetry is performed nearly exclusively on automatic commercial instruments that differ mainly in the highest operative pressure, which determines the size of smallest attainable pores. The highest pressure is limited by the uncertainty about the validity of the Washburn equation, which forms the basis of data evaluation. In pores with sizes similar to the mercury atom the assumption that physical properties of liquid mercury (surface tension, contact angle) are equal to bulk properties is, probably, not fully substantiated. For this reason the up-to-date instruments work with pressures up to 2000 - 4000 atm, only. 

Below 45 MPa, the high dispersive precipitated silica sample with or without membrane collapses without mercury intrusion. The buckling mechanism of pores edges can be assumed as in the case of low density xerogels. Consequently, equation (2) can be used to interpret the mercury porosimetry curve in this low pressure domain. The constant A, to be used in equation (2) can be calculated from the P, value using equation (4). With a mercury surface tension 0.485 N/m, a contact angle 0= 130° and P, = 45 MPa, one obtains K = 86.3 nm MPa" . 

Figure 4 7 Open-end manometers. Open-end manometers are governed by the same principles as mercury barometers (Fig. 4.6). The pressure of the gas, Pg, is exerted on the mercury surface in the closed (left) leg of the manometer. Atmospheric pressure, P, is exerted on the mercury surface in the open (right) leg. With a meter stick, the difference between these two pressures, P[jg, may be measured directly in millimeters of mercury (torr). Gas pressure is determined by equating the total pressures at the lower liquid mercury level, indicated with a dashed line. 

Tho equation is satisfied over fairly wide limits of variation in the parameters, and the value E = -0.045 V is obtained this does not differ greatly from the tabular value of E = —0.076 V. The same authors [18] measured the decomposition rate of hydrc en peroxide at a mercury surface at pH 12-13. At low peroxide concentrations the results were fomid to be in proximate agreem t with the hypothesis of linked electrochemical reactions the rate increases sharply at c 0.15 mole/liter, which evidently indicates an increasing contribution from the chain mechanism. 

Smith [113] studied the adsorption of n-pentane on mercury, determining both the surface tension change and the ellipsometric film thickness as a function of the equilibrium pentane pressure. F could then be calculated from the Gibbs equation in the form of Eq. ni-106, and from t. The agreement was excellent. Ellipsometry has also been used to determine the surface compositions of solutions [114,115], as well polymer adsorption at the solution-air interface [116]. 

Like the analogous equation for capillary condensation (Equation (3.74) Equation (3.81) is based on the tacit assumption that the pore is of constant cross-section. Integration of Equation (3.81) over the range of the mercury penetration curve gives an expression for the surface area -4(Hg) of the walls of all the pores which have been penetrated by the mercury ... 

The mercury film electrode has a higher surface-to-volume ratio than the hanging mercury drop electrode and consequently offers a more efficient preconcentration and higher sensitivity (equations 3-22 through 3-25). hi addition, the total exhaustion of thin mercury films results in sharper peaks and hence unproved peak resolution in multicomponent analysis (Figure 3-14). 

Equation (9.2) can be used to calculate the metal s surface potential. The value of the electron work function X can be determined experimentally. The chemical potential of the electrons in the metal can be calculated approximately from equations based on the models in modem theories of metals. The accuracy of such calculations is not very high. The surface potential of mercury determined in this way is roughly -F2.2V. 

This equation was hrst obtained by Gabriel Lippmann in 1875. The Lippmann equation is of basic importance for electrochemistry. It shows that surface charge can be calculated thermodynamically from data obtained when measuring ESE. The values of ESE can be measured with high accuracy on liquid metals [e.g., on mercury (tf= -39°C)] and on certain alloys of mercury, gallium, and other metals that are liquid at room temperature. 

In 1873, Gabriel Lippmann (1845-1921 Nobel prize, 1908) performed extensive experiments of the electrocapiUary behavior of mercury and established his equation describing the potential dependence of the surface tension of mercury in solutions. In 1853, H. Helmholtz, analyzing electrokinetic phenomena, introduced the notion of a capacitor-like electric double layer on the surface of electrodes. These publications... 

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