Vacant proton level

Different Types of Proton Transfers. Molecular Ions. The Electrostatic Energy. The ZwiUertons of Amino Acids. Aviopro-tolysis of the Solvent. The Dissociation Constant of a Weak Acid. Variation of the Equilibrium Constant with Temperature. Proton Transfers of Class I. Proton Transfers of Classes II, III, and IV. The Temperature at Which In Kx Passes through Its Maximum. Comparison between Theory and Experiment. A Chart of Occupied and Vacant Proton Levels. 

A Chart of Occupied and Vacant Proton Levels. With two exceptions, each of the values of J given in Tables 9, 10, and 11 refers to the process where a proton is raised to the vacant proton level of an HsO molecule from a lower occupied proton level of a species of molecule or molecular ion in each case the value of J gives the amount by which this initially occupied level lies below the vacant level of H20. Obviously, using these values, it is at once possible to map out a chart of the proton levels of these various particles in aqueous solution, as has been done in Fig. 36. The two exceptions in Table 9 are the values derived from the KB of glycine and alanine. In these cases, as shown in (125), a proton is transferred to a vacant level from the ordinary occupied proton level in a water molecule the value of J gives the amount by which the vacant level lies above this occupied proton level of H20. 

Occupied % proton i levels J Vacant proton levels Cl-... 

In Fig. 37 two areas have been shaded. The area in the upper left corner, where protons in occupied levels are unstable, we have already discussed. In the lower right-hand corner the shaded area is one where vacant proton levels cannot remain vacant to any great extent. In aqueous solution any solute particle that has a vacant proton level lower than that of the hydroxyl ion will capture a proton from the solvent molecule, since the occupied level of the latter has the same energy as the vacant level of a hydroxyl ion. Consequently any proton level that would lie in this shaded area will be vacant only on the rare occasions when the thermal agitation has raised the proton to the vacant level of a hydroxyl ion. On the other hand, there are plenty of occupied proton levels that lie below the occupied level of the H2O molecule. For example, the occupied level of the NH3 molecule in aqueous solution lies a long way below that of H20. 

There are, of course, many substances, soluble in water, whose molecules contain one or more protons, but which, like the Nll.t molecule, show no spontaneous tendency to lose a proton when hydroxyl ions are present. In each of these molecules the energy level occupied by the proton must, as in NII3, lie below the occupied level of II20. If methanol is an example of this class, the vacant proton level of the moth date ion (CH3O)- in aqueous solution must lie below the vacant level of (OH)-. 

In Fig. 38 it will be seen that for the (H2PO4)- ion there are two entries, one for its occupied proton level and one for its vacant proton level. In the aqueous solution of Nal PCh under consideration the thermal agita-... 

Even recent textbooks mention only the traditional view that if water were not dissociated at all, hydrolysis would not occur. From Fig. 30, however, it is quite clear that in the proton transfer (150) we are concerned with the gap between the occupied proton level of the (NJIi)+ ion and the vacant level of the H2O molecule near the top of the diagram. The existence of the vacant proton level of the (OII) ion, near the bottom of the diagram, is irrelevant. 

In contrast to this, consider next a solution of sodium acetate. From vSec. 09 we know that in such a solution the thermal agitation raises a certain number of protons from the solvent molecules to the vacant proton levels of the (CH GOO) ions. In the aqueous solution of such a salt, this process is known as the hydrolysis of the salt and is traditionally regarded as a result of the self-ionization of the water. In Fig. 36, however, it is clear that in the proton transfer... 

The contribution that this quantity makes to the e.m.f. of the cell containing HC1 in Fig. 61 is indicated at the right-hand side of that diagram. The result, (204), implies that, when an H20 molecule is present in methanol solution, its vacant proton level lies about 0.12 electron-volt lower... 

Let us now ask where the vacant proton level must lie, in order that an indicator molecule shall be suitable for use in a very dilute acid solution —where the ratio [Ha0+]/[H20] will be very small compared with unity. According to (216) in order that [BH+]/[B] shall be near unity, obviously J must have a large negative value in other words, the vacant proton level of the molecule B must lie considerably below the occupied proton level of (HaO)+ otherwise, an insufficient crop of (BII)+ ions will be obtained. 

As an example, take the molecule aminoazobenzene, one of the solutes listed in Table 39. When colorimetric measurements were made at room temperature on very dilute aqueous solutions of HC1, containing a trace of this substance, it was found that neutral molecules and (BH)+ ions were present in equal numbers when the concentration of the HCl was 0.0016 molal.1 At this low concentration the activity coefficient of the HCl is very near unity, and we may use (216) to find how far the vacant proton level provided by the aminoazobenzene molecule in aque-... 

The vacant proton level lies 0.268 electron-volt below the occupied level of (H30)+. Referring to Table 12 we see that this level lies at about the same depth as the vacant level of the chloraniline molecule. 

The indicators numbered 1 and 2 at the bottom of Table 39 both have vacant proton levels low enough for use in dilute solution the circles in Fig. 67 give the experimental results obtained in aqueous solutions of HC1. In each case the slope of the line does not differ from the theoretical slope of (218) by as much as 5 per cent. Reading off the constant vertical distance between the two curves (the length of the vertical arrow in Fig. 67), we find... 

In Table 39 this value is recorded at the bottom of column 3. We have already found above that Ji is equal to —0.268 electron-volt. We find then Ji = (—0.268 + 0.076) = —0.192. This is the amount by which the vacant proton level lies below the occupied proton level of the (HjO)+ ion the value is included in column 2 of Table 39. 

In Sec. 128 it was found that the vacant proton level of indicator 2 lies at 0.192 electron-volt below the occupied level of (HaO)+ in dilute aqueous solution. Using the successive increments listed in the last column of Table 39, we find, counting upward, that the value for indicator 5 is —0.052, referred to the same zero of energy. Proceeding by the same stepwise method to No. 6 we find for the energy of the vacant proton level the positive value +0.038. This still refers to the occupied level of the (II30)+ ion in dilute aqueous solution. It means that work equal to 0.038 electron-volt would be required to transfer a proton from the (H30)+ ion in very dilute solution to the vacant level of No. 6 in the concentrated acid solution in which the measurements were made. A further amount of work would be required to transfer the proton from the occupied level of No. 6 to the vacant proton level of one of the H2O molecules in the same concentrated solution. This is the situation because, as mentioned above, the changing environment has raised the proton level of the (HaO)+ ion relative to that of each of the indicator molecules. 

As shown in Table 39, by the successive increments, the value +0.448 was obtained for the position of the vacant proton level of this indicator. 

As for the proton level in gaseous molecules of hydrogen chloride, HClmc, the following reaction cycle (Fig. 3-2) may be used to estimate the occupied proton level of HClwc at Ph (ho,d) = this also represents the vacant proton level... 

Fig. 3-Z Energy of ionic dissociation of gaseous HCl molecules and proton levels h-= proton level fiH.ojci.D)= unitary occupied proton level (donor level) in gaseous HC(L molecules Xj4.,n-, = unitary vacant proton level (acceptor level) of gaseous Cl ions.

In addition to the acidic proton level, there is the basic proton level in basic aqueous solution which is represented by the unitary vacant proton level (the... 

Fig. 3-16. Hie unitary levels of acidic proton HgOVIIjO and basic proton HgO/OH in pure water, and proton transfer between two levels Copl = occupied proton level cvpl = vacant proton level fiH cHgo-. D) = unitary occupied (donor) level of acidic proton, 1h (H20.a> = unitary vacant (acceptor) level of acidic proton.

For the acidic proton transfer of Eqn. 3-44, the proton solvation processes of Eqns. 3-32 and 3-42 are represented by the proton level versus concentration curves of Eqns. 3-39 and 3-43, respectively, as shown in Fig. 3-19. In this proton level diagram, the proton level in an acetic acid solution is given by the intersecting point (mH,o - where cross each other the occupied proton level versus concentration curve of H3O ion and the vacant proton level versus concentration curve of Ac" ion, as expressed in Eqn. 3-46 ... 

Since acetic acid is a weak add with its unitary proton level (HAc/Ac") lower than the unitary addic proton level (H30 /H20), the proton moves from the unitary occupied acidic proton level to the unitary vacant proton level of acetic acid, thereby reducing the concentration of H3O" ions toward the acetic acid. Contrastively, in strong adds such as hydrochloric add whose unitary proton level (HC1/C1 ) is higher than the unitary addic proton level, the proton moves from the occupied proton level of hydrochloric acid to the vacant level of acidic proton ( H30 /H20 ), thereby increasing the concentration of H3O ions. 

In aquatic chemistry, the unitary proton level of the proton dissociation reaction is expressed by the logarithm of the reciprocal of the proton dissociation constant i.e. p = - log K here, a higher level of proton dissociation corresponds with a lower pK. When the pKy of the adsorbed protons is lower than the pH of the solution, the protons in the adsorbed hydronium ions desorb, leave acidic vacant proton levels in adsorbed water molecules, and form hydrated protons in the aqueous solution. Fig. 9-22 shows the occupied and vacant proton levels for the acidic and basic dissociations of adsorbed hydronium ions and of adsorbed water molecules on the interface of semiconductor electrodes. 

Fig. 9-22. Unitary proton levels of hydrated and adsorbed hydronium ions (acidic proton) and of hydrated and adsorbed water molecules (basic proton) the left side is the occupied proton level (the real potential of acidic protons), and the right side is the vacant proton level. Hi/HjO) = unitary occupied proton level of adsorbed hydronium ions (acidic proton level) H20.d = unitary vacant proton level of adsorbed hydronium ions (acidic proton level) and unitary occupied proton level of adsorbed water molecules (basic proton level) OH = unitary vacant proton level of adsorbed water molecules (basic proton level) (pHi, ) = hydrated proton level at iso-electric point pR...

Equation 9-72 indicates that the logarithm of the ratio of the concentrations of adsorbed protons (acidic occupied proton level) to adsorbed hydroxide ions (basic vacant proton level) depends linearly on the pH of the solution. 

The pH at which the concentration of acidic occupied proton levels of adsorbed h3dronium ions equals the concentration of basic vacant proton levels of adsorbed water molecules is called the iso-electric point pHi, here, the net interfacial charge of adsorbed ions at the interface is zero. The iso-electric point pH,, is expressed in Eqn. 9-73 ... 

FIGURE 22.3 Energy levels of protons and proton vacancies in aqueous solution showing the ionic dissociation of water molecules aH+ = occupied proton level (donor), o[i = vacant proton level (acceptor), and a0 = the standard level. 

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