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. 

In the ionic dissociation of water itself, discussed in Sec. 62, the proton is raised to the vacant level of one H20 molecule from the occupied level of another (distant) H20 molecule the value of J at 25°C is very nearly 1 electron-volt, as shown in Table 12. Since both these proton levels of the II20 molecule are important, two energy scales have been provided in Fig. 36. The scale on the left counts downward from the vacant level of H20, while the scale on the right counts upward from the occupied level of H20. 

For the sake of illustration, the proton levels of HC1 and Cl- have been drawn in Fig. 37 a little above the level of (HaO)+. Starting with the protons in HOI, we can imagine an experiment, in which wc cause these protons to fall, by a series of steps, toward the bottom of the diagram. When a little HC1 is dissolved in water, the protons from nearly all the HC1 molecules will immediately fall to vacant levels in H2O molecules, to form (HjO)+ ions, as indicated by the arrows at the top of Fig. 37. 

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-... 

The Dissociation Constant of Nitric Acid. The largest value of K in Table 9 is that for the (HS04) ion. In Fig. 36 there is a gap of more than 0.2 electron-volt below the level of the (H30)1 ion. As is well known, several acids exist which in aqueous solution fall iu the intermediate region between the very weak acids and the recognized strong acids the proton levels of these acids will fall in this gap. The values of K for these acids obtained by different methods seldom show close agreement. Results obtained by various methods were compared in 1946 by Redlich,1 who discussed the difficulties encountered. 

Using this value, the positions of the proton levels of HNOs and of the (NO i) ion are shown in Fig. 40 the vacant level of the (N03) ion lies 0.052 electron-volt below the vacant level of the H20 molecule. (If we were to use the value K — 21, derived from measurements of Raman spectrum at high concentrations, the gap between these two levels in Fig. 40 would be about half as wide.)... 

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... 

For comparison, consider now the same ions in methanol solution. Each ionic field will contain more electrostatic energy than the corresponding ionic field in aqueous solution. Suppose that again we raise a proton from the occupied level of a (NIIi) ion to the vacant level of a (CH3COO)- ion. In this process the amount of electrostatic energy released will be greater than in water. If then the value of, / is roughly the same as before, the total amount of work required to transfer the proton will be smaller than in water. Hence, in the chart of the proton levels in methanol, we expect that the interval between these two proton levels will be narrower than in Fig. 36. 

This is 0.22 electron-volt greater than the value of J for nitric acid in water. The relative positions of the proton levels in methanol, using this value, is shown in Fig. 65. 

If then we construct a tentative diagram for the proton levels in formic acid solution, the gap between the vacant level of (JICOO)- and the occupied level of HjO will be a little wider than in Fig. 36. This has been shown in Fig. 65. 

This value, which is only about half as large as the corresponding quantity for water or methanol, has been used in constructing Fig. 65 for the proton levels in formic acid. 

Furthermore, since in Sec. 121 we found the value J = 0.36 electron-volt for the proton transfer (211), this gives the occupied proton level of the (HCOOII2)+ ion a position at (0.52 — 0.36) = 0.16 electron-volt above that of the (H30)+ ion in formic acid as solvent. This is shown in Fig. 65, where, for comparison, a diagram for proton levels in aqueous solution has been included, the level of the (H30)+ ion in aqueous solution being drawn opposite to the level of the same ion in formic acid solution. This choice is quite arbitrary, but was made in order to show more clearly that we may expect that one or more acids that are strong... 

It is found that IIC1 is likewise incompletely dissociated in formic acid solution. There do not appear to be any accurate data on the degree of dissociation so we do not know whether it is necessary to place the proton level of HC1 below that of (H30)+ in formic acid solution. 

On the other hand, for liquid ammonia at —33°C, we find a value of J greater than that of all the other solvents. A tentative scheme for the proton levels in these two solvents is sketched in Fig. 66, in comparison with the scheme of levels in water. 

If the occupied proton level of the CH3COOH molecule dissolved in liquid ammonia lies above the vacant level of NH3, as it does in aqueous solution, acetic acid should be a strong acid in liquid ammonia. This is found to be the case the carboxylic acids are strong acids in this solvent, the protons being transferred to NH3 to form (NH4)+. 

Proton Transfers in More Concentrated Solutions. Measurements with Indicators. The Proton Levels of Indicator Molecules in Dilute Solution. Indicators in More Concentrated Solutions. 

The Proton Levels of Indicator Molecules in Dilute Solution. 

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. 

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