Autoprotolysis

resulting in the formation of H3O+ and CN. This means that the reaction 

The dual entry of H2O in Fig. 3 reflects the fact that water plays more than the passive role of a solvent in acid-base chemistry. Water is in fact a direct participant in any proton transfer reaction that takes place in aqueous solution, and its conjugate acid H30+ and base OH are respectively the strongest acid and the strongest base that can exist in aqueous solution. 

This principle, which says that all acids stronger than H3O+ or bases stronger than OH appear to be equally strong (that is, totally dissociated) in aqueous solution, is known as the leveling effect. Another way of expressing the same idea is that the difference between degrees of dissociation of 99%, 99.9%, and 99.99% is rarely significant. 

The acid dissociation constant and the pK i In order to express the strength of an acid quantitatively, we write the equilibrium constant for the reaction in Eq 4  

For the same reasons that it is convenient to express hydrogen ion concentrations on the logarithmic pH scale, it is common practice to express acid strengths as pKa = — log Aa. Strong acids have pKaS of zero or less, while those of weak acids are positive. 

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The linear variation of the anticatalysis with the concentration of nitrate, even in very small concentrations, shows that the extent of the autoprotolysis is small. 

The dissociation, or autoprotolysis constant for a solvent, SH, relates the concentration of the protonated solvent, SH2, to that of the deprotonated solvent, S . For amphoteric solvents, which can act as both proton donors and proton acceptors, the autoprotolysis reaction is... 

Until now we have been discussing the kinetics of catalyzed reactions. Losses due to volatility and side reactions also raise questions as to the validity of assuming a constant concentration of catalyst. Of course, one way of avoiding this issue is to omit an outside catalyst reactions involving carboxylic acids can be catalyzed by these compounds themselves. Experiments conducted under these conditions are informative in their own right and not merely as means of eliminating errors in the catalyzed case. As noted in connection with the discussion of reaction (5.G), the intermediate is stabilized by coordination with a proton from the catalyst. In the case of autoprotolysis by the carboxylic acid reactant, the rate-determining step is probably the slow reaction of intermediate [1] ... 

Many compounds that contain hydrogen can donate protons to a solvent sueh as water and so behave as aeids. Water itself undergoes ionie dissoeiation to a small extent by means of autoprotolysis the proeess is usually represented formally by the equilibrium... 

Although the reaction has the overall stoichiometry of a dehydration it is more complex than this and involves a mutual redox reaction between N and N. This is at once explicable in terms of the volt-equivalent diagram in Fig. 11.9 which also interprets why NO and N2 are formed simultaneously as byproducts. It is probable that the mechanism involves dissociation of NH4NO3 into NH3 and HNO3, followed by autoprotolysis of HNO3 to give N02, which is the key intermediate ... 

In addition, the liquid undergoes self-ionic dissociation to a greater extent than any other nominally covalent pure liquid (cf. BF3.2H2O, p. 198) initial autoprotolysis is followed by rapid loss of water which can then react with a further molecule of HNO3 ... 

NOj ions/ Addition of water to nitric acid at first diminishes its electrical conductivity by repressing the autoprotolysis reactions mentioned above. For example, at -10° the conductivity decrea.ses from 3.67 x 10 ohm cm to a minimum of 1.08 x 10" ohm" cm at 1.75 molal H2O (82.8% NjOs) before rising again due to the increasing formation of the hydroxonium ion according to the acid-base equilibrium... 

Despite this enormous viscosity, fused H3PO4 (and D3PO4) conduct electricity extremely well and this has been shown to arise from extensive self-ionization (autoprotolysis) coupled with a proton-switch conduction mechanism for the... 

H2SO4.Z2H2O, are known with = 1, 2, 3, 4 (mps 8.5", -39.5". -36.4" and -28.3% respectively). Other compounds in the H2O/SO3 system are H2S2O7 (mp 36") and H2S4O13 (mp 4"). Anhydrous H2SO4 is a remarkable compound with an unusually high dielectric constant, and a very high electrical conductivity which results from the ionic self-dissociation (autoprotolysis) of the compound coupled with a proton-switch mechanism for the rapid... 

This value is compared with those for other acids and protonic liquids in Table 15.21 " the extent of autoprotolysis in H2SO4 is greater than that in water by a factor of more than lO " and is exceeded only by anhydrous H3PO4 and [HBp3(OH)] (p. 198). In addition to autoprotolysis, H2SO4 undergoes ionic selfdehydration ... 

Ammonolysis of 2-chlorobenzothiazole in liquid ammonia was studied by Lemons et al. and found to be approximately first-order with respect to this substrate at the fairly high concentrations used. The actual nucleophilic reagent was, as expected, the neutral species NH3, and reaction via the amide ion NH2 arising from the autoprotolysis equilibrium [Eq. (5)] was excluded on the grounds that addition of ammonium chloride did not depress the reaction rate. In accordance with this interpretation and in connection with the existence of aromatic substitutions other than normal it is of interest that 2-chlorobenzothiazole was found to react difiFerently with sodamide, although the products were unidentified in this case. 

Autoprotolysis of the Solvent. While studying these proton transfers, there is another type that may be discussed at the same time, namely, the self-dissociation of the solvent itself. As is well known, highly purified solvents show at least a small electrical conductivity. In methanol, for example, it is generally recognized that this conductivity arises from the fact that, a certain number of protons havo been transferred according to the process... 

Proton Transfers in Various Solvents. The Autoprotolysis of Methanol. Formic Acid as Solvent. The Sulfate Ion. Autoprotolysis of Formic Add. The Urea Molecule. Sulfuric Add and Liquid Ammonia as Solvents. 

The AutoprotolySis of Methanol. The table gives the value log K = —16.6 for the autoprotolysis constant at 25°C. From this value we find... 

Autoprotolysis of Formic Acid. The self-dissociation of pure formic acid yields, in addition to the formate ion, the positive ion (HCOOII2)+, according to... 

In Table 38 the autoprotolysis constant of sulfuric acid is given by — log K = 3.1, from which we calculate... 

The reaction is very fast in both directions, and so is always at equilibrium in water and in aqueous solutions. In every glass of water, protons from the hydrogen atoms are ceaselessly migrating between the molecules. This type of reaction, in which one molecule transfers a proton to another molecule of the same kind, is called autoprotolysis (Fig. 10.9). 

In dilute aqueous solutions (the only ones we consider in this chapter), the solvent, water, is very nearly pure, and so its activity may be taken to be 1. The resulting expression is called the autoprotolysis constant of water and is written Kw ... 

The concentrations of H30 + and OH are very low in pure water, which explains why pure water is such a poor conductor of electricity. To imagine the very tiny extent of autoprotolysis, think of each letter in this book as a water molecule. We would need to search through more than 50 books to find one ionized water molecule. The autoprotolysis reaction is endothermic (AH° = +56 kj-mol l), and so we can expect Kw to increase with temperature, and aqueous solutions to have higher concentrations of both hydronium and hydroxide ions at higher temperatures. Unless otherwise stated, all the calculations in this chapter will be for 25°C. 

Now we come to a very important point that will be the basis of much of the discussion in this chapter and the next. Because Kw is an equilibrium constant. the product of the concentrations ofHjO+ and OH ions is always equal to Kw. We can increase the concentration of H30+ ions by adding acid, and the concentration of OH ions will immediately respond by decreasing to preserve the value of Kk. Alternatively, we can increase the concentration of OH ions by adding base, and the concentration of H30 ions will decrease correspondingly. The autoprotolysis equilibrium links the concentrations of H30+ and OH" ions rather like a seesaw when one goes up, the other must go down (Fig. 10.10). 

FIGURE 10.9 As a result of autoprotolysis, pure water consists of hydronium ions and hydroxide ions as well as water molecules. The concentration of ions that results from autoprotolysis is only about 10 mol-L and so only about I molecule in ZOO million is ionized. The overlay shows only the ions. 

STRATEGY When Ba(OH)2 dissolves in water, it provides OH ions most hydroxides of Groups 1 and 2 can be treated as fully dissociated in solution. Decide from the chemical formula how many OH ions are provided by each formula unit and calculate the concentrations of these ions in the solution. To find the concentration of H,Oj ions, use the water autoprotolysis constant Kw = [H,0 1 [OH ]. 

In aqueous solutions, the concentrations ofH O and OH ions are related by the autoprotolysis equilibrium if one concentration is increased, then the other must decrease to maintain the value of KIV. 

The values of pH and pOH are related. To find that relation, we start with the expression for the autoprotolysis constant of water Kw = [H3Oh [Of I ]. Then we take logarithms of both sides ... 

The autoprotolysis of water contributes significantly to the pH when the acid is so dilute or so weak that the calculation predicts an H30+ concentration close to 10 mol-E l. In such cases, we must use the procedures described in Sections 10.18 and 10.19. We can ignore the contribution of the autoprotolysis of water in an acidic solution only when the calculated H30+ concentration is substantially (about 10 times) higher than 10-7 mol-L-1, corresponding to a pH of 6 or less. 

The blue square in the grid in the final box represents the percentage of the acid molecules that are deprotonated. We see that x is less than 5% of 0.10, and the approximation is valid. Because the pH < 6, the assumption that the autoprotolysis of water can be ignored is valid. 

We calculate the pH of solutions of weak bases in the same way as we calculate the pH of solutions of weak acids—by using an equilibrium table. The protonation equilibrium is given in Eq. 9. To calculate the pH of the solution, we first calculate the concentration of OH ions at equilibrium, express that concentration as pOH, and then calculate the pH at 25°C from the relation pH + pOH = 14.00. For very weak or very dilute bases, the autoprotolysis of water must be taken into consideration. 

The calculation of x can often be simplified, as explained in Toolbox 10.1. We ignore contributions from the autoprotolysis of water to the hydroxide ion concentration if the concentration of hydroxide ions is greater than 10 h mol-L-. Step 5 Determine the pOH of the solution and then calculate the pH from the pOH by using Eq. 6b. 

That is, 4.2% of the methylamine is present as the protonated form, CH3NH3+. Because the pH is greater than 8, the assumption that this equilibrium dominates the pH and that autoprotolysis can be ignored is valid. 

The approximation that x is less than 5% of 0.15 is valid (by a large margin). Moreover, the H30+ concentration (9.2 X 10 6 mol-F ) is much larger than that generated by the autoprotolysis of water (1.0 X 10 mol-L ), and so ignoring the latter contribution is valid. 

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