Fraction deprotonated

The extent of deprotonation of a weak acid in solution depends on the acidity constant and the initial concentration of the acid, its concentration as prepared. The fraction deprotonated, the fraction of acid molecules HA that have donated... 

By completely deprotonated, we mean that each acid molecule or ion has lost the proton of its acidic hydrogen atom by transferring it as a hydrogen ion to a solvent molecule. Completely protonated means that each base species has acquired a proton. By incompletely deprotonated or incompletely protonated, we mean that only a fraction (usually a very tiny fraction) of the acid molecules or ions have lost acidic hydrogen atoms as protons or only a tiny fraction of the base species have acquired protons. 

Acetic acid, on the other hand, is a weak acid in water. Only a small fraction of its molecules undergo deprotonation, according to the equation... 

Figure 10-3. Theoretical titration curves for the model compounds of Asp and His obtained from REX-CPHMD simulations [41]. Solid curves are the obtained by fitted the computed deprotonated fraction to the generalized Henderson-Hasselbach equation. The dashed lines indicate the computed pKa values...

The more favorable partitioning of [1+ ] to form [l]-OH than to form [2] must be due, at least in part, to the 4.0 kcal mol-1 larger thermodynamic driving force for the former reaction (Kadd = 900 for conversion of [2] to [l]-OH, Table 1). However, thermodynamics alone cannot account for the relative values of ks and kp for reactions of [1+] that are limited by the rate of chemical bond formation, which may be as large as 600. A ratio of kjkp = 600 would correspond to a 3.8 kcal mol-1 difference in the activation barriers for ks and kp, which is almost as large as the 4.0 kcal mol 1 difference in the stability of [1]-OH and [2]. However, only a small fraction of this difference should be expressed at the relatively early transition states for the reactions of [1+], because these reactions are strongly favored thermodynamically. These results are consistent with the conclusion that nucleophile addition to [1+] is an inherently easier reaction than deprotonation of this carbocation, and therefore that nucleophile addition has a smaller Marcus intrinsic barrier. However, they do not allow for a rigorous estimate of the relative intrinsic barriers As — Ap for these reactions. 

The equilibrium constant for this reaction depends on the stability constants of the ionophore-M+ complexes and on the distribution of ions in aqueous test solution and organic membrane phases. For a membrane of fixed composition exposed to a test solution of a given pH, the optical absorption of the membrane depends on the ratio of the protonated and deprotonated indicator which is controlled by the activity of M+ in the test solution (H,tq, is fixed by buffer). By using a to represent the fraction of total indicator (Ct) in the deprotonated form ([C]), a can be related to the absorbance values at a given wavelength as... 

S)-4-Phenyloxazolidine-2-one (98), (S)-4-phenyloxazolidine-2-thione (99) and (4R,5S)-4,5-diphenyloxazolidine-2-one (100) are very poor nucleophiles. A substoichiometric amount (10 mol%) of potassium hydride is necessary to generate a fraction of the potassium salt of 13 which has a sufficient nucleophilicity. This holds for the anions generated by deprotonation at the carbamate position and activation by addition of dibenzo-18-crown-6 to the reaction mixtime, and causes the Michael addition to be very slow at -78 °C. The best temperatme is -20 0 °C. The higher the temperature, the more decomposition product is formed dming the Michael addition. 

FIGURE 2-17 The titration curve of acetic acid. After addition of each increment of NaOH to the acetic acid solution, the pH of the mixture is measured. This value is plotted against the amount of NaOH expressed as a fraction of the total NaOH required to convert all the acetic acid to its deprotonated form, acetate. The points so obtained yield the titration curve. Shown in the boxes are the predominant ionic forms at the points designated. At the midpoint of the titration, the concentrations of the proton donor and proton acceptor are equal, and the pH is numerically equal to the pAfa. The shaded zone is the useful region of buffering power, generally between 10% and 90% titration of the weak acid. 

The principal species of a monoprotic or polyprotic system is found by comparing the pH with the various pKa values. For PH < pKh the fully protonated species, H A, is the predominant form. For pA) < pH < pK2, the form H , A is favored and, at each successive pK value, the next deprotonated species becomes principal. Finally, at pH values higher than the highest pK, the fully basic form (A"-) is dominant. The fractional composition of a solution is expressed by a, given in Equations 10-17 and 10-18 for a monoprotic system and Equations 10-19 through 10-21 for a diprotic system. 

Why do we say virtually Complete deprotonation is an ideal model in practice, an insignificantly small fraction of acid molecules may keep their protons. 

Because only a fraction of the HCN molecules donate their protons, HCN is classified as a weak acid in water. As in any chemical reaction, the equilibrium between HCN and its deprotonated form, CN, is dynamic. In a molecular picture of the solution, we would think of protons ceaselessly exchanging between HCN and H20 molecules, such that there is a constant, but low concentration of CN- and H (01 ions. 

In the first term, the rate constant is multiplied by cHe / K% + cH ), the fraction of total enol present in neutral form E, and in the second term, k A is multiplied by K /(K + cH ), the fraction of total enol present in basic form Ee [Equation (4)]. The observed coefficient for general base catalysis is now seen to arise from the pre-equilibrium reaction shown in the second line of Scheme 3. Replacing (A /ch )cha by (K /K A)cAe we find k e=kf A / A. Thus, pre-equilibrium deprotonation of the enol by the general base followed by carbon protonation of the ensuing enol anion is operationally equivalent to general base catalysis. 

Fractions of protonated and deprotonated enzyme are given by the dissociation equilibria, with appropriate dissociation constants. The substrate S shown in this scheme does not have acido-basic properties in the given pH range. Solving the equations outlined in Scheme 1 yields (for this reaction) the following relationship. 

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