The p Scale

Log normal distribution, the distribution of a sample that is normal only when plotted on a logarithmic scale. The most prevalent cases in pharmacology refer to drug potencies (agonist and/or antagonist) that are estimated from semilogarithmic dose-response curves. All parametric statistical tests on these must be performed on their logarithmic counterparts, specifically their expression as a value on the p scale (-log values) see Chapter 1.11.2. 

The susceptibility or mixing coefficients, pj and pj , depend upon the position of the substituent (indicated by the index, /) with respect to the reaction (or detector) center, the nature of the measurement at this center, and the conditions of solvent and temperature. It has been held that the p/scale of polar effects has wide general applicability (4), holding for substituents bonded to an sp or sp carbon atom (5) and, perhaps, to other elements (6). The or scale, however, has been thought to be more narrowly defined (7), holding with precision only for systems of analogous pi electronic frameworks (i.e., having a dependence on reaction type and conditions, as well as on position of substitution). 

The P scale of solvent polarity is based on a combination of gas-liquid partition coefficients reported by Rohrschneider [43]. 

Attempts have also been made to separate non-specific effects of the local electrical field from hydrogen-bonding effects for a small group of ionic liquids through the use of the K scale of dipolarity/polarizability, the a scale of hydrogen bond donor acidity, and the P scale of hydrogen bond basicity (see Table 3.5-1) [13, 16]. 

For reviews, sec Abraham Doherty Kamlet Taft Chem. Br. 1986, 551-554 Kamlet Abboud Taft Prog. Phys. Org. Chem. 1981,13, 485-630. For a comprehensive table and a and p values, see Kamlet Abboud Abraham Taft J. Org. Chem. 1983, 48, 2877. For a criticism of the p scale, see Laurence Nicolet Helbert J. Chem. Soc., Perkin Trans. 2 1986, 1081. See also Nicolet Laurence Lugon J. Chem. Soc., Perkin Trans. 2 1987, 483 Abboud Roussel Gcntric Sraidi Lauransan Guihgncuf Kamlet Taft./. Org. Chem. 1988,53, 1545 Abraham Grcllier Prior Morris Taylor J. Chem. Soc., Perkin Trans. 2 1990, 521. 

It was later shown by Laurence and coworkers that there are significant systematic differences between P values of solvents obtained with indicators with an oxygen donor atom and those with a nitrogen donor atom (Nicolet and Laurence 1986). These authors recommended the use of a single indicator, preferably 4-nitrophenol relative to 4-nitroanisole or else 4-nitroaniline relative to 4-nitro-N,N-di/rae%>/aniline (rather than 4-nitro-N,N-die// y/aniline used by Kamlet and Taft 1976), to establish a basicity scale. The main point of difference is with respect to solvents that do not have an oxygen donor atom, such as amines, pyridines, and sulfides. In order to save the P scale, Kamlet and Taft proposed a family-dependent covalency parameter, equal to -0.20 for P=0 bases, 0.00 for C=0, S=0, and N=0 bases, 0.20 for -O-bases, 0.60 for pyridines, and 1.00 for amines, for use in linear free energy relationships (Kamlet etal. 1985). 

Many other scales of electron-pair donation abilities have been proposed over the years, which are in general in good correlation with DN e g., the heat of complexation of the solvent molecules with boron trifluoride in dichloromethane (Maria and Gal 1985), and P e.g., SB, the solvatochromism of 5-nitroindoline compared with l-methyl-5-nitroindoline in neat solvents (Catalan el al. 1996) scales. The latter, the SB scale, has the advantage that the N-H acid function of the 5-nitroindoline probe has only a single hydrogen atom, contrary to the nitroanilines used for the P scale, that have two. It was devised quite recently for... 

Another property that characterizes solvents is their softness, in terms of the HSAB concept (Pearson 1963), according to which the interactions of soft solvents are strongest with soft solutes, of hard solvents with hard solutes, but are weaker for hard solvents with soft solutes and vice versa. The applicability of the softness property takes into account that it is superimposed on the more general electron pair donation property discussed above. In fact, it can replace (Marcus 1987) the notion of the family dependence of the P scale, expressed by the , parameter (Kamlet etal. 1985). A few quantitative scales have been... 

ATw is known as the autoionization constant of water, and is sometimes identified as the ion product of water. The magnitude of ATw is very small, being equal to 1.007 x 10 " at a temperature of 25°C.i i For the sake of convenience, Sprensen proposed the p scale, where numbers such as AT would be... 

The p scale was proposed to measure solvent hydrogen bond basicity, i.e. the ability of a bulk solvent to act as hydrogen bond acceptor. This scale was derived by systematic application of the solvatochromic comparison method the final p values were calculated by averaging 13 p parameters for each solvent obtained with different solutes and different physicochemical properties [Kamlet et al, 1981a Kamlet et al, 1983]. 

The Gutmann s Donor Number (DN) was proposed [Gutmann, 1978] as a quantitative empirical parameter for solvent nueleophilicity. For most solvents it was found to correlate well with the p scale. 

The p scale was proposed for solute HBA basicity based on log/C values for 1 1 complexation of series of bases against a number of reference adds in dilute solution of CCI4 [Abraham et al., 1990]. Thirty-four linear equations have been solved for each considered reference acid by a series of bases ... 

For the sake of convenience, Sprensen (1909) proposed the p scale, w here numbers such as Kw would be expressed as the negative of their base 10 logarithms. The value of pKw would then be calculated as ... 

At the exact pH for which the solubility constant is exceeded, one may equate the St relations of equations (54) and (59), solve for the hydronium ion concentration, and convert to the p scale. After solving the resulting quadratic equation, one obtains an expression for this critical pH value ... 

Coherence level scheme of a ID l C, IH HMQC pulse sequence using the p scale. 

Kamlet MJ, Taft RW. The solvatochromic comparison method. 1. The p-scale of solvent hydrogen-bond acceptor (HBA) basicities. J Am Chem Soc 1976 98 377-383. 

Low concentrations are sometimes expressed as negative logarithms, the p scale. This is most familiar as pH, the negative logarithm of the H+ ion concentration ... 

The p scale is also used for other ions—pNa, pH2PC>4, and pCa—and for the negative logarithm of equilibrium constants (pK) and solubility products (pKsp). The negative logarithm increases as the concentration or value decreases. 

Enter the nomograph on the p scale at the left with the vapor density. 

To express small numbers conveniently, chemists often use the "p scale/ which is based on common logarithms (base 10 logs). In this system, if N represents some number, then... 

Because the [H" ] in an aqueous solution is typically quite small, using the p scale in the form of the pH scale provides a convenient way to represent solution acidity. The pH is defined as... 

---