Acidity, also statistical effects

Scatter in free energy correlations may also be caused by a statistical effect when more than one reaction centre can be involved.The reactivity of a base or nucleophile possessing q identical basic or nucleophilic sites compared with a dissociation equilibrium where the conjugate acid possesses p identical acidic sites requires the following statistical correction to the simple Bronsted type relationship (Equations 23 and 24). 

Matrix schemes which assign end effects to each end of a helical segment are also proposed. A 3 x3 statistical weight matrix B using this weighting scheme is used here. Row index states of amino acid residues i-1 and /, while columns index states of amino acid residues i and /+ 1. 

Along with the electrostatic effect, a statistical or entropy effect is also present and accounts for the increased dependence of the equilibrium constant on the degree of neutralization, f, with decreased acid strength of the polyelectrolyte. Thus, cations from the base compete with protons from the acid for positions on the PAA chain. There are more possibilities or opportunities for a cation with respect to replacing a proton when f is below 0.5 (that is when neutralization is less than one half). The counter is true when f is above 0.5. Thus, PAA is a stronger acid compared with monoacids such as propenoic acid at low fractions of neutralization, whereas PAA is a weaker acid at high fractions of neutralizations. However, this entropy effect is overwhelmed for PAA by the electrostatic effect with the end result that PAA is a weaker acid than propenoic acid throughout its neutralization. 

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