The acidity of various substituted acetophenones in DMSO is...

The acidity of various substituted acetophenones in DMSO is given below. Would you expect the $\rho$ value to correlate best with $\sigma, \sigma^{+}$, or $\sigma^{-}$? Explain, considering each of the $\sigma$ parameters explicitly. Do a plot of the $\mathrm{p} K / \mathrm{p} K_{0}$ values for each $\sigma$ parameter.

Key Concepts

Hammett Equation

The Hammett equation is a linear free?energy relationship (LFER) that relates the rate or equilibrium constants of chemical reactions to the electronic characteristics of substituents on an aromatic ring. It quantifies how electron?withdrawing or electron?donating groups alter the reactivity of a functional group attached to the aromatic system. This principle is fundamental in physical organic chemistry for understanding substituent effects on reaction mechanisms and equilibria.

Standard Sigma Constants (?)

Standard sigma constants (?) represent the substituent effects based on both inductive and resonance effects in reactions where neither a full positive nor a full negative charge is developed at the reaction center. They provide a general scale for how substituents alter electron density and are most applicable when the reaction mechanism is not influenced by extensive charge delocalization in the transition state.

Sigma Plus Constants (?+)

Sigma plus constants (??) are modified substituent constants specifically designed for reactions where positive charge is developing or is present in the transition state or intermediate. They place greater emphasis on resonance donation effects of substituents, and are more relevant when substituents can stabilize a positive charge through resonance, such as in electrophilic aromatic substitutions or in the formation of cationic intermediates.

Sigma Minus Constants (??)

Sigma minus constants (??) are adjusted substituent constants used in reactions where a negative charge is being developed or stabilized in the transition state or intermediate. These constants emphasize the resonance withdrawing abilities of substituents and are particularly useful in reactions such as nucleophilic substitutions or deprotonation events where the stabilization of a negative charge is important.

Correlation Analysis in Linear Free Energy Relationships

Correlation analysis in the context of linear free energy relationships involves plotting reaction parameters, such as pK? values or reaction rates, against substituent constants (?, ??, ??) to assess which electronic effects dominate the reaction mechanism. This analysis helps determine whether the mechanism involves significant charge development that aligns more closely with standard, positive, or negative sigma parameters, thus guiding the selection of the most appropriate Hammett parameter for predicting reactivity trends.

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