The correct order for the Hammett Reaction constant (ρ) for the deprotonation of the following Carboxylic acids is

Concept:

• The Hammett equation describes a linear free-energy relationship that relates the reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para-substituents to each other with just two parameters:

a substituent constant and a reaction constant.

• The basic equation is

\(\log {K \over {{K_o}}} = \sigma \rho \),

where K is the equilibrium constant,

K_o is the reference constant, 

\(\sigma \) is the substituent constant, and \(\rho \) is the reaction constant.

Explanation:

• The reaction constant ρ (sensitivity constant), describes the susceptibility of the reaction to substituents, compared to the ionization of benzoic acid.
• It is equivalent to the slope of the Hammett plot. Information on the reaction is obtained from the value obtained for ρ.
• Now, 

If \(\rho\; \rangle 1\), then the reaction is more sensitive to substituents than benzoic acid, and a positive charge is lost from the molecule.

If \(0\langle\;\rho\; \langle 1\), then the reaction is less sensitive to substituents than benzoic acid, and a positive charge is lost from the molecule.

If \(\rho = 0\), then the sensitivity of the substituents is zero and no charge is built or lost from the molecule.

If \(\rho \langle 1\), then a negative charge is lost from the molecule.

• By definition for the ionization of benzoic acid,

\(\rho = 1\).​

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The correct order for the Hammet Reaction constant (ρ) of the following Carboxylic acids is :

• In the case of Carboxylic acid B, the reaction center is separated by one saturated carbon. Therefore, the substituent has a lesser effect on the dissociation of the acid compared to Carboxylic acid A.
• Hence, the dissociation of Carboxylic acid B will be more faster compared to Carboxylic acid A.
• So,

​\(\rho_A>\rho_B\)

• Whereas in Carboxylic acid C, the reaction center is separated by two saturated carbons.
• Therefore, the substituent has the least effect on the dissociation of the acid compared to the other Carboxylic acids.
• Thus, the Hammett Reaction constant (ρ) is the least for Carboxylic acid C.

\(\rho_A>\rho_B>\rho_C\)

Conclusion:

Hence, the correct order for the Hammett Reaction constant (ρ) for the deprotonation of the following Carboxylic acids is A > B > C.