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

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Correct option is C

​In organic chemistry, the Hammett equation describes a linear free-energy relationship relating 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.

$$\text{The basic equation is:} \\\log \left( \frac{K}{K_0} \right) = \sigma \rho$$

​$${\displaystyle {K}_{0}}$$​ = Reference constant
$${\displaystyle \sigma }$$​ = Substituent constant
$${\displaystyle \rho }$$​= Reaction rate constant

relating the equilibrium constant, K, for a given equilibrium reaction with substituent R and the reference constant K₀ when R is a hydrogen atom to the substituent constant which depends only on the specific substituent R and the reaction rate constant which depends only on the type of reaction but not on the substituent used.

The Hammett reaction constant ρ  measures the sensitivity of the reaction to electronic effects. A positive ρ value means more electrons in the transition state than in the starting material. A negative ρ value means fewer electrons in the transition state than in the starting material.

If we simply move the carboxylic acid away from the ring, the ρ value for ionization gets less. This is just the effect of a more distant substituent. When there are two saturated carbons between the benzene ring and the carboxylic acid, there is almost no effect. When we are using the aromatic ring as a probe for a reaction mechanism, it must be placed not too far away from the reaction centre. However, if we restore electronic communications with a double bond, ρ goes back up again to a useful value.

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