Question

Consider the following two reactions and their corresponding Hammett plots

• A. s $\rightarrow$ \( \sigma_X \)(X=Cl); t $\rightarrow$ \( \sigma_X \)(X=OMe); u $\rightarrow$ \( \sigma_X \)(X=NH\( _2 \)); r $\rightarrow$ \( \sigma_X \)(X=NO\( _2 \))
• B. s $\rightarrow$ \( \sigma_X \)(X=Me); u $\rightarrow$ \( \sigma_X \)(X=NH\( _2 \)); t $\rightarrow$ \( \sigma_X \)(X=OMe); r $\rightarrow$ \( \sigma_X \)(X=Br)
• C. p $\rightarrow$ \( \sigma_X \)(X=Me); q $\rightarrow$ \( \sigma_X \)(X=CN); r $\rightarrow$ \( \sigma_X \)(X=NO\( _2 \)); t $\rightarrow$ \( \sigma_X \)(X=OMe)
• D. p $\rightarrow$ \( \sigma_X \)(X=Cl); q $\rightarrow$ \( \sigma_X \)(X=NO\( _2 \)); r $\rightarrow$ \( \sigma_X \)(X=CN); t $\rightarrow$ \( \sigma_X \)(X=Me)

Hint:

The Hammett plot shows the relationship between the logarithm of the rate constant (or equilibrium constant) for a reaction involving substituted benzene rings and the substituent constant \( \sigma \). The slope of the plot (\( \rho \)) indicates the sensitivity of the reaction to electronic effects. The sign of \( \rho \) reveals whether the reaction is favored by electron-withdrawing (\( \rho>0 \)) or electron-donating (\( \rho<0 \)) groups.

Answer 1

The Correct Option is A, C

Reaction M is an S_N1 reaction where the rate-determining step involves the formation of a carbocation. Electron-donating groups (EDGs) stabilize the carbocation and increase the reaction rate (negative σ values lead to positive log(k_X/k_H)), while electron-withdrawing groups (EWGs) destabilize the carbocation and decrease the reaction rate (positive σ values lead to negative log(k_X/k_H)). The Hammett plot for Reaction M shows a negative slope (ρ < 0), consistent with carbocation formation.

Reaction N is the hydrolysis of an ester, likely proceeding through a mechanism where EWGs facilitate the attack of water (positive σ → positive log(k_X/k_H)) and EDGs hinder it (negative σ → negative log(k_X/k_H)). The Hammett plot for Reaction N shows a positive slope (ρ > 0), consistent with this mechanism.

σ_X values for substituents:

• NH₂: strong EDG, σ_p ≈ −0.66
• NO₂: strong EWG, σ_p ≈ +0.78
• OMe: EDG, σ_p ≈ −0.27
• Cl: weak EWG (inductive), weak EDG (resonance), σ_p ≈ +0.23
• Me: weak EDG, σ_p ≈ −0.17
• CN: strong EWG, σ_p ≈ +0.66

Analysis of Hammett Plots:

Reaction M (ρ < 0):

• Positive log(k_X/k_H) → EDGs (σ negative): e.g., NH₂, Me, OMe
• Negative log(k_X/k_H) → EWGs (σ positive): e.g., NO₂, CN, Cl

Reaction N (ρ > 0):

• Positive log(k_X/k_H) → EWGs (σ positive)
• Negative log(k_X/k_H) → EDGs (σ negative)

Option A:

• s = Cl → σ ≈ +0.23: Consistent (positive log in N, negative in M)
• t = OMe → σ ≈ −0.27: Consistent (negative log in N, positive in M)
• u = NH₂ → σ ≈ −0.66: Most negative log in N, most positive in M → Consistent
• r = NO₂ → σ ≈ +0.78: Most positive in N, most negative in M → Consistent

Option C:

• p = Me → σ ≈ −0.17: Slightly negative log in N, slightly positive in M → Consistent
• q = CN → σ ≈ +0.66: Positive log in N, negative in M → Consistent
• r = NO₂ → σ ≈ +0.78: Consistent (most extreme EWG)
• t = OMe → σ ≈ −0.27: EDG pattern consistent → negative in N, positive in M

✅ Both options (A) and (C) align with expected trends in both Reaction M and N Hammett plots.
❌ Options (B) and (D) contradict expected behavior and are inconsistent.