The rate constants for nucleophilic addition to para-substituted benzaldehydes p-X-C6H4-CHO obey log_10(k/k_0) = rho sigma_p with rho = +1.8. Given sigma_p = +0.78 for NO2 and -0.83 for N(CH3)2, the ratio k(NO2)/k(N(CH3)2) is about

JEE Advanced levelSingle correct optionDifficulty 3 of 3o1040

The rate constants for nucleophilic addition to para-substituted benzaldehydes $p - X - C X_{6} H X_{4} - CHO$ obey $lo g_{10} (k / k_{0}) = ρ σ_{p}$ with $ρ = + 1.8$ . Given $σ_{p}$ = +0.78 for $NO X_{2}$ and -0.83 for $N (CH X_{3}) X_{2}$ , the ratio $k (NO X_{2}) / k (N (CH X_{3}) X_{2})$ is about

The ratio is

lo g_{10} (k_{1} / k_{2}) = ρ (σ_{1} - σ_{2}) = 1.8 \times (0.78 + 0.83) = 2.898

, so

k_{1} / k_{2} = 1 0^{2.898} \approx 791

. Using only one of the two sigma values gives 25 or 31, and inverting the sign (a donor-accelerated reaction) would give 0.0013. Positive

ρ

means electron-withdrawing groups speed up the addition.