One-pot synthesis of some 1N-acetyl pyrazoles including 1-(3-(3,4-dimethylphenyl)-5-(substituted phenyl)-4,5-dihydro-1H-pyrazole-1-yl) ethanones has been achieved via solvent-free microwave irradiation using substituted chalcones, hydrazine hydrate and acetic anhydride in the presence of catalytic amount of fly-ash: PTS catalyst. The yield of these 1N-acetyl pyrazole derivatives is more than 75%. The synthesized 1N-acetyl pyrazoline derivatives were characterized by their physical constants and spectral data. The infrared spectral νCN and CO (cm−1) frequencies, NMR chemical shifts (δ, ppm) of Ha, Hb, Hc, CH3 protons, CN, CO and CH3 carbons of 1-(3-(3,4-dimethylphenyl)-5-(substituted phenyl)-4,5-dihydro-1H-pyrazole-1-yl) ethanones have been assigned and correlated with Hammett substituent constants and Swain-Lupton’s parameters using single and multi-regression analysis. From the results of statistical analyses, the effect of substituents on the above group frequencies and chemical shifts of the acetylated pyrazoles were discussed.