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How would you compare the acidities of these two compounds?

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The deprotonation is obviously alpha to the carbonyl/amine. I think that the diphenyl substituent will be more electron withdrawing than the di methyl, just because the lone pair of nitrogen will have conjugation with the benzene rings, vs methyl groups electron donating onto N.

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Yeah, you're thinking in the right way! In the first structure, the hydrogen atom will not have a tendency to leave since the negative charge on the corresponding conjugate base is destabilized due to lone pair of nitrogen atom(the N atom intensifies the negative charge on the carbanion formed by donating its electrons in the p orbital of carbanion). Whereas in the second structure the lone pair of N atom is already dispersed in the two phenyl rings so the lone pairs have very less tendency of going into the p orbital of carbanion. Therefore, the second structure is more acidic since its conjugate base is more stable( or less destabilized) than the first structure

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