Account for the indicated order of base strength among the compounds shown. \(\mathrm{CH}_{3} \mathrm{NH}_{2}>\mathrm{NH}_{3}>\mathrm{NF}_{3}\)

When discussing base strength in organic chemistry, it's crucial to have a good grasp of conjugate acids. A conjugate acid forms when a base gains a proton (\r\(H^+\)). This protonation reflects the ability of a base to bind to a proton, and it's an essential concept in acid-base reactions. For instance, the transformation of \r\(CH_{3}NH_{2}\) to \r\(CH_{3}NH_3^+\) demonstrates how a simple organic base forms its conjugate acid by accepting a proton.

\rThe strength of a conjugate acid is important because it reveals information about the parent base. A stronger conjugate acid typically arises from a weaker base, and vice versa. Understanding this relationship helps us predict the outcome of chemical reactions and the acidity or basicity of a substance in different environments.

The electronic effects of substituents dramatically influence the stability of conjugate acids, and thus, the strength of the base. Atoms or groups attached to the base molecule can either donate electron density through inductive effects or withdraw electron density from the base, affecting its ability to share or accept a proton.

\rFor example, the methyl group (\r\(CH_3\)) in \r\(CH_{3}NH_{3}^+\) donates electron density to the nitrogen, stabilizing the conjugate acid and indicating that its corresponding base, \r\(CH_{3}NH_{2}\), is strong. On the other hand, when electronegative atoms like fluorine are present, as in \r\(NF_{3}H^+\), they withdraw electron density, destabilize the conjugate acid, and signify a weaker base. Recognizing inductive and resonance effects lets us predict and rationalize the strengths of different bases.

The stabilization of conjugate acids directly correlates to base strength. A stable conjugate acid means the original base is less likely to attract a proton, thus making it a weaker base. Conversely, if the conjugate acid is less stable, the original base will have a higher tendency to accept a proton, indicating a stronger base.

\rBy analyzing the substituents' effects on the conjugate acids, we can draw conclusions about base strengths. The electron-donating methyl group in \r\(CH_{3}NH_{3}^+\) makes it a more stable conjugate acid, hinting at a less potent base in \r\(CH_{3}NH_{2}\). Without any strongly electron-withdrawing or donating groups, \r\(NH_{4}^+\) shows medium stability, and its parent base \r\(NH_{3}\) has medium strength. Meanwhile, \r\(NF_{3}H^+\) is an unstable conjugate acid due to fluorine's strong electron-withdrawing effects, suggesting \r\(NF_{3}\) is the strongest base among the three analyzed.