The question asks for the correct increasing order of basic strength of the given amines. The basic strength of an amine depends on the availability of the lone pair of electrons on the nitrogen atom for donation to a proton (H⁺). The easier it is for the nitrogen to donate its lone pair, the stronger the base.

Factors Affecting Amine Basic Strength

Several factors influence the availability of the lone pair on the nitrogen atom:

• Electron-Donating Groups: Groups that push electron density towards the nitrogen atom increase the electron density on nitrogen, making the lone pair more available and increasing basicity. Alkyl groups (like ethyl, C₂H₅) are common electron-donating groups via the inductive effect (+I effect).
• Electron-Withdrawing Groups: Groups that pull electron density away from the nitrogen atom decrease the electron density on nitrogen, making the lone pair less available and decreasing basicity. Phenyl groups (C₆H₅) are electron-withdrawing, especially via resonance (mesomeric effect) when directly attached to the nitrogen.
• Resonance: If the lone pair on nitrogen can participate in resonance with an adjacent group (like in aniline), it is delocalized and less available for protonation, significantly decreasing basicity.
• Solvation Effects: In aqueous solution, the basic strength is also affected by the stability of the protonated amine (conjugate acid) due to solvation by water molecules. Greater solvation releases more energy, stabilizing the conjugate acid and thus favoring protonation (increasing basicity). Solvation is hindered by steric bulk around the positively charged nitrogen.

Analyzing the Given Amines and Their Basic Strength

Let's analyze each amine provided: C₆H₅NH₂, NH₃, C₆H₅CH₂NH₂, C₂H₅NH₂, and (C₂H₅)₂NH.

1. C₆H₅NH₂ (Aniline): The phenyl group is directly attached to the nitrogen. The lone pair on the nitrogen is delocalized into the benzene ring through resonance. This delocalization makes the lone pair much less available for protonation. Therefore, aniline is a very weak base compared to ammonia and alkyl amines.

   \(\text{C}_6\text{H}_5\text{NH}_2\)

2. NH₃ (Ammonia): Ammonia serves as a reference point. The lone pair on nitrogen is not involved in resonance and is attached to hydrogen atoms.

   \(\text{NH}_3\)

3. C₆H₅CH₂NH₂ (Benzylamine): Here, the phenyl group is attached to a \(\text{CH}_2\) group, which is then attached to the \(\text{NH}_2\) group. The phenyl group's electron-withdrawing effect is primarily inductive and is weakened by the intervening \(\text{CH}_2\) group. The lone pair on the nitrogen is not directly delocalized into the benzene ring. The \(\text{CH}_2\) group is slightly electron-donating. Benzylamine is generally a stronger base than aniline and slightly stronger than ammonia.

   \(\text{C}_6\text{H}_5\text{CH}_2\text{NH}_2\)

4. C₂H₅NH₂ (Ethylamine - 1° amine): The ethyl group (\(\text{C}_2\text{H}_5\)) is an electron-donating group (+I effect). It increases the electron density on the nitrogen atom, making the lone pair more available. This makes ethylamine a stronger base than ammonia.

   \(\text{C}_2\text{H}_5\text{NH}_2\)

5. (C₂H₅)₂NH (Diethylamine - 2° amine): There are two ethyl groups attached to the nitrogen. The combined +I effect of two ethyl groups further increases the electron density on the nitrogen compared to ethylamine. In aqueous solution, 2° amines are typically stronger bases than 1° amines and 3° amines due to a balance between the positive inductive effect and the solvation of the protonated amine. Diethylamine is expected to be the strongest base among the simple alkyl amines listed.

   \((\text{C}_2\text{H}_5)_2\text{NH}\)

Determining the Increasing Order

Based on the analysis:

• Aniline (\(\text{C}_6\text{H}_5\text{NH}_2\)) is the weakest base due to resonance delocalization of the lone pair.
• Ammonia (\(\text{NH}_3\)) is a moderate base.
• Benzylamine (\(\text{C}_6\text{H}_2\text{CH}_2\text{NH}_2\)) is slightly stronger than ammonia as the lone pair is not delocalized, and the phenyl ring's inductive effect is attenuated.
• Ethylamine (\(\text{C}_2\text{H}_5\text{NH}_2\)) is stronger than ammonia and benzylamine due to the electron-donating ethyl group.
• Diethylamine (\((\text{C}_2\text{H}_5)_2\text{NH}\)) is the strongest base among these due to the presence of two electron-donating ethyl groups and favourable solvation (compared to hypothetical triethylamine which would be more sterically hindered).

So, the increasing order of basic strength is:

\(\text{C}_6\text{H}_5\text{NH}_2 < \text{NH}_3 < \text{C}_6\text{H}_5\text{CH}_2\text{NH}_2 < \text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH}\)

Comparing this order with the given options:

• Option (A): \(\text{C}_6\text{H}_5\text{NH}_2 < \text{NH}_3 < \text{C}_6\text{H}_5\text{CH}_2\text{NH}_2 < \text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH}\) - Matches our derived order.
• Option (B): \(\text{NH}_3 < \text{C}_6\text{H}_5\text{NH}_2 < \text{C}_6\text{H}_5\text{CH}_2\text{NH}_2 < \text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH}\) - Incorrect, Aniline is less basic than Ammonia.
• Option (C): \(\text{C}_6\text{H}_5\text{CH}_2\text{NH}_2 < \text{C}_6\text{H}_5\text{NH}_2 < \text{NH}_3 < \text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH}\) - Incorrect, Benzylamine and Ammonia are more basic than Aniline.
• Option (D): \(\text{C}_2\text{H}_5\text{NH}_2 < (\text{C}_2\text{H}_5)_2\text{NH} < \text{C}_6\text{H}_5\text{NH}_2 < \text{NH}_3\) - Incorrect, Aniline and Ammonia are less basic than alkyl amines.

Therefore, option (A) represents the correct increasing order of basic strength.

Revision Table: Amine Basic Strength Summary

Additional Information on Amine Basicity

Understanding the basic strength of amines is crucial in organic chemistry. The relative basicity of 1°, 2°, and 3° alkyl amines can vary depending on the solvent (gas phase vs. aqueous solution). In the gas phase, basicity is solely determined by the inductive effect, leading to 3° > 2° > 1° > NH₃. However, in aqueous solution, solvation of the conjugate acid (\(\text{R}_3\text{NH}^+\)) plays a significant role. Solvation stabilizes the charged species through hydrogen bonding with water molecules. As the number of alkyl groups increases, steric hindrance to solvation also increases. This explains why in aqueous solution, the order for ethyl amines is typically 2° > 1° > 3° > NH₃, or sometimes 2° > 3° > 1° > NH₃ depending on the alkyl group. For methyl amines, the order is usually 2° > 1° > 3° > NH₃. The question implies an aqueous solution context unless otherwise specified, making the 2° amine ((C₂H₅)₂NH) the strongest among the simple alkyl/ammonia options.

Aromatic amines like aniline are significantly weaker bases than aliphatic amines because the lone pair is involved in resonance with the aromatic ring. Any substituent on the aromatic ring can further affect the basicity. Electron-donating substituents on the ring (like \(-\text{OCH}_3\), \(-\text{CH}_3\)) increase basicity, while electron-withdrawing substituents (like \(-\text{NO}_2\), \(-\text{Cl}\)) decrease basicity.