Question:

Arrange NH$_3$, C$_2$H$_5$NH$_2$, (C$_2$H$_5$)$_2$NH and (C$_2$H$_5$)$_3$N in the increasing order of their basic strength.

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In water: 2°>1°>3°>NH$_3$ (solvation matters). In gas phase, simple +I effect often gives 3°>2°>1°.
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Solution and Explanation

Step 1: Principle.
In aqueous solution, basicity of amines depends on the electron-releasing (+I) effect of alkyl groups \emph{and} solvation. General order:
\[ \text{secondary}>\text{primary}>\text{tertiary}>\text{ammonia} \] because secondary amines have strong +I effect and still good solvation; tertiary amines suffer from steric hindrance and poorer solvation.
Step 2: Apply to given amines.
Least basic $\to$ most basic: \[ \boxed{ \mathrm{NH_3 \;<\; (C_2H_5)_3N \;<\; C_2H_5NH_2 \;<\; (C_2H_5)_2NH } } \] Step 3: Check.
This follows the aqueous-phase basicity trend: 2°>1°>3°>NH$_3$.
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