Amines in gas phase or in non-aqueous solvents , there is no solvation effect(getting influenced by the solvent).It means that the stabilization of conjugate acid formed due to the formation of hydrogen bonding are absent.

Hence, the basic strength of amines depends only on the +I effect of the alkyl groups. Alkyl groups are electron releasing groups, they release electron to the nitrogen in amine and increase the overall electron density of electrons and thus is easily available to donate electron. This property makes it more basic. As s result, more alkyl groups are attached, the higher the +I effect. Hence, the higher the +I effect, stronger is the base(high tendency to accept electrons)

In (C₂H₅)₃N, 3 alkyl groups are present, hence it is more basic. In (C₂H₅)₂NH, 2 alkyl groups are present, hence it is less basic than (C₂H₅)₃N. In C₂H₅NH_2, only one alkyl group is present, hence it is less basic than (C₂H₅)₃N and (C₂H₅)₂NH. In NH₃, no alkyl group is present, so there is no +I effect. Hence it is less basic among all the amines.

Combining all these facts, the relative basic strength of these four amines decreases in the order:

(C₂H₅)₃N > (C₂H₅)₂NH > C₂H₅NH₂ > NH₃