Arrange the following:
$(i)$ In decreasing order of the $pK_{b}$ values:
$C_{2}H_{5}NH_{2}, C_{6}H_{5}NHCH_{3}, (C_{2}H_{5})_{2}NH$ and $C_{6}H_{5}NH_{2}$
$(ii)$ In increasing order of basic strength:
$C_{6}H_{5}NH_{2}, C_{6}H_{5}N(CH_{3})_{2}, (C_{2}H_{5})_{2}NH$ and $CH_{3}NH_{2}$
$(iii)$ In increasing order of basic strength:
$(a)$ Aniline,$p-$nitroaniline and $p-$toluidine
$(b)$ $C_{6}H_{5}NH_{2}, C_{6}H_{5}NHCH_{3}, C_{6}H_{5}CH_{2}NH_{2}$
$(iv)$ In decreasing order of basic strength in gas phase:
$C_{2}H_{5}NH_{2}, (C_{2}H_{5})_{2}NH, (C_{2}H_{5})_{3}N$ and $NH_{3}$
$(v)$ In increasing order of boiling point:
$C_{2}H_{5}OH, (CH_{3})_{2}NH, C_{2}H_{5}NH_{2}$
$(vi)$ In increasing order of solubility in water:
$C_{6}H_{5}NH_{2}, (C_{2}H_{5})_{2}NH, C_{2}H_{5}NH_{2}$

(N/A) $(i)$ The basic strength order is $C_{6}H_{5}NH_{2} < C_{6}H_{5}NHCH_{3} < C_{2}H_{5}NH_{2} < (C_{2}H_{5})_{2}NH$. Since $pK_{b} \propto 1/\text{basic strength}$,the decreasing order of $pK_{b}$ is: $C_{6}H_{5}NH_{2} > C_{6}H_{5}NHCH_{3} > C_{2}H_{5}NH_{2} > (C_{2}H_{5})_{2}NH$.
$(ii)$ Basic strength order: $C_{6}H_{5}NH_{2} < C_{6}H_{5}N(CH_{3})_{2} < CH_{3}NH_{2} < (C_{2}H_{5})_{2}NH$.
$(iii)$ $(a)$ $p-$Nitroaniline $ < $ Aniline $ < $ $p-$Toluidine. $(b)$ $C_{6}H_{5}NH_{2} < C_{6}H_{5}NHCH_{3} < C_{6}H_{5}CH_{2}NH_{2}$.
$(iv)$ In gas phase,basicity depends on $+I$ effect: $(C_{2}H_{5})_{3}N > (C_{2}H_{5})_{2}NH > C_{2}H_{5}NH_{2} > NH_{3}$.
$(v)$ Boiling point depends on $H$-bonding: $(CH_{3})_{2}NH < C_{2}H_{5}NH_{2} < C_{2}H_{5}OH$.
$(vi)$ Solubility depends on $H$-bonding and hydrophobic part: $C_{6}H_{5}NH_{2} < (C_{2}H_{5})_{2}NH < C_{2}H_{5}NH_{2}$.