Rank the conjugate bases of each group of acids in order of increasing basicity:

a.${\mathbf{NH}}_{\mathbf{3}}\mathbf{,}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{,}{\mathbf{CH}}_{\mathbf{4}}$

b.${\mathbf{CH}}_{\mathbf{2}}\mathbf{=}{\mathbf{CH}}_{\mathbf{2}}\mathbf{,}\mathbf{HC}\mathbf{\equiv }\mathbf{CH}\mathbf{,}{\mathbf{CH}}_{\mathbf{4}}$

The bases that can receive a proton are referred to as conjugate bases. Weak acids have a strong conjugate base and vice-versa.

A substance that can contribute its electron pair is called a base. The addition of a base to acid makes the solution neutral.

The ${\mathrm{pK}}_{\mathrm{a}}$values of ammonia, water, and methane are 38, 15.7, and 50, respectively.

The ${\mathrm{pK}}_{\mathrm{a}}$value of methane is the highest among all the given compounds. Hence, the acidity order becomes ${\mathrm{H}}_2\mathrm{O}>{\mathrm{NH}}_3>{\mathrm{CH}}_4$.

A conjugate base is created when a proton is removed from the acid. The conjugate base of ammonia is ${\mathrm{NH}}_2^{-}$, of water is ${\mathrm{OH}}^{-}$, and that of methane is ${\mathrm{CH}}_3^{-}$. The conjugate bases of weak acids are strong.

The conjugate base of methane is strong. The increasing order of basicity is

${\mathrm{OH}}^{-}<{\mathrm{NH}}_2^{-}<{\mathrm{CH}}_3^{-}$

The ${\mathrm{pK}}_{\mathrm{a}}$values for methane, ethene, and ethyne are 50, 44, and 25, respectively.

The hybridization of methane, ethene, and ethyne are ${\mathrm{sp}}^3$,${\mathrm{sp}}^2$and sp, respectively. The order of s character is

$\mathrm{ethyne}>\mathrm{ethene}>\mathrm{methane}$.

The order of acidity is

$\mathrm{ethyne}>\mathrm{ethene}>\mathrm{methane}$

The conjugate base is formed when a proton is removed from the acid.

The conjugate base of ethyne is $\mathrm{HC}\equiv {\mathrm{C}}^{-}$.

The conjugate base of ethene is ${\mathrm{CH}}_2={\mathrm{CH}}^{-}$.

The conjugate base of methane is ${\mathrm{CH}}_3^{-}$ion. Strong acids form weak conjugate bases. Hence, the basicity of conjugate bases increases with an increase in their ${\mathrm{pK}}_{\mathrm{a}}$value.

The order of basicity is

$\mathrm{ethyne}<\mathrm{ethene}<\mathrm{methane}$