Which is the stronger base: solid sodium hydroxide or solid sodium hydride (NaH)?
NaOH is a strong base and NaH is an uncommon compound so could be strong or weak. The context of the question suggests that NaH is also a strong base.
Use thermodynamic data to find ΔG° for each acid/base reaction. The more negative ΔG° is the stronger base.
NaOH:
NaOH(s) → Na+(aq) + OH–(aq)
ΔGf°(NaOH(s)) = –379.5 kJ/mol
ΔGf°(Na+(aq)) = –261.9 kJ/mol
ΔGf°(OH–(aq)) = –157.2 kJ/mol
ΔG° = [–261.9 + (–157.2)] – [–379.5] = –39.6 kJ/mol
NaH:
NaH(s) + H2O(l) → H2(g) + Na+(aq) + OH–(aq)
ΔGf°(NaH(s)) = –33.5 kJ/mol
ΔGf°(H2O(l)) = –237.2 kJ/mol
ΔGf°(H2(g)) = 0 kJ/mol
ΔGf°(Na+(aq)) = –261.9 kJ/mol
ΔGf°(OH–(aq)) = –157.2 kJ/mol
ΔG° = [(0) + (–261.9) + (–157.2)] – [(–33.5) + (–237.2)] = –148.4 kJ/mol
Thus, per mole of base, ΔG° (NaOH) = –39.6 kJ/mol and ΔG° (NaH) = –148.4 kJ/mol
NaH is a much stronger base.