State the $E^o$ values of lanthanoids and provide their reactions with the following: $(i)$ $H_2$,$(ii)$ Carbon,$(iii)$ Dilute acid,$(iv)$ Halogens,$(v)$ $O_2$,and $(vi)$ $H_2O$.

(A) Similarity of lanthanoids with $Ca$ and $Al$: Generally,the early members of the lanthanoid series are highly reactive,similar to calcium,but as the atomic number increases,they behave more like aluminum.
Electrode potential of lanthanoids:
Half-reaction: $Ln^{3+}_{(aq)} + 3e^- \rightarrow Ln_{(s)}$
The $E^o_{Ln^{3+}/Ln}$ values range from $-2.2 \ V$ to $-2.24 \ V$,except for $Eu$,where $E^o_{Eu^{3+}/Eu} = -2.0 \ V$.
Chemical reactions of lanthanoids:
$(i)$ When lanthanoids are heated with hydrogen gas,they form hydrides: $2Ln + 3H_2 \rightarrow 2LnH_3$.
$(ii)$ Heating lanthanoids with carbon forms carbides: $Ln + C \xrightarrow{2773 \ K} Ln_3C, Ln_2C_3, LnC_2$.
$(iii)$ Lanthanoids react with dilute acids to liberate hydrogen gas: $2Ln_{(s)} + 6H^+_{(aq)} \rightarrow 2Ln^{3+}_{(aq)} + 3H_{2(g)}$.
$(iv)$ They burn in halogens $(X_2)$ to form halides: $2Ln + 3X_2 \rightarrow 2LnX_3$.
$(v)$ They burn in $O_2$ to form oxides: $4Ln + 3O_2 \rightarrow 2Ln_2O_3$.
$(vi)$ They react with water to form hydroxides: $2Ln + 6H_2O \rightarrow 2Ln(OH)_3 + 3H_2$.