Gas evolved during the reaction of sodium metal on ethyl amine is

• The chemical formula of ethyl amine is ${\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}_2$ which is a primary amine. 
• Ethyl amine when treated with sodium metal forms ${\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}^{-}{\mathrm{Na}}^{+}$along with ${\mathrm{H}}^{+}$ion. Here sodium metal acts as a base and removes an acidic hydrogen from the ethyl amine thus forming ${\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}^{-}{\mathrm{Na}}^{+}$. The reaction equation is as follows,

${\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}_2+\mathrm{Na}\to {\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}^{-}{\mathrm{Na}}^{+}+1/2{\mathrm{H}}_2$

Hence, the gas evolved during this reaction is ${\mathrm{H}}_2$gas.

Therefore, option (C) is correct.