Write a balanced chemical equation for each of the following reactions and also classify them.
$(a)$ Lead acetate solution is treated with dilute hydrochloric acid to form lead chloride and acetic acid solution.
$(b)$ $A$ piece of sodium metal is added to absolute ethanol to form sodium ethoxide and hydrogen gas.

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(N/A) $Pb(CH_3COO)_2(aq) + 2HCl(aq) \longrightarrow PbCl_2(s) + 2CH_3COOH(aq)$ : Double displacement reaction.
$(b)$ $2Na(s) + 2C_2H_5OH(l) \longrightarrow 2C_2H_5ONa(alc) + H_2(g)$ : Displacement reaction (specifically,a single displacement or redox reaction).

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