If sodium metal is dropped into a beaker of aqueous hydrochloric acid, a reaction will occur in which hydrogen gas is produced.

a$)$ Write a balanced equation for this reaction.

b$)$ If $14\mathrm{.}74g$ of sodium metal was added to an excess of aqueous hydrogen chloride in a beaker, calculate the resulting work. The room temperature and external pressure are constant at $22\mathrm{.}65C$ and $101\mathrm{.}8$kPa, respectively.

$W=-P_{\text{e}\text{x}\text{t}}+V$