When hydrogen sulfide, $\mathrm{H}_{2} \mathrm{~S}$, gas is bubbled through a solution of lead(II) nitrate, $\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$, a black precipitate of lead(II) sulfide, $\mathrm{PbS},$ forms, and nitric acid, $\mathrm{HNO}_{3},$ is produced. Write the unbalanced chemical equation for this reaction.