The great French chemist Antoine Lavoisier discovered the Law of Conservation of Mass in part by doing a famous experiment in $1775.$ In this experiment Lavoisier found that mercury$($II$)$ oxide, when heated, decomposed into liquid mercury and an invisible and previously unknown substance: oxygen gas.

Write a balanced chemical equation, including physical state symbols, for the decomposition of solid mercury$($II$)$ oxide $(HgO)$ into liquid mercury and gaseous dioxygen.

Suppose $58\mathrm{.}0mL$ of dioxygen gas are produced by this reaction, at a temperature of $100\mathrm{.}0C$ and pressure of exactly $1$atm. Calculate the mass of mercury$($II$)$ oxide. that must have reacted. Be sure your answer has the correct number of significant digits.

$g$