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 $34\mathrm{.}0mL$ of dioxygen gas are produced by this reaction, at a temperature of $110\mathrm{.}0C$ and pressure of exactly $1$atm. Calculate the mass of mercury$($II$)$ oxide that must have reacted. Round your answer to $3$ significant digits.

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