If $1.6\,\text{g}$ of $\text{SO}_2$ and $1.5 \times 10^{22}$ molecules of $\text{H}_2\text{S}$ are mixed and allowed to remain in contact in a closed vessel until the reaction $2\text{H}_2\text{S} + \text{SO}_2 \rightarrow 3\text{S} + 2\text{H}_2\text{O}$ proceeds to completion, which of the following statements is true?