Determine the limiting reactant. \[ \mathrm{CS}_{2}(g)+3 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{SO}_{2}(g) \] Express your answer as a chemical formula.

We cannot determine the limiting reactant without knowing the initial amounts (in moles, mass, etc.) of the reactants. To decide which reagent is limiting, you must compare the available mole ratio of the reactants to the mole ratio required by the balanced equation. The balanced equation is \[ \mathrm{CS}_2 + 3\,\mathrm{O}_2 \rightarrow \mathrm{CO}_2 + 2\,\mathrm{SO}_2. \] This tells us that 1 mole of \(\mathrm{CS}_2\) reacts with 3 moles of \(\mathrm{O}_2\). If you are given amounts of each reagent, you would follow these steps: 1. Convert the given amounts into moles (if they aren’t already). 2. Determine how many moles of \(\mathrm{O}_2\) are needed to completely react with the moles of \(\mathrm{CS}_2\) present. For example, if you have \( n \) moles of \(\mathrm{CS}_2\), then you need \( 3n \) moles of \(\mathrm{O}_2\). 3. Compare the calculated required moles of \(\mathrm{O}_2\) with the available moles of \(\mathrm{O}_2\). - If the available moles of \(\mathrm{O}_2\) is less than \( 3n \), then \(\mathrm{O}_2\) is the limiting reactant. - Otherwise, if there is more than enough \(\mathrm{O}_2\), then \(\mathrm{CS}_2\) limits the reaction. Without the specific initial amounts, the limiting reactant cannot be identified as either \(\mathrm{CS}_2\) or \(\mathrm{O}_2\).