Carbon disulfide gas and oxygen gas react to form sulfur dioxide gas and carbon dioxide gas. What volume of carbon dioxide would be produced by this reaction if \( 6.74 \mathrm{~m}^{3} \) of carbon disulfide were consumed? Also, be sure your answer has a unit symbol, and is rounded to 3 significant digits.

To find the volume of carbon dioxide produced by the reaction, we need to use the balanced chemical equation for the reaction between carbon disulfide (\(CS_2\)) and oxygen (\(O_2\)) to form sulfur dioxide (\(SO_2\)) and carbon dioxide (\(CO_2\)). The balanced chemical equation for the reaction is: \[ CS_2(g) + 3O_2(g) \rightarrow CO_2(g) + 2SO_2(g) \] From the balanced equation, we can see that 1 mole of carbon disulfide reacts to produce 1 mole of carbon dioxide. Given that \(6.74 \, \text{m}^3\) of carbon disulfide is consumed, we can calculate the volume of carbon dioxide produced using the stoichiometry of the reaction. First, we need to convert the volume of carbon disulfide to moles using the molar volume of an ideal gas at standard temperature and pressure (STP), which is \(22.4 \, \text{L/mol}\). \[ \text{Moles of } CS_2 = \frac{6.74 \, \text{m}^3}{22.4 \, \text{L/mol}} \] Next, since 1 mole of carbon disulfide produces 1 mole of carbon dioxide, the moles of carbon dioxide produced will be the same as the moles of carbon disulfide consumed. Finally, we can convert the moles of carbon dioxide to volume using the molar volume of an ideal gas at STP. Let's calculate the volume of carbon dioxide produced. Calculate the value by following steps: - step0: Calculate: \(\frac{6.74}{22.4}\) - step1: Convert the expressions: \(\frac{\frac{337}{50}}{\frac{112}{5}}\) - step2: Multiply by the reciprocal: \(\frac{337}{50}\times \frac{5}{112}\) - step3: Reduce the numbers: \(\frac{337}{10}\times \frac{1}{112}\) - step4: Multiply the fractions: \(\frac{337}{10\times 112}\) - step5: Multiply: \(\frac{337}{1120}\) The moles of carbon disulfide consumed is approximately \(0.3009\) moles. Since 1 mole of carbon disulfide produces 1 mole of carbon dioxide, the moles of carbon dioxide produced will also be approximately \(0.3009\) moles. Now, we can convert the moles of carbon dioxide to volume using the molar volume of an ideal gas at STP, which is \(22.4 \, \text{L/mol}\). \[ \text{Volume of } CO_2 = 0.3009 \, \text{mol} \times 22.4 \, \text{L/mol} \] Let's calculate the volume of carbon dioxide produced. Calculate the value by following steps: - step0: Calculate: \(0.3009\times 22.4\) - step1: Multiply the numbers: \(6.74016\) The volume of carbon dioxide produced by the reaction is approximately \(6.740\) cubic meters. Therefore, the volume of carbon dioxide produced by the reaction when \(6.74 \, \text{m}^3\) of carbon disulfide is consumed is \(6.740 \, \text{m}^3\), rounded to 3 significant digits.