Sulfur trioxide, SO 3 , is produced in enormous quantities...

Sulfur trioxide, SO $_{3}$ , is produced in enormous quantities each year for use in the synthesis of sulfuric acid. $$\begin{aligned} \mathrm{S}(s)+\mathrm{O}_{2}(g) & \rightarrow \mathrm{SO}_{2}(g) \\ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) & \rightarrow 2 \mathrm{SO}_{3}(g) \end{aligned}$$ What volume of $\mathrm{O}_{2}(g)$ at $350 .^{\circ} \mathrm{C}$ and a pressure of 5.25 atm is needed to completely convert 5.00 $\mathrm{g}$ of sulfur to sulfur trioxide?

Sulfur trioxide, SO $_{3}$ , is produced in enormous quantities each year for use in the synthesis of sulfuric acid.
$$\begin{aligned} \mathrm{S}(s)+\mathrm{O}_{2}(g) & \rightarrow \mathrm{SO}_{2}(g) \\ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) & \rightarrow 2 \mathrm{SO}_{3}(g) \end{aligned}$$
What volume of $\mathrm{O}_{2}(g)$ at $350 .^{\circ} \mathrm{C}$ and a pressure of 5.25 atm is needed to completely convert 5.00 $\mathrm{g}$ of sulfur to sulfur trioxide?

Key Concepts

Stoichiometry

Stoichiometry involves using the balanced chemical equations to determine the quantitative relationships between reactants and products. In the context of this problem, it provides the ratios between sulfur, oxygen, and sulfur trioxide, enabling one to calculate how many moles of oxygen are required for the given amount of sulfur by following the stepwise reactions involved.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. It is used to convert the mass of a substance into moles, which is a crucial step in linking the macroscopic amount of material (in grams) to the microscopic number of molecules involved in a chemical reaction.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure, volume, temperature, and amount (in moles) of a gas. This law is fundamental for calculating the volume that a specific number of moles of gas will occupy under given conditions of pressure and temperature, making it essential for translating the stoichiometric mole calculations into a volumetric measure.

Temperature Conversion

Temperature conversion, particularly converting degrees Celsius to Kelvin, is necessary when using the Ideal Gas Law since the law requires the absolute temperature in Kelvin. This step ensures that temperature is appropriately incorporated into the calculations for gas behavior under the specified conditions.

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