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The ideal gas law is a fundamental equation that relates the pressure, volume, amount, and temperature of a gas. It is written as \(PV = nRT\), where:

• \(P\) is the pressure of the gas
• \(V\) is the volume of the gas
• \(n\) is the number of moles of the gas
• \(R\) is the ideal gas constant, which is approximately 0.0821 L·atm/mol·K
• \(T\) is the temperature in Kelvin

To find the volume of a gas, you can rearrange the equation to \(V = \frac{nRT}{P}\). This relation allows you to calculate one parameter if the others are known. For instance, in this problem, knowing the pressure, temperature, and moles of \(O_2\), the volume was calculated to determine how much space the gas occupies under specified conditions.
Understanding the ideal gas law is essential when studying gases, as it helps predict how a gas will behave under different conditions of temperature and pressure.

Balancing a chemical equation is a key skill in chemistry that ensures the quantities of reactants and products are in proportion according to the law of conservation of mass. In the production of sulfur trioxide from sulfur, we observe two sequential reactions:- \(\text{S}(s) + \text{O}_2(g) \rightarrow \text{SO}_2(g)\)- \(2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g)\)In these reactions, each sulfur atom and oxygen molecule is accounted for in the products. Balancing chemical equations involves adjusting the coefficients in front of chemical formulas to obtain the same number of each type of atom on both sides of the equation. This practice is crucial, as it allows chemists to determine the exact stoichiometries for reactants and products and ensures that calculations related to the amounts of substances involved are accurate.

Molar mass is an important concept when converting between the mass of a substance and the amount in moles. It is the mass of one mole of a chemical element or compound. For sulfur, the molar mass is approximately 32.06 g/mol.

• To calculate the number of moles: \(\text{Number of moles} = \frac{\text{Mass of element}}{\text{Molar mass}}\).
• Here, the calculation becomes \( \frac{5.00 \text{ g}}{32.06 \text{ g/mol}} = 0.1559 \text{ mol}\).

This conversion is critical for chemical problem-solving, as it links the macroscopic property (mass) to a microscopic property (moles), allowing precise calculations of reaction requirements and product yields.

Gas volume calculation involves determining how much space a gaseous substance occupies under given conditions of temperature and pressure, often using the ideal gas law. After finding the required number of moles of \(O_2\) (0.3118 mol) needed to react with sulfur, we used the conditions provided:

• Pressure (\(P\)) = 5.25 atm
• Temperature (\(T\)) = 623.15 K (converted from 350°C)
• Gas constant (\(R\)) = 0.0821 L·atm/mol·K

The volume \(V\) is obtained from the rearranged ideal gas law: \(V = \frac{nRT}{P}\).
This approach provides the theoretical framework to predict how gases will respond to changes in conditions, ensuring accuracy in fields ranging from chemistry to meteorology. In this problem, it showed that 3.09 liters of oxygen gas are needed for the full conversion process.