91Ó°ÊÓ

The Ideal Gas Law is a fundamental concept in chemistry that allows us to relate the pressure, volume, temperature, and number of moles of a gas. The law is represented by the equation \( PV = nRT \), where:

• \( P \) is the pressure of the gas,
• \( V \) is the volume of the gas,
• \( n \) is the number of moles,
• R is the ideal gas constant, and
• \( T \) is the temperature in Kelvin.

In this exercise, we use the Ideal Gas Law to find the amount of oxygen gas present in the enclosure. This is achieved by solving for \( n \), the number of moles of oxygen. First, we need to ensure all units are compatible. It's important to convert the temperature from Celsius to Kelvin by adding 273.15. Also, converting pressure from torr to atm is essential since the gas constant \( R \) is often given in atm.L/(mol.K). By plugging in the converted values into the equation, we can solve for \( n \), the moles of oxygen present. This paves the way for further calculations to determine the amount of magnesium needed for the reaction.

In chemical reactions, reactants transform into products through a process involving rearrangement of atoms. The accuracy of stoichiometric relationships in reaction equations is crucial for quantitative predictions about the amounts of substances consumed and produced. In this exercise's context, the balanced chemical reaction is:\[ 2 \text{Mg}(s) + \text{O}_2(g) \longrightarrow 2 \text{MgO}(s) \]This tells us that two moles of magnesium react with one mole of oxygen to form two moles of magnesium oxide. The stoichiometry of the reaction is essential because it dictates the proportion in which reactants combine and products form. By understanding the stoichiometric coefficients from the balanced equation, we can calculate how much magnesium is required if we know how much oxygen is available. This step involves direct application of the mole ratio derived from the balanced equation. Each stoichiometric calculation is rooted in these ratios, ensuring the chemical equation is balanced to reflect real-world chemical processes.

Moles are a basic unit in chemistry used for expressing amounts of a substance. The concept of a mole allows chemists to count and use macroscopic quantities of material based on atomic and molecular scale measurements. In the present problem, once we have determined the number of moles of oxygen using the Ideal Gas Law, stoichiometry allows us to find the amount of magnesium needed. For this:

• Determine the amount of oxygen in moles - a key outcome of utilizing the Ideal Gas Law in computations.
• Use the mole ratio from the balanced equation (2 mol Mg : 1 mol \( \text{O}_2 \)) to find the moles of magnesium.
• Multiply the moles of magnesium by its molar mass (24.31 g/mol) to get the mass in grams.

This calculation demonstrates how converting between moles and mass requires multiplication by a substance's molar mass and is a practice fundamental to solving many stoichiometry problems. A good grasp of mole calculations and stoichiometric conversions is thus essential for conducting precise chemical calculations.