Magnesium can be used as a “getter” in evacuated enclosures to react with the last traces of oxygen. (The magnesium is usually heated by passing an electric current through a wire or ribbon of the metal.) If an enclosure of 0.452 L has a partial pressure of O2 of 3.5×10−6 torr at 27°C, what mass of magnesium will react according to the following equation?

Verified step by step guidance

1. Convert the given partial pressure of O2 from torr to atm using the conversion factor: 1 atm = 760 torr.
2. Use the ideal gas law equation, PV = nRT, to calculate the number of moles of O2. Here, P is the pressure in atm, V is the volume in liters, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin (convert 27°C to Kelvin by adding 273.15).
3. From the balanced chemical equation, determine the stoichiometric relationship between moles of O2 and moles of Mg. The equation is: 2 Mg + O2 -> 2 MgO, which shows that 1 mole of O2 reacts with 2 moles of Mg.
4. Calculate the moles of Mg needed using the stoichiometric ratio from the balanced equation.
5. Convert the moles of Mg to mass using the molar mass of magnesium (24.31 g/mol).

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the amount of gas present in a given volume and pressure, allowing us to determine how many moles of oxygen are available for reaction with magnesium in the enclosure.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. Understanding stoichiometry is crucial for determining the mass of magnesium needed to react with a specific amount of oxygen, as it allows us to convert moles of oxygen to moles of magnesium using the coefficients from the balanced chemical equation.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. Knowing the molar mass of magnesium is necessary to convert the number of moles of magnesium calculated from stoichiometry into grams, which is the final answer required for the problem.