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 5.67 L has a partial pressure of O2 of 7.066 mPa at 30 °C, what mass of magnesium will react according to the following equation? 2 Mg1s2 + O21g2¡2 MgO1s2

Verified step by step guidance

1. Identify the balanced chemical equation: \(2 \text{Mg}_{(s)} + \text{O}_2_{(g)} \rightarrow 2 \text{MgO}_{(s)}\).
2. Calculate the number of moles of \(\text{O}_2\) using the ideal gas law: \(PV = nRT\). Convert the pressure from mPa to Pa and use \(R = 8.314 \text{ J/mol·K}\) and \(T = 30 + 273.15 \text{ K}\).
3. Use the stoichiometry of the balanced equation to find the moles of \(\text{Mg}\) needed. From the equation, 2 moles of \(\text{Mg}\) react with 1 mole of \(\text{O}_2\).
4. Calculate the mass of \(\text{Mg}\) using its molar mass (24.305 g/mol). Multiply the moles of \(\text{Mg}\) by its molar mass to find the mass.
5. Ensure all units are consistent and check calculations for accuracy.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the amount of a substance needed or produced in a reaction. In this case, the stoichiometric coefficients from the equation 2 Mg + O2 → 2 MgO indicate that two moles of magnesium react with one mole of oxygen, which is essential for calculating the mass of magnesium required.

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 crucial for determining the number of moles of oxygen present in the enclosure at the given conditions. By using the partial pressure of O2 and the volume of the enclosure, we can calculate the moles of oxygen available for the reaction with magnesium.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between moles and grams when calculating the mass of magnesium needed for the reaction. For magnesium, the molar mass is approximately 24.31 g/mol, which will be used to find the total mass of magnesium that reacts with the calculated moles of oxygen.