Final answer:
To find the grams of oxygen gas needed, we convert the given number of magnesium atoms to moles and use the stoichiometry of the reaction 2Mg + O2 → 2MgO to find the moles of O2 required, which is then converted to grams, resulting in 0.08 grams of O2 needed.
Step-by-step explanation:
To calculate the amount of oxygen gas needed to react with magnesium, we need to follow the stoichiometry of the balanced chemical equation for the combustion of magnesium:
2Mg + O2 → 2MgO
This indicates that 2 moles of magnesium react with 1 mole of oxygen gas to produce 2 moles of magnesium oxide.
To find the moles of magnesium, we use Avogadro's number (6.022 × 1023 atoms/mol). Thus, for 3.01 × 1021 atoms of magnesium:
Moles of Mg = (3.01 × 1021 atoms) / (6.022 × 1023 atoms/mol) = 0.005 moles of Mg
According to the balanced equation, we need half the number of moles of O2 as there are moles of Mg. Hence:
Moles of O2 = 0.005 moles of Mg / 2 = 0.0025 moles of O2
To convert moles of O2 to grams, we multiply by the molar mass of O2 (32 g/mol):
Mass of O2 = 0.0025 moles × 32 g/mol = 0.08 grams of O2