Final answer:
After calculations based on chemical reaction equations and molar masses, the mass of lithium needed to react with oxygen to produce 167g of lithium oxide is found to be 78g. This result does not match any of the provided options, indicating a potential error in the calculation or given options.
Step-by-step explanation:
To determine the mass of lithium that reacts with oxygen to make 167g of lithium oxide, we need to start with the chemical reaction equation, which is 4Li + O2 → 2Li2O. Here, 4 moles of lithium react with 1 mole of oxygen to form 2 moles of lithium oxide. Since the problem provides the relative atomic masses of lithium (7) and oxygen (16), and we are looking for the mass of lithium, let's first calculate the molar mass of lithium oxide. Lithium oxide (Li2O) has a molar mass of 2*(7) + 16 = 30g/mol.
Next, we use the mass of lithium oxide produced (167g) to find the moles of lithium needed. We find the number of moles of lithium oxide by dividing the mass of the compound by its molar mass: 167g / 30g/mol = 5.57 moles of Li2O. From the balanced chemical equation, we see that 4 moles of lithium produce 2 moles of Li2O. So for 5.57 moles of Li2O, we would need 4/2 * 5.57 moles of lithium, which gives us 11.14 moles of lithium.
Finally, to find the mass of lithium, we multiply the number of moles by its atomic mass: 11.14 moles * 7g/mol = 78g. However, this mass doesn't match any of the given options (a) 47g, (b) 67g, (c) 87g, (d) 107g. There seems to be an error in calculation or in the options provided.