Final answer:
To determine the formula of a chloride of rhenium with 63.6% rhenium, 100 grams of the compound is assumed, translating to 0.341 moles of Re and 1.027 moles of Cl, providing a molar ratio of 1:3. The empirical formula of the compound is ReCl3.
Step-by-step explanation:
To determine the formula of a chloride of rhenium that contains 63.6% rhenium by mass, we need to find the simplest whole number ratio of moles of rhenium to moles of chlorine in the compound. Let's assume we have 100 grams of this compound, which will contain 63.6 grams of rhenium and 36.4 grams of chlorine (since the total must equal 100%).
First, we convert the masses into moles using the atomic masses from the periodic table (for rhenium, Re, approximately 186.2 g/mol; for chlorine, Cl, approximately 35.45 g/mol):
Moles of Re = 63.6 g / 186.2 g/mol ≈ 0.341 moles
Moles of Cl = 36.4 g / 35.45 g/mol ≈ 1.027 moles
Next, we divide both amounts by the smallest number of moles to find the simplest ratio:
Moles of Re / 0.341 = 1
Moles of Cl / 0.341 ≈ 3
Thus, we find that the rhenium and chlorine are in a 1:3 ratio by moles, suggesting that the empirical formula of the compound is ReCl3.