An unknown highly reactive solid element reacts violently with pure oxygen gas to synthesize a stabl — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
An unknown highly reactive solid element $X$ reacts violently with pure oxygen gas to synthesize a stable compound with the molecular formula $X_4O_6$. If exactly $8.4\text{ g}$ of this element $X$ combines completely and stoichiometrically with exactly $6.5\text{ g}$ of oxygen, determine the exact atomic weight of element $X$ (rounded to the nearest integer).
💡 Solution & Explanation
Step 1: Analyze the molecular formula. The formula $X_4O_6$ dictates that the molar ratio of atoms $X : O$ is strictly $4 : 6$, which simplifies to $2 : 3$. Step 2: Calculate the actual moles of Oxygen used. Moles of Oxygen ($O$) atoms = $\frac{6.5\text{ g}}{16\text{ g/mol}} = 0.40625\text{ moles}$. Step 3: Determine the moles of Element $X$ required. Based on the $2:3$ ratio, Moles of $X$ = $\frac{2}{3} \times (\text{Moles of } O) = \frac{2}{3} \times 0.40625 \approx 0.27083\text{ moles}$. Step 4: Calculate the atomic weight of $X$. Atomic Weight = $\frac{\text{Given Mass}}{\text{Calculated Moles}} = \frac{8.4\text{ g}}{0.27083\text{ moles}} \approx 31.01\text{ g/mol}$. Rounding to the nearest integer yields 31 (Phosphorus).