An unknown inorganic compound contains exactly nitrogen and of a transition metal by mass. If of the — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
An unknown inorganic compound contains exactly $28\%$ nitrogen and $72\%$ of a transition metal by mass. If $3\text{ atoms}$ of the metal combine stoichiometrically with $2\text{ atoms}$ of nitrogen, find the atomic weight of the metal.
💡 Solution & Explanation
Step 1: The stoichiometric ratio defines the empirical formula as $M_3N_2$. Step 2: Set up the molecular weight equation. Let atomic weight of M be $x$. Molar mass $= 3x + (2 \times 14) = 3x + 28$. Step 3: Use the mass percentage of Nitrogen to solve for $x$. $\% N = \frac{28}{3x + 28} \times 100 = 28\%$. $\implies \frac{28}{3x + 28} = 0.28 \implies 3x + 28 = 100 \implies 3x = 72 \implies x = 24$.