Exactly of pure solid carbon is made to react with of aluminium powder to synthesize Aluminium carbi — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
Exactly $24\text{ g}$ of pure solid carbon is made to react with $54\text{ g}$ of aluminium powder to synthesize Aluminium carbide ($Al_4C_3$). Assuming standard conditions and a $100\%$ chemical yield, calculate the maximum amount (in grams) of $Al_4C_3$ formed.
💡 Solution & Explanation
Step 1: Write the balanced synthesis equation: $4Al + 3C \rightarrow Al_4C_3$. Step 2: Convert given masses to moles. Moles of Al = $54\text{ g} / 27\text{ g/mol} = 2.0\text{ moles}$. Moles of C = $24\text{ g} / 12\text{ g/mol} = 2.0\text{ moles}$. Step 3: Identify the limiting reagent. For Al: $2.0 / 4 = 0.5$. For C: $2.0 / 3 = 0.667$. Since $0.5 < 0.667$, Aluminium is the limiting reagent. Step 4: Calculate product formed. $4\text{ moles}$ of Al yield exactly $1\text{ mole}$ of $Al_4C_3$. Therefore, $2.0\text{ moles}$ of Al yield exactly $0.5\text{ moles}$ of $Al_4C_3$. Step 5: Calculate mass. Molar mass of $Al_4C_3 = (4 \times 27) + (3 \times 12) = 108 + 36 = 144\text{ g/mol}$. Mass = $0.5\text{ moles} \times 144\text{ g/mol} = 72\text{ g}$.