Exactly of an impure natural chalk sample (containing and inert silicates) is completely dissolved i — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
Exactly $20.0\text{ g}$ of an impure natural chalk sample (containing $CaCO_3$ and inert silicates) is completely dissolved in an excess volume of dilute $HCl$ solution. The reaction quantitatively produces exactly $3.36\text{ L}$ of $CO_2$ gas, measured meticulously at $273\text{ K}$ and $1\text{ atm}$ pressure (STP). Assuming the impurities do not generate any gas, what is the exact percentage purity of the $CaCO_3$ within the chalk sample?
💡 Solution & Explanation
Step 1: Write the balanced dissolution equation. $CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)$. Step 2: Convert the volume of product gas to moles. Moles of $CO_2$ produced = $\frac{3.36\text{ L}}{22.4\text{ L/mol}} = 0.15\text{ moles}$. Step 3: Apply reaction stoichiometry. The balanced equation dictates that $1\text{ mole}$ of $CO_2$ is produced from exactly $1\text{ mole}$ of pure $CaCO_3$. Therefore, moles of pure $CaCO_3$ reacted = $0.15\text{ moles}$. Step 4: Calculate the mass of pure $CaCO_3$. Mass = $0.15\text{ moles} \times 100\text{ g/mol} = 15.0\text{ g}$. Step 5: Calculate percentage purity. % Purity = $\left(\frac{15.0\text{ g}}{20.0\text{ g}}\right) \times 100 = 75\%$.