In a laboratory synthesis, exactly of Barium chloride () is mixed with exactly of Sodium phosphate ( — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
In a laboratory synthesis, exactly $0.5\text{ moles}$ of Barium chloride ($BaCl_2$) is mixed with exactly $0.2\text{ moles}$ of Sodium phosphate ($Na_3PO_4$) in aqueous medium. The maximum number of moles of the completely insoluble precipitate Barium phosphate, $Ba_3(PO_4)_2$, that can theoretically be formed is $x \times 10^{-1}$. Find the integer value of $x$.
💡 Solution & Explanation
Step 1: Write the balanced precipitation equation: $3BaCl_2(aq) + 2Na_3PO_4(aq) \rightarrow Ba_3(PO_4)_2(s) + 6NaCl(aq)$. Step 2: Determine limiting reagent by dividing given moles by stoichiometry coefficients. For $BaCl_2$: $0.5 / 3 = 0.166$. For $Na_3PO_4$: $0.2 / 2 = 0.10$. Since $0.10 < 0.166$, Sodium phosphate ($Na_3PO_4$) is the limiting reagent. Step 3: Calculate product based on LR. $2\text{ moles}$ of $Na_3PO_4$ yield exactly $1\text{ mole}$ of $Ba_3(PO_4)_2$. Therefore, $0.2\text{ moles}$ of $Na_3PO_4$ will yield $0.1\text{ moles}$ of $Ba_3(PO_4)_2$. Step 4: Match to the format. $0.1\text{ moles} = 1 \times 10^{-1}$. Therefore, the integer coefficient $x$ is 1.