An aqueous laboratory solution containing exactly Sodium hydroxide () by mass has a measured density — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
An aqueous laboratory solution containing exactly $12.0\%$ Sodium hydroxide ($NaOH$) by mass has a measured density of $1.131\text{ g/mL}$. What is the exact volume (in Litres) of this solution that must be taken to obtain precisely $5.00\text{ moles}$ of $NaOH$?
💡 Solution & Explanation
Step 1: Calculate the mass of $5.00\text{ moles}$ of $NaOH$. Mass = Moles $\times$ Molar Mass = $5.00\text{ mol} \times 40\text{ g/mol} = 200\text{ g}$. Step 2: Determine the total mass of the solution required. The solution is $12.0\%$ $NaOH$ by mass, meaning $100\text{ g}$ of solution contains $12\text{ g}$ of $NaOH$. Mass of solution = $\frac{100\text{ g solution}}{12\text{ g NaOH}} \times 200\text{ g NaOH} = 1666.67\text{ g}$. Step 3: Convert the mass of the solution to volume using density. Volume = $\frac{\text{Mass}}{\text{Density}} = \frac{1666.67\text{ g}}{1.131\text{ g/mL}} = 1473.6\text{ mL} = 1.4736\text{ L}$. Rounding to appropriate significant figures yields $1.47\text{ L}$.