What volume in milliliters of concentrated HCl (12 M) is required to prepare 1500 mL of a 3.5 M HCl solution?

• A. 438 mL
• B. 525 mL
• C. 150 mL
• D. 292 mL

Answer: (A)

Verified step by step guidance

1. Identify the dilution equation to use, which relates the concentrations and volumes before and after dilution: \(C_1 \times V_1 = C_2 \times V_2\), where \(C_1\) and \(V_1\) are the concentration and volume of the concentrated solution, and \(C_2\) and \(V_2\) are those of the diluted solution.
2. Assign the known values: \(C_1 = 12\,M\) (concentrated HCl), \(C_2 = 3.5\,M\) (desired concentration), and \(V_2 = 1500\,mL\) (final volume of the diluted solution).
3. Rearrange the dilution equation to solve for the volume of concentrated HCl needed: \(V_1 = \frac{C_2 \times V_2}{C_1}\).
4. Substitute the known values into the rearranged equation: \(V_1 = \frac{3.5\,M \times 1500\,mL}{12\,M}\).
5. Calculate \(V_1\) to find the volume of concentrated HCl required to prepare the 1500 mL of 3.5 M solution.