How many milliliters of a 0.250 M sucrose solution are required to prepare 400.0 mL of a 0.0310 M sucrose solution?

• A. 400.0 mL
• B. 12.4 mL
• C. 31.0 mL
• D. 49.6 mL

Answer: (D)

Verified step by step guidance

1. Identify the known values: the initial concentration of the sucrose solution \(C_1 = 0.250\ \text{M}\), the final concentration \(C_2 = 0.0310\ \text{M}\), and the final volume \(V_2 = 400.0\ \text{mL}\).
2. Recognize that this is a dilution problem where the amount of solute remains constant before and after dilution. Use the dilution equation: \(C_1 \times V_1 = C_2 \times V_2\), where \(V_1\) is the volume of the initial concentrated solution needed.
3. Rearrange the dilution equation to solve for \(V_1\): \(V_1 = \frac{C_2 \times V_2}{C_1}\).
4. Substitute the known values into the equation: \(V_1 = \frac{0.0310\ \text{M} \times 400.0\ \text{mL}}{0.250\ \text{M}}\).
5. Calculate \(V_1\) to find the volume of the 0.250 M sucrose solution required to prepare 400.0 mL of the 0.0310 M solution.