What volume of 1.0 M sodium phosphate solution is required to prepare 4.0 L of 0.80 M sodium phosphate solution?

• A. 3.2 L
• B. 0.80 L
• C. 5.0 L
• D. 4.8 L

Answer: (A)

Verified step by step guidance

1. Identify the dilution problem where a concentrated solution is diluted to a lower concentration. Use the dilution formula: \(C_1 V_1 = C_2 V_2\), where \(C_1\) and \(V_1\) are the concentration and volume of the initial solution, and \(C_2\) and \(V_2\) are those of the diluted solution.
2. Assign the known values: \(C_1 = 1.0\, M\) (initial concentration), \(C_2 = 0.80\, M\) (final concentration), and \(V_2 = 4.0\, L\) (final volume). The unknown is \(V_1\), the volume of the initial solution needed.
3. Rearrange the dilution formula to solve for \(V_1\): \(V_1 = \frac{C_2 V_2}{C_1}\).
4. Substitute the known values into the equation: \(V_1 = \frac{0.80\, M \times 4.0\, L}{1.0\, M}\).
5. Calculate \(V_1\) to find the volume of the 1.0 M sodium phosphate solution required to prepare 4.0 L of 0.80 M solution.