What volume of concentrated (14.7 M) phosphoric acid is required to prepare 25.0 L of 3.0 M H3PO4 solution?

• A. 5.10 L
• B. 8.80 L
• C. 1.60 L
• D. 12.5 L

Answer: (A)

Verified step by step guidance

1. Identify the known values: the concentration of the concentrated phosphoric acid solution (C_1 = 14.7 M), the desired concentration of the diluted solution (C_2 = 3.0 M), and the volume of the diluted solution (V_2 = 25.0 L).
2. Recall the dilution formula, which relates the concentrations and volumes before and after dilution: \(C_1 \times V_1 = C_2 \times V_2\), where \(V_1\) is the volume of the concentrated solution needed.
3. Rearrange the dilution formula to solve for \(V_1\): \(V_1 = \frac{C_2 \times V_2}{C_1}\).
4. Substitute the known values into the equation: \(V_1 = \frac{3.0 \text{ M} \times 25.0 \text{ L}}{14.7 \text{ M}}\).
5. Calculate \(V_1\) to find the volume of concentrated phosphoric acid required to prepare 25.0 L of 3.0 M solution.