Which formula is used to calculate the volume of stock solution needed to prepare a dilute solution from a concentrated solution?

• A. C_1 + C_2 = C_3
• B. PV = nRT
• C. m_1 v_1 = m_2 v_2
• D. M_1 V_1 = M_2 V_2

Answer: (D)

Verified step by step guidance

1. Identify the variables involved in dilution problems: \( M_1 \) and \( V_1 \) represent the molarity and volume of the concentrated (stock) solution, while \( M_2 \) and \( V_2 \) represent the molarity and volume of the diluted solution.
2. Understand that during dilution, the amount of solute remains constant before and after dilution, meaning the moles of solute in the stock solution equal the moles of solute in the diluted solution.
3. Express the moles of solute in terms of molarity and volume: \( \text{moles} = M \times V \). Therefore, the moles before dilution are \( M_1 V_1 \) and after dilution are \( M_2 V_2 \).
4. Set the moles before and after dilution equal to each other to reflect conservation of solute: \( M_1 V_1 = M_2 V_2 \). This is the dilution equation used to calculate the volume of stock solution needed.
5. Use the equation \( M_1 V_1 = M_2 V_2 \) to solve for the unknown volume or concentration by rearranging the formula depending on the given values.