Why does the dilution equation, M_1 V_1 = M_2 V_2, work for preparing solutions of lower concentration from a stock solution?

• A. Because the concentration of the solute increases as more solvent is added
• B. Because the number of moles of solute remains constant before and after dilution
• C. Because the temperature of the solution is always constant during dilution
• D. Because the volume of solvent remains unchanged during dilution

Answer: (B)

Verified step by step guidance

1. Understand that the dilution equation \(M_1 V_1 = M_2 V_2\) relates the concentrations and volumes of a solution before and after dilution.
2. Recognize that \(M_1\) and \(V_1\) represent the molarity and volume of the initial (stock) solution, while \(M_2\) and \(V_2\) represent the molarity and volume after dilution.
3. Recall that molarity (\(M\)) is defined as moles of solute divided by volume of solution: \(M = \frac{\text{moles of solute}}{V}\).
4. Since dilution involves adding solvent without adding or removing solute, the number of moles of solute remains constant before and after dilution. This means \(\text{moles}_1 = \text{moles}_2\).
5. Expressing moles in terms of molarity and volume, we have \(M_1 V_1 = M_2 V_2\), which shows why the equation works: it ensures the amount of solute stays the same while volume and concentration change.