Let's solve the problem step by step using the dilution equation: **C1 V1 = C2 V2** Given: - C1 (stock concentration) = 80 mM - C2 (final concentration) = 20 mM - V2 (final volume) = 10 ml We need to find V1 (volume of stock to use): **Step 1: Plug in the values** 80 mM × V1 = 20 mM × 10 ml **Step 2: Solve for V1** V1 = (20 mM × 10 ml) / 80 mM V1 = (200) / 80 V1 = 2.5 ml **Step 3: Find the volume of water to add** Volume of water = Final volume (V2) - Volume of stock (V1) Volume of water = 10 ml - 2.5 ml Volume of water = 7.5 ml --- **Final answers:** - **Volume of stock:** 2.5 ml - **Volume of water:** 7.5 ml **Calculations shown above.**

Certainly! Let's go through the problem and solution step by step in a clear and organized manner. --- ### **Problem Recap:** - **Stock solution concentration (C₁):** 80 mM - **Desired final concentration (C₂):** 20 mM - **Final total volume (V₂):** 10 ml **Question:** How much of the stock solution (V₁) should be used, and how much water should be added to prepare the 10 ml of 20 mM solution? *(Express your answers in milliliters)* --- ### **Step 1: Use the dilution equation** The fundamental equation for dilutions is: \[ C_1 V_1 = C_2 V_2 \] where: - \( C_1 \) = concentration of stock solution - \( V_1 \) = volume of stock solution needed - \( C_2 \) = final concentration after dilution - \( V_2 \) = final total volume of the solution --- ### **Step 2: Plug in the known values** \[ 80\, \text{mM} \times V_1 = 20\, \text{mM} \times 10\, \text{ml} \] --- ### **Step 3: Solve for \( V_1 \)** \[ V_1 = \frac{20\, \text{mM} \times 10\, \text{ml}}{80\, \text{mM}} \] \[ V_1 = \frac{200}{80} \text{ ml} \] \[ V_1 = 2.5\, \text{ml} \] **Interpretation:** You need **2.5 ml** of the 80 mM stock solution. --- ### **Step 4: Calculate the volume of water to add** Total final volume desired is 10 ml, so: \[ \text{Volume of water} = V_2 - V_1 = 10\, \text{ml} - 2.5\, \text{ml} = 7.5\, \text{ml} \] --- ### **Final Answer:** | **Component** | **Volume (ml)** | |--------------|----------------| | **Stock solution** | **2.5 ml** | | **Water** | **7.5 ml** | --- ### **Summary:** To prepare 10 ml of a 20 mM solution from an 80 mM stock: - **Use 2.5 ml** of the stock solution. - **Add 7.5 ml** of water to dilute. This ensures the final concentration is 20 mM in a total volume of 10 ml. --- If you have any further questions or need additional explanations, feel free to ask!