1.Dilution Reducing the concentration of a solute in a solution by adding more solvent, usually water. The number of moles of solute remains constant before and after dilution. 2. Dilution Formula The dilution formula is: C1 V1 = C2 V2 Where: • C1 : Initial concentration (stock solution). • V1 : Initial volume. • C2 : Final concentration (diluted solution). • V2 : Final volume. This formula ensures that the total moles of solute remain constant: Moles of solute before dilution: C1 V1 = Moles of solute after dilution: C2 V2 3. Practical Applications • Preparing solutions of desired concentrations for laboratory experiments. • Reducing the concentration of chemical reagents for safer handling. • Serial dilutions in microbiology to achieve countable colonies. 4. Practice Problems Problem 1: Basic Dilution You have 50 mL of a 2 M sodium chloride solution. How much water must you add to dilute it to 0.5 M? Solution: C1 = 2 M, V1 = 50 mL, C2 = 0.5 M, V2 =? 1 Using C1 V1 = C2 V2 : 2 × 50 = 0.5 × V2 2 × 50 V2 = = 200 mL 0.5 Total volume after dilution is 200 mL. Water added: Vadded = V2 − V1 = 200 − 50 = 150 mL Problem 2: Preparing a Specific Volume How would you prepare 250 mL of a 0.1 M HCl solution from a 1 M HCl stock solution? Solution: C1 = 1 M, V1 =?, C2 = 0.1 M, V2 = 250 mL Using C1 V1 = C2 V2 : 1 × V1 = 0.1 × 250 0.1 × 250 = 25 mL V1 = 1 Take 25 mL of the stock solution and dilute it with water to a total volume of 250 mL. Problem 3: Serial Dilution You need to perform a serial dilution to achieve a concentration of 10−5 M from a 1 M stock solution. If each step dilutes the solution by a factor of 10, how many steps are required? Solution: C1 = 1 M, C2 = 10−5 M, Dilution factor per step = 10 After n steps: C2 = C1 10n Rearranging: n = log10 C1 C2 = log10 1 10−5 = log10 (105 ) = 5 You need 5 serial dilution steps. Problem 4: Unknown Final Concentration You add 100 mL of water to 200 mL of a 0.75 M glucose solution. What is the final concentration? Solution: C1 = 0.75 M, V1 = 200 mL, V2 = V1 + 100 = 300 mL, C2 =? 2 Using C1 V1 = C2 V2 : 0.75 × 200 = C2 × 300 0.75 × 200 = 0.5 M C2 = 300 The final concentration is 0.5 M. 5. Key Tips for Dilutions • Always add solute to solvent, not the other way around, for safety. • Double-check units for volume and concentration to ensure consistency. • For serial dilutions, track each step carefully to avoid errors. • Use volumetric flasks for precise dilutions when accuracy is critical. 3