Stock solutions are concentrated solutions used to prepare working solutions of lower concentrations. Here’s how to calculate the amount of water needed to dilute stock solutions:

**Formula:**

C₁V₁ = C₂V₂

Where:

- C₁ – Concentration of the stock solution (units vary based on the solution)
- V₁ – Volume of stock solution needed (units typically in mL)
- C₂ – Concentration of the desired working solution (units vary based on the solution)
- V₂ – Total volume of the desired working solution (units typically in mL)

**Examples:**

**9. 20% SDS Stock Solution to 0.1% SDS Working Solution (100 mL):**

- C₁ = 20% (which is equivalent to 20 g/100 mL for most solid solutes)
- C₂ = 0.1% (which is equivalent to 0.1 g/100 mL)
- V₂ = 100 mL (desired working solution volume)

**Solve for V₁ (volume of stock solution needed):**

V₁ = (C₂ * V₂) / C₁ V₁ = (0.1 g/100 mL * 100 mL) / 20 g/100 mL V₁ = 0.5 mL

**Therefore, you need 0.5 mL of 20% SDS stock solution and add enough water to reach a final volume of 100 mL to make a 0.1% SDS working solution.**

**10. 0.5 M Tris Stock Solution to 10 mM Tris Working Solution (350 mL):**

- C₁ = 0.5 M (Molarity)
- C₂ = 10 mM (Millimolarity) – Convert to M by dividing by 1000: C₂ = 0.01 M
- V₂ = 350 mL

**Solve for V₁:**

V₁ = (C₂ * V₂) / C₁ V₁ = (0.01 M * 350 mL) / 0.5 M V₁ = 7 mL

**Therefore, you need 7 mL of 0.5 M Tris stock solution and add enough water to reach a final volume of 350 mL to make a 10 mM Tris working solution.**

**11. 1 M Tris & 0.2 M EDTA Stock Solutions to 10 mM Tris & 1 mM EDTA (400 mL):**

This requires a two-step dilution process.

**Step 1: Dilute Tris:**

- C₁ (Tris) = 1 M
- C₂ (Tris) = 10 mM (0.01 M)
- V₂ (Tris) = Volume of diluted Tris solution needed for the final mix (we don’t know this yet, so let’s call it X mL)

**Solve for V₁ (Tris stock solution needed for Tris dilution):**

V₁ (Tris) = (C₂ * V₂ (Tris)) / C₁ (Tris)

**Step 2: Combine diluted Tris and EDTA:**

- C₁ (EDTA) = 0.2 M
- C₂ (EDTA) = 1 mM (0.001 M)
- V₂ (total) = 400 mL (desired final volume)
- V₁ (total) = Combined volume of diluted Tris solution from step 1 (X mL) + volume of EDTA stock solution needed (we need to solve for this)

**We need to find the volume of diluted Tris solution (X mL) that, when combined with EDTA, will result in a final volume of 400 mL and the desired concentrations.**

**Here’s the approach, but solving for X algebraically can be complex. You can use a spreadsheet or trial and error:**

- Assume a value for X (e.g., X = 300 mL).
- Calculate the volume of EDTA stock solution needed using the formula from step 2, considering the combined volume (X mL + volume of EDTA).
- Check if the combined volume (X mL + volume of EDTA) equals 400 mL.
- If not, adjust the assumed value for X and repeat steps 2 and 3 until you find a value for X that gives a combined volume of 400 mL.

**12. 3 M NaCl & 10% NP-40 Stock Solutions to 300 mM NaCl & 0.2% NP-40 (500 mL):**

Similar to example 11, this requires a two-step dilution process