To find out how many milliliters of a 2% stock solution are needed to make 200 mL of a 0.5% solution, you can use the dilution formula:
\[ C_1 \times V_1 = C_2 \times V_2 \]
Where:
- \(C_1\) = concentration of the stock solution (2% or 0.02 as a fraction)
- \(V_1\) = volume of the stock solution to be found (in mL)
- \(C_2\) = concentration of the final solution (0.5% or 0.005 as a fraction)
- \(V_2\) = volume of the final solution (200 mL)
Now, rearranging the formula to solve for \(V_1\):
\[ V_1 = \frac{C_2 \times V_2}{C_1} \]
Substituting in the values:
\[ V_1 = \frac{0.005 \times 200}{0.02} \]
Calculating it step by step:
- Calculate \(0.005 \times 200 = 1\)
- Now divide that by \(0.02\): \[ V_1 = \frac{1}{0.02} = 50 \text{ mL} \]
So, you will need 50 mL of the 2% stock solution to prepare 200 mL of a 0.5% solution.