Question

A pharmacist asks you to dilute 400ml of 5% to 1%. How many ml of the final solution will be made?

Answer 1

To dilute a solution from 5% to 1%, you need to determine the total volume after dilution. The initial concentration is 5%, and you want to achieve a final concentration of 1%.

1. **Understand the existing solution**:
- You have 400 ml of a 5% solution.
- This means there are 20 grams of solute in the 400 ml (since 5% of 400 ml is 20 grams).

2. **Use the dilution equation**:
\[
C_1V_1 = C_2V_2
\]

Where:
- \(C_1\) = initial concentration (5% or 0.05)
- \(V_1\) = initial volume (400 ml)
- \(C_2\) = final concentration (1% or 0.01)
- \(V_2\) = final volume (what we are trying to find)

3. **Plugging in the values**:
\[
(0.05)(400) = (0.01)(V_2)
\]
\[
20 = 0.01V_2
\]

4. **Solving for \(V_2\)**:
\[
V_2 = \frac{20}{0.01} = 2000 \text{ ml}
\]

So, the final solution will be 2000 ml.