Question

A pharmacy technician added enough distilled water to 200ml of 10% solution to increase the volume to 1000ml. What is the percent strength of the final solution?

Use the C1Q1=C2Q2 method to solve this problem.

Answer 1

To solve the problem using the C1Q1 = C2Q2 method, we need to define the variables:

- \( C_1 \): Concentration of the initial solution (10%).
- \( Q_1 \): Volume of the initial solution (200 ml).
- \( C_2 \): Concentration of the final solution (unknown, this is what we want to find).
- \( Q_2 \): Volume of the final solution (1000 ml).

Now we will substitute these values into the formula:

\[
C_1 \times Q_1 = C_2 \times Q_2
\]

First, we need to convert the percentage concentration into a decimal:

\[
C_1 = 10\% = 0.10
\]
\[
Q_1 = 200 \text{ ml}
\]
\[
Q_2 = 1000 \text{ ml}
\]

Now substitute the known values into the equation:

\[
0.10 \times 200 = C_2 \times 1000
\]

Calculating the left side:

\[
0.10 \times 200 = 20
\]

So we have:

\[
20 = C_2 \times 1000
\]

Now solve for \( C_2 \):

\[
C_2 = \frac{20}{1000}
\]

Calculating \( C_2 \):

\[
C_2 = 0.02
\]

Now convert back to percentage:

\[
C_2 = 0.02 \times 100\% = 2\%
\]

Thus, the percent strength of the final solution is **2%**.