To dilute a solution, you can use the formula:
\[ C_1V_1 = C_2V_2 \]
where:
- \( C_1 \) is the initial concentration,
- \( V_1 \) is the initial volume,
- \( C_2 \) is the final concentration, and
- \( V_2 \) is the final volume.
Given:
- \( C_1 = 18 , \text{mol/dm}^3 \)
- \( V_1 = 30 , \text{cm}^3 \)
- To dilute it 20 times, the final concentration \( C_2 \) will be \( \frac{C_1}{20} = \frac{18 , \text{mol/dm}^3}{20} = 0.9 , \text{mol/dm}^3 \).
Now, we need to find \( V_2 \), the final volume after dilution.
Using the equation:
\[ C_1 V_1 = C_2 V_2 \]
Substituting the known values:
\[ 18 , \text{mol/dm}^3 \times 30 , \text{cm}^3 = 0.9 , \text{mol/dm}^3 \times V_2 \]
Calculating the left side:
\[ 540 , \text{mol·cm}^3/dm^3 = 0.9 , \text{mol/dm}^3 \times V_2 \]
Now solve for \( V_2 \):
\[ V_2 = \frac{540 , \text{mol·cm}^3/dm^3}{0.9 , \text{mol/dm}^3} = 600 , \text{cm}^3 \]
Now, to find the volume of distilled water to be added, calculate:
\[ \text{Volume of water} = V_2 - V_1 = 600 , \text{cm}^3 - 30 , \text{cm}^3 = 570 , \text{cm}^3 \]
Thus, you would need to add 570 cm³ of distilled water to dilute 30 cm³ of 18 mol/dm³ HCl to a concentration that is 20 times less.