To solve this question, we will need to go through the following steps systematically:
1. Identify the known quantities and conversions:
- Initial strength of the solution: 2% (w/v), which means 2 grams of the substance in 100 mL of the solution.
- Initial volume: 120 mL.
- Final volume: 1 pint.
- Conversion factor: 1 pint = 473.176 mL.
2. Calculate the final volume in mL:
- Since 1 pint equals 473.176 mL, the final volume after dilution will be 473.176 mL.
3. Determine the amount of the active substance in the initial solution:
- The initial strength of the solution is 2%, which can be translated into 2 grams of the substance per 100 mL.
- Therefore, the initial 120 mL solution contains:
[tex]\[ \text{Amount of substance} = 2\% \cdot 120 \text{ mL} = \frac{2}{100} \cdot 120 = 2.4 \text{ grams} \][/tex]
4. Calculate the final strength of the solution after dilution:
- The total amount of the substance (2.4 grams) remains the same after dilution.
- The final volume is 473.176 mL.
- The final strength (in %) can be calculated as follows:
[tex]\[ \text{Final Strength} = \left(\frac{\text{Total Amount of the Substance}}{\text{Final Volume}}\right) \times 100
= \left(\frac{2.4 \text{ grams}}{473.176 \text{ mL}}\right) \times 100 \approx 0.5070210847549325\% \][/tex]
Thus, the strength of the dilution will be approximately 0.507%.
