Question
Enough distilled water was added to 150ml of 5% solution to bring the volume to 750ml. What is the percent strength of the resulting solution?
Answers
GPT-4o mini
To solve this problem, we need to determine the total amount of solute in the original 5% solution and then find the new percent concentration after diluting it with distilled water.
1. **Calculate the amount of solute in the original solution:**
- A 5% solution means that there are 5 grams of solute in every 100 ml of solution.
- In 150 ml of a 5% solution, the amount of solute is calculated as follows:
\[
\text{Amount of solute} = \text{Volume of solution} \times \text{Concentration} = 150 \, \text{ml} \times \frac{5 \, \text{g}}{100 \, \text{ml}} = 7.5 \, \text{g}
\]
2. **Determine the total volume of the diluted solution:**
- The new total volume after adding distilled water is 750 ml.
3. **Calculate the new percent concentration:**
- The percent concentration of the new solution is calculated by finding the ratio of the amount of solute to the total volume of the solution, then multiplying by 100 to convert it to a percentage:
\[
\text{Percent strength} = \left( \frac{\text{Amount of solute}}{\text{Total volume of solution}} \right) \times 100
\]
\[
\text{Percent strength} = \left( \frac{7.5 \, \text{g}}{750 \, \text{ml}} \right) \times 100 = 1\%
\]
Therefore, the percent strength of the resulting solution is **1%**.
1. **Calculate the amount of solute in the original solution:**
- A 5% solution means that there are 5 grams of solute in every 100 ml of solution.
- In 150 ml of a 5% solution, the amount of solute is calculated as follows:
\[
\text{Amount of solute} = \text{Volume of solution} \times \text{Concentration} = 150 \, \text{ml} \times \frac{5 \, \text{g}}{100 \, \text{ml}} = 7.5 \, \text{g}
\]
2. **Determine the total volume of the diluted solution:**
- The new total volume after adding distilled water is 750 ml.
3. **Calculate the new percent concentration:**
- The percent concentration of the new solution is calculated by finding the ratio of the amount of solute to the total volume of the solution, then multiplying by 100 to convert it to a percentage:
\[
\text{Percent strength} = \left( \frac{\text{Amount of solute}}{\text{Total volume of solution}} \right) \times 100
\]
\[
\text{Percent strength} = \left( \frac{7.5 \, \text{g}}{750 \, \text{ml}} \right) \times 100 = 1\%
\]
Therefore, the percent strength of the resulting solution is **1%**.