Question
A scientist makes an acid solution by adding drops of acid to 1.2 L of water. The final volume of the acid solution is 1.202 L. Assuming the volume of each drop is 0.05 mL, how many drops were added to the water? About what percent of the acid solution is acid?
Question content area bottom
Part 1
Find the number of drops of acid that were added to the solution.
Question content area bottom
Part 1
Find the number of drops of acid that were added to the solution.
Answers
GPT-4o mini
To find the number of drops of acid added to the solution, we can follow these steps:
1. **Calculate the volume of the acid added:**
The final volume of the acid solution is 1.202 L. The initial volume of water is 1.2 L. Thus, the volume of the acid added can be calculated as follows:
\[
\text{Volume of acid} = \text{Final volume} - \text{Initial volume of water}
\]
\[
\text{Volume of acid} = 1.202\, \text{L} - 1.2\, \text{L} = 0.002\, \text{L}
\]
2. **Convert the volume of acid from liters to milliliters:**
Since \(1 \text{ L} = 1000 \text{ mL}\), the volume of acid in mL is:
\[
0.002\, \text{L} \times 1000\, \text{mL/L} = 2\, \text{mL}
\]
3. **Calculate the number of drops:**
Given that the volume of each drop is 0.05 mL, we can find the number of drops as follows:
\[
\text{Number of drops} = \frac{\text{Volume of acid}}{\text{Volume per drop}}
\]
\[
\text{Number of drops} = \frac{2\, \text{mL}}{0.05\, \text{mL}} = 40 \text{ drops}
\]
### Conclusion for Part 1
The number of drops of acid that were added to the solution is **40 drops**.
---
### Part 2: Calculate the percent of the acid solution that is acid
To find this percentage, we can use the formula:
\[
\text{Percent of acid solution} = \left( \frac{\text{Volume of acid}}{\text{Total volume of acid solution}} \right) \times 100
\]
Substituting in the values we have:
\[
\text{Percent of acid solution} = \left( \frac{2\, \text{mL}}{1202\, \text{mL}} \right) \times 100
\]
\[
\text{Percent of acid solution} \approx \left( \frac{2}{1202} \right) \times 100 \approx 0.166%
\]
### Conclusion for Part 2
About **0.166%** of the acid solution is acid.
1. **Calculate the volume of the acid added:**
The final volume of the acid solution is 1.202 L. The initial volume of water is 1.2 L. Thus, the volume of the acid added can be calculated as follows:
\[
\text{Volume of acid} = \text{Final volume} - \text{Initial volume of water}
\]
\[
\text{Volume of acid} = 1.202\, \text{L} - 1.2\, \text{L} = 0.002\, \text{L}
\]
2. **Convert the volume of acid from liters to milliliters:**
Since \(1 \text{ L} = 1000 \text{ mL}\), the volume of acid in mL is:
\[
0.002\, \text{L} \times 1000\, \text{mL/L} = 2\, \text{mL}
\]
3. **Calculate the number of drops:**
Given that the volume of each drop is 0.05 mL, we can find the number of drops as follows:
\[
\text{Number of drops} = \frac{\text{Volume of acid}}{\text{Volume per drop}}
\]
\[
\text{Number of drops} = \frac{2\, \text{mL}}{0.05\, \text{mL}} = 40 \text{ drops}
\]
### Conclusion for Part 1
The number of drops of acid that were added to the solution is **40 drops**.
---
### Part 2: Calculate the percent of the acid solution that is acid
To find this percentage, we can use the formula:
\[
\text{Percent of acid solution} = \left( \frac{\text{Volume of acid}}{\text{Total volume of acid solution}} \right) \times 100
\]
Substituting in the values we have:
\[
\text{Percent of acid solution} = \left( \frac{2\, \text{mL}}{1202\, \text{mL}} \right) \times 100
\]
\[
\text{Percent of acid solution} \approx \left( \frac{2}{1202} \right) \times 100 \approx 0.166%
\]
### Conclusion for Part 2
About **0.166%** of the acid solution is acid.