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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?

Ask by Bob Pena. in the United States
Jan 20,2025

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Answer

40 drops were added, and about 0.17% of the solution is acid.

Solution

To determine the number of drops added and the percentage of acid in the solution, follow these steps: 1. **Calculate the Volume of Acid Added:** - **Initial Volume of Water:** 1.2 liters (L) - **Final Volume of Solution:** 1.202 liters (L) - **Volume of Acid Added:** \[ 1.202\,L - 1.2\,L = 0.002\,L = 2\,\text{mL} \] 2. **Determine the Number of Drops Added:** - **Volume per Drop:** 0.05 milliliters (mL) - **Number of Drops:** \[ \frac{2\,\text{mL}}{0.05\,\text{mL/drop}} = 40\,\text{drops} \] 3. **Calculate the Percentage of Acid in the Solution:** - **Total Volume of Solution:** 1.202 liters = 1202 milliliters (mL) - **Percentage of Acid:** \[ \left( \frac{2\,\text{mL}}{1202\,\text{mL}} \right) \times 100\% \approx 0.166\% \approx 0.17\% \] **Conclusion:** - **Number of Drops Added:** 40 drops - **Percentage of Acid in the Solution:** Approximately 0.17% **Final Answer:** 40 drops were added, and roughly 0.17 percent of the final solution consists of acid.

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To find out how many drops of acid were added, we first need to determine the volume of the acid itself. The final volume of the solution is 1.202 L, which is equivalent to 1202 mL. Since 1.2 L of water is 1200 mL, the volume of the acid added can be calculated as: 1202 mL (final volume) - 1200 mL (water) = 2 mL (volume of acid). Since each drop is 0.05 mL, we can find the number of drops by dividing the volume of the acid by the volume of a single drop: 2 mL / 0.05 mL per drop = 40 drops. Next, to calculate the percent of the acid solution that is acid, we use the formula: % Acid = (Volume of Acid / Total Volume of Solution) x 100. Substituting the values, we get: % Acid = (2 mL / 1202 mL) x 100 ≈ 0.166%. So, about 0.166% of the acid solution is acid.

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