Question

Calculate the number of grams of sulfuric acid in 1 gallon of battery acid if the solution has a density of 1.34 g/ mL and is 38.6 % sulfuric acid by mass.
Express your answer in grams to three significant figures.

Answer 1

To calculate the number of grams of sulfuric acid in 1 gallon of battery acid, we can follow these steps:

1. **Convert gallons to milliliters**:
- 1 gallon = 3,785.41 mL.

2. **Calculate the mass of the battery acid solution**:
- Using the density (\(d = 1.34 \, \text{g/mL}\)):
\[
\text{mass of solution} = \text{density} \times \text{volume} = 1.34 \, \text{g/mL} \times 3,785.41 \, \text{mL} \approx 5,065.30 \, \text{g}
\]

3. **Calculate the mass of sulfuric acid in the solution**:
- Since the solution is 38.6% sulfuric acid by mass:
\[
\text{mass of } \text{H}_2\text{SO}_4 = \text{mass of solution} \times \frac{\text{percentage}}{100} = 5,065.30 \, \text{g} \times 0.386 \approx 1,954.05 \, \text{g}
\]

4. **Express the result in three significant figures**:
\[
\approx 1,950 \, \text{g}
\]

Thus, the number of grams of sulfuric acid in 1 gallon of battery acid is approximately **1,950 grams**.