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.

Question

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.