Automobile batteries contain sulfuric acid, which is commonly referred to as "battery acid." Calculate the number of grams of sulfuric acid in 1.00 gallon of battery acid if the solution has a density of \(1.28 \mathrm{~g} / \mathrm{mL}\) and is \(38.1 \%\) sulfuric acid by mass.

Short Answer

Expert verified
There are 1845.09 grams of sulfuric acid in a 1.00-gallon battery acid solution.

Step by step solution

01

Convert gallons to milliliters

In order to convert gallons to milliliters, we will use the following conversion factors: 1 gallon = 3.78541 liters, 1 liter = 1000 milliliters. Thus: \(1.00 \, \text{gallon} \times \frac{3.78541 \, \text{liters}}{1 \, \text{gallon}} \times \frac{1000 \, \text{mL}}{1 \, \text{liter}} = 3785.41 \, \text{mL}\) Now, we know that the battery acid solution has a volume of 3785.41 mL.
02

Calculate the total mass of the battery acid solution

We are given the density of the solution as 1.28 g/mL. We will now use this to determine the mass of the 1.00-gallon battery acid solution. To calculate the mass, we use the following formula: density = mass/volume Rearranging for mass, we get: mass = density × volume mass = \(1.28 \, \frac{\text{g}}{\text{mL}} \times 3785.41 \, \text{mL}\) mass = 4845.32 g The total mass of the 1.00-gallon battery acid solution is 4845.32 g.
03

Determine the mass of sulfuric acid within the battery acid solution

The problem states that the battery acid solution is 38.1% sulfuric acid by mass. Using this percentage, we can calculate the mass of sulfuric acid in the 1.00-gallon solution: mass of sulfuric acid = total mass × mass percentage mass of sulfuric acid = \(4845.32 \, \text{g} \times \frac{38.1 \, \%}{100}\) mass of sulfuric acid = 1845.09 g Hence, there are 1845.09 grams of sulfuric acid in a 1.00-gallon battery acid solution.

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