Problem 73 - Chemistry The Central Science

Question

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.

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.

Key Concepts

Density Calculation

Density is a fundamental property of materials and is especially important when dealing with chemical solutions. It helps us understand the relationship between the mass of a substance and its volume. In our exercise, we are given the density of the sulfuric acid solution, which is 1.28 g/mL, meaning that one milliliter of this solution weighs 1.28 grams. This information allows us to calculate the total mass of the solution when we know its volume.

To calculate the total mass of a solution using density, you can use the formula:

• Density = Mass / Volume

By rearranging this formula to solve for mass, we get:

• Mass = Density × Volume

In the problem, we converted the volume from gallons to milliliters (1 gallon = 3785.41 mL) and then used the density to find that the total mass of the battery acid solution was 4845.32 grams. This step is crucial as it sets the stage for calculating the mass percentage of sulfuric acid later.

Mass Percentage

Mass percentage is a way of expressing how much of one substance is present in a mixture, compared to the total mass of that mixture. It is expressed as a percentage and is important in chemistry to understand the concentration of a solution.

In our example, the battery acid solution is described as 38.1% sulfuric acid by mass. This indicates that out of every 100 grams of this solution, 38.1 grams are sulfuric acid. To find the actual mass of sulfuric acid in the entire 1-gallon solution, you multiply the total mass of the solution by this percentage.

• Mass of Sulfuric Acid = Total Mass × (Mass Percentage / 100)

Plugging in the numbers from our exercise, we calculated:

• Mass of Sulfuric Acid = 4845.32 g × (38.1 / 100) = 1845.09 g

This means that in the 1-gallon solution, there are 1845.09 grams of sulfuric acid. Understanding mass percentage helps chemists prepare solutions with precise concentrations and is crucial for many chemical processes.

Chemical Solution

A chemical solution is a homogeneous mixture of two or more substances. In a solution, a solute is the substance dissolved in another substance, known as the solvent. In our exercise, sulfuric acid is the solute, and the solution's behavior is determined by its concentration and properties such as density.

When working with solutions, there are several important concepts:

• Concentration: This indicates how much solute is present in a given amount of solution. It can be expressed in various ways, such as molarity or mass percentage.
• Solubility: The ability of the solute to dissolve in the solvent. This can vary based on temperature and the nature of the substances involved.
• pH: Indicates the acidity or alkalinity of a solution. Sulfuric acid solutions are acidic, and their pH can affect many chemical reactions.

Understanding chemical solutions is essential for various applications, including industrial, laboratory, and biological systems. These concepts help predict how substances will interact and ensure the correct composition of solutions for specific purposes.