Problem 98 - Chemistry and Chemical Reactivity

Question

Automobile batteries are filled with an aqueous solution of sulfuric acid. What is the mass of the acid (in grams) in \(500 .\) mL of the battery acid solution if the density of the solution is \(1.285 \mathrm{g} / \mathrm{cm}^{3}\) and if the solution is \(38.08 \%\) sulfuric acid by mass?

Step-by-Step Solution

Answer

The mass of sulfuric acid is 244.65 grams.

Step 1: Calculate the Mass of the Solution

Convert the volume of the solution from milliliters to cubic centimeters, knowing that 1 mL is equivalent to 1 cm³. Therefore, 500 mL is 500 cm³. Use the density formula to compute the mass of the solution: \( \text{mass} = \text{density} \times \text{volume} \). Thus, the mass of the solution is \( 1.285 \, \text{g/cm}^3 \times 500 \, \text{cm}^3 = 642.5 \, \text{g} \).

Step 2: Calculate the Mass of Sulfuric Acid

To find the mass of sulfuric acid in the solution, use the percentage by mass formula. Multiply the total mass of the solution by the percentage of sulfuric acid divided by 100: \( \text{mass of } \text{H}_2\text{SO}_4 = 642.5 \, \text{g} \times \frac{38.08}{100} = 244.65 \, \text{g} \).

Key Concepts

Density Calculation

Density plays a crucial role in many scientific calculations, especially in chemistry. It is a measure of how much mass is contained in a given volume. This is particularly important when dealing with solutions and is expressed as \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}}. \] To find the mass of a solution, if you know the density and volume, you simply multiply the density by the volume.
Imagine you have 500 milliliters of a solution, as in the original exercise. Since 1 milliliter is equal to 1 cubic centimeter, you have 500 cubic centimeters. Suppose the density of this solution is 1.285 grams per cubic centimeter. The mass can then be calculated as follows:

• Convert the volume to appropriate units (in this case, it's already in cubic centimeters).
• Use the formula: \[ \text{Mass} = 1.285 \, \text{g/cm}^3 \times 500 \, \text{cm}^3 = 642.5 \, \text{g}. \]
• This yields a mass of 642.5 grams.

Understanding density calculations is key in chemistry because it helps determine how concentrated a solution is. This knowledge is beneficial for everything from brewing coffee to designing rocket fuels!

Mass Percentage

Mass percentage is a way to express the concentration of a component in a mixture. It tells you how much of the total mass of the mixture is made up of a specific component. In the context of solutions, it helps understand how much of a solute is present in a solvent.
To calculate mass percentage, you use the formula: \[ \text{Mass Percentage} = \left(\frac{\text{Mass of component}}{\text{Total mass of mixture}} \right) \times 100 \].
In the original exercise, to find the mass of sulfuric acid in a solution:

• The solution's total mass was 642.5 grams.
• The sulfuric acid made up 38.08% of this mixture.
• Hence, the mass of sulfuric acid is calculated as \[ 642.5 \, \text{g} \times \frac{38.08}{100} = 244.65 \, \text{g}. \]

Therefore, 244.65 grams of the solution is actually sulfuric acid. Knowing mass percentage is essential in industries and laboratories to ensure the correct formulation of products and to maintain safety standards.

Automobile Battery Chemistry

Automobile batteries, commonly lead-acid batteries, rely on a chemical reaction involving sulfuric acid. They are energy storages that provide the power necessary to start the engine and run electrical systems. Understanding the chemistry behind these batteries can help one appreciate their maintenance and efficiency.
Lead-acid batteries consist of lead dioxide (PbO₂), sponge lead (Pb), and a sulfuric acid (H₂SO₄) solution. When the battery discharges, the following reactions occur:

• At the positive plate, lead dioxide reacts with sulfuric acid, producing lead sulfate and water.
• At the negative plate, sponge lead reacts with sulfuric acid, also forming lead sulfate and releasing electrons.

The sulfuric acid acts as an electrolyte, facilitating the flow of electrons between the plates, which leads to the generation of electrical energy. As the battery discharges, the concentration of sulfuric acid decreases, which can lower the battery's ability to produce power. Understanding the percentage of sulfuric acid in the solution, as calculated through mass percentage, allows for effective monitoring and maintenance of battery health, ensuring optimal performance and longevity.