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 gal 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

The number of grams of sulfuric acid in 1.00 gal of battery acid is approximately 1843.32 grams.

Step-by-step solution

Convert volume from gallons to milliliters

First, we need to convert the volume of battery acid given in gallons to milliliters. We will use the conversion factor: 1 gallon = 3785.41 mL. \[1.00 \, \text{gal} \times \frac{3785.41\, \text{mL}}{1 \, \text{gal}} = 3785.41\, \text{mL}\] So, the volume of battery acid in milliliters is 3785.41 mL.

Calculate the mass of the solution using its density

Now, let's calculate the mass of the solution using the given density. We know that density = mass/volume, so we can get the mass of the solution by multiplying the density by the volume. The given density is 1.28 g/mL, and we have just calculated the volume to be 3785.41 mL. Mass of solution = Density × Volume Mass of solution = \(1.28 \frac{\text{g}}{\text{mL}} \times 3785.41 \text{mL}\) Mass of solution = \(4841.32 \, \text{g}\)

Calculate the mass of sulfuric acid using the percentage by mass

Finally, we will calculate the mass of sulfuric acid using the given percentage by mass, which is 38.1%. Mass of sulfuric acid = Mass of solution × Percentage by mass Mass of sulfuric acid = \(4841.32 \, \text{g} \times \frac{38.1}{100}\) Mass of sulfuric acid = \(1843.32 \, \text{g}\) So, the number of grams of sulfuric acid in 1.00 gal of battery acid is approximately 1843.32 grams.

Key concepts

Understanding Density and Its Role in Calculations

Density is a critical property in chemistry because it connects mass and volume, two fundamental metrics in many calculations. In the problem of determining how much sulfuric acid is in a battery solution, density acts as a bridge. It allows us to convert between the amount of space a liquid takes up (its volume) and its weight or mass.

The formula for density is given by: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] This equation means that the density of a substance tells us how much mass there is in a specific volume. For example, if we know that 1 mL of a liquid has a mass of 1.28 g (as in our sulfuric acid solution), this is the liquid’s density. We can then multiply the density by any volume (in mL) to find the total mass.

Understanding density is essential not only for chemistry problems but also in real-world applications like determining if an object will float in water (which has a density of about 1 g/mL). Here, it helps us find out exactly how much sulfuric acid is present in a specific volume of battery acid. Once the volume is known and density is provided, one quick multiplication handles the conversion to mass.

Exploring Mass Percentage for Sulfuric Acid

Mass percentage is a helpful way to express the concentration of a component in a mixture. It expresses how much of a part, like sulfuric acid, contributes to the total mass of a solution. In our exercise, we see sulfuric acid accounts for 38.1% of the solution's total mass.

The formula for mass percentage is: \[\text{Mass Percentage} = \left( \frac{\text{Mass of the Component}}{\text{Total Mass of the Solution}} \right) \times 100 \]
To find out how much sulfuric acid is in a solution using mass percentage, you multiply the total mass of the solution by the mass percentage (expressed as a decimal). For example, if you have 1 kg of a solution, and the mass percentage of sulfuric acid is 38.1%, this means that 381 grams of sulfuric acid are present in that 1 kg of solution.

This method is very straightforward and useful for converting concentrations from percentages to actual mass values in grams. It enables chemists and students to work accurately with chemical solutions and understand component distributions easily.

Unit Conversion in Chemical Calculations

Unit conversion is often an early step in solving chemistry problems, especially those involving measurements in different unit systems. Different countries and scientific fields use different measurement units, and converting between these is crucial for accurate calculations.

In our example, we start by converting gallons to milliliters. Since 1 gallon equals 3785.41 mL, we use this conversion factor to transform the initial volume into a more manageable and standard scientific unit.
\[1.00 \, \text{gal} \times \frac{3785.41\, \text{mL}}{1 \, \text{gal}} = 3785.41\, \text{mL}\]
This ensures that subsequent calculations, like mass determination using density, are correct. Without proper unit conversion, calculations might result in significant errors, which is why understanding and applying unit prefixes and conversion factors are fundamental skills in chemistry.

Ultimately, paying attention to units helps to avoid confusion and ensures consistency and accuracy throughout a problem-solving process. Every chemistry student should reinforce their grasp on unit conversions to seamlessly tackle diverse scientific problems.