Question

The density of sulfuric acid is \(1.84 \mathrm{~g} / \mathrm{mL}\). What volume of this acid will weigh 100 . g?

Short answer

54.35 mL

Step-by-step solution

- Understand the Density Formula

To solve this problem, use the formula for density, which is given by \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\). Rearrange this formula to find the volume.

- Rearrange the Formula

To find the volume, rearrange the formula to solve for volume: \(\text{Volume} = \frac{\text{Mass}}{\text{Density}}\)

- Plug in the Values

Insert the given values into the formula. Here, the mass of sulfuric acid is 100 g and the density is 1.84 g/mL: \(\text{Volume} = \frac{100 \text{ g}}{1.84 \text{ g/mL}}\)

- Perform the Calculation

Carry out the division to find the volume. \(\text{Volume} = \frac{100}{1.84} \approx 54.35 \text{ mL}\)

Key concepts

density formula

Understanding the concept of density is crucial for solving many chemistry problems, including this one involving sulfuric acid. The density formula is given by \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\). It describes how much mass is packed into a given volume of a substance. In this formula:

• Density is usually measured in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³).
• Mass is the amount of matter in the substance, typically measured in grams (g) or kilograms (kg).
• Volume is the space the substance occupies, measured in milliliters (mL), liters (L), or cubic meters (m³).

In this exercise, you need to rearrange this formula to find the volume if the density and mass are known.

rearranging equations

Rearranging equations is an essential skill in chemistry and other fields of science. In our problem, we start with the formula for density: \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\). To isolate volume (\text{Volume}), we need to get rid of density and mass from the denominator of the fraction. To do this, we multiply both sides by the volume (\text{Volume}): \(\text{Density} \times \text{Volume} = \text{Mass}\). Next, divide both sides by density (\text{Density}) to solve for volume (\text{Volume}): \(\text{Volume} = \frac{\text{Mass}}{\text{Density}}\). This rearranged formula allows you to calculate the volume of an object or substance if you know its mass and density.

chemical problem-solving

Chemical problem-solving often requires you to apply basic principles methodically. In this case, the problem involves determining the volume of sulfuric acid with a given mass and density. Here are steps to approach such problems:

• Identify the known values: From the exercise, we know that the mass is 100 grams (g) and the density is 1.84 grams per milliliter (g/mL).
• Rearrange the formula: As mentioned earlier, use \(\text{Volume} = \frac{\text{Mass}}{\text{Density}}\)
• Insert the known values: \(\text{Volume} = \frac{100 \text{ g}}{1.84 \text{ g/mL}}\)
• Carry out the calculation: Performing the division, you will find that the volume is approximately 54.35 milliliters (mL).

These steps ensure that you methodically solve the problem by applying the given data and the correct formula.

sulfuric acid properties

Sulfuric acid (H₂SO₄) is a highly corrosive and dense liquid that is widely used in industrial processes. Knowing its properties helps explain why the density value used in our problem (1.84 g/mL) is significant. Some key properties include:

• Highly acidic and corrosive: Sulfuric acid can cause severe burns and should be handled with care.
• High density: As seen in the problem, the density is 1.84 g/mL, meaning it is much denser than water (which has a density of 1 g/mL).
• Colorless to slightly yellow: In its pure form, sulfuric acid is colorless, but it can appear yellow due to impurities.
• Wide industrial use: It is used in the manufacture of fertilizers, in petroleum refining, wastewater processing, and chemical synthesis.

Understanding these properties allows chemists to safely and effectively use sulfuric acid in various applications and accurately calculate parameters such as volume and mass.