Problem 2 - Chemistry Matter and Change

Question

What is the volume of a sample that has a mass of 20 \(\mathrm{g}\) and a density of 4 \(\mathrm{g} / \mathrm{mL}\) ?

Step-by-Step Solution

Answer

The volume is 5 mL.

Step 1: Understand the Formula for Volume

To find the volume of a sample when the mass and density are given, use the formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \). This formula comes from rearranging the basic density formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).

Step 2: Substitute Known Values into the Formula

Substitute the given mass (\(20 \, \mathrm{g}\)) and density (\(4 \, \mathrm{g/mL}\)) into the formula: \( \text{Volume} = \frac{20 \, \mathrm{g}}{4 \, \mathrm{g/mL}} \).

Step 3: Calculate the Volume

Perform the division: \( \frac{20}{4} = 5 \). Thus, the volume is \(5\) mL.

Key Concepts

Volume Calculation

The concept of volume calculation is essential when you want to determine how much space a particular substance occupies. In mathematics and science, volume is commonly measured in units such as liters, milliliters, and cubic meters. To calculate the volume of a sample, especially when you are given the mass and density, you'll need to use a specific formula.

When you know the mass and density of a substance, you can use the rearranged density formula:

• \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \)

This equation is useful because it allows you to isolate the volume on one side, making it easy to calculate as long as the mass and density are known. So, you simply divide the mass by the density to find the volume. In our example, with a mass of 20 grams and a density of 4 grams per milliliter, the volume calculates to 5 milliliters.Breaking down the problem into these steps makes volume calculation straightforward.

Mass and Density Relationship

The relationship between mass and density is fundamental in understanding physical properties of matter. Mass refers to the amount of matter in an object, often measured in grams or kilograms. Density, on the other hand, describes how tightly matter is packed within a given volume.

Understanding this relationship is crucial:

• Mass is a measure of how much matter there is.
• Density indicates how much mass is contained in a particular volume.

This means that for a fixed mass, increasing the density decreases the volume and vice versa. This principle is why different substances have different volumes at the same mass if they have different densities. For instance, a high-density material like lead takes up less space than the same mass of a low-density substance like cork. In our example, knowing the sample's density allowed us to determine how the 20 grams of material is distributed in a volume of 5 milliliters. This relates directly to how the density characterizes the material's compactness.

Density Formula

The density formula is a key tool in both science and engineering to determine how compact a substance is. This formula expresses density as a ratio of mass to volume:

Density is calculated using the equation:

• \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \)

The formula indicates that density is derived from dividing the mass by the volume of a substance. It's a measurement of how much mass occupies a certain amount of space. The units commonly used are grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³).^

To apply this formula effectively, you need to understand how it can be rearranged to solve for different variables. As seen in our example, the formula can be rearranged to solve for volume, allowing us to find out how much space the substance occupies based on a given mass and density. Understanding this simple yet powerful formula is pivotal in evaluating the properties of materials.