Question

Iron pyrite (fool's gold, Figure 1.11 ) has a shiny golden metallic appearance. Crystals are often in the form of perfect cubes. A cube \(0.40 \mathrm{cm}\) on each side has a mass of \(0.064 \mathrm{g}\) (a) Which of these observations are qualitative and which are quantitative? (b) Which of the observations are extensive and which are intensive? (c) What is the density of the sample of iron pyrite?

Short answer

(a) Qualitative: shiny appearance; Quantitative: mass, side length. (b) Extensive: mass, volume; Intensive: appearance, density. (c) Density = 1.00 g/cm³.

Step-by-step solution

Identify Qualitative and Quantitative Observations

We have two types of observations in the problem: 1. **Qualitative**: Describes qualities or characteristics that are observable but not measurable, such as color and shape. The observation "shiny golden metallic appearance" is qualitative. 2. **Quantitative**: Describes observations based on measurement or counting, such as mass and volume. The observations "a cube 0.40 cm on each side" and "mass of 0.064 g" are quantitative.

Identify Extensive and Intensive Properties

Properties can be classified into two categories: 1. **Extensive Properties**: Depend on the amount of matter present, such as mass and volume. In this problem, the mass (0.064 g) and volume (inferred from 0.40 cm on each side) are extensive. 2. **Intensive Properties**: Do not depend on the amount of matter and remain constant regardless of size, such as density and color. The "shiny golden metallic appearance" and calculated density (in the next step) are intensive properties.

Calculate the Density of Iron Pyrite

Density is the mass per unit volume. We can calculate the density of the iron pyrite sample using the formula:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}} \]**Calculate Volume**: Since the sample is a perfect cube with each side of 0.40 cm:\[\text{Volume} = (0.40 \, \text{cm})^3 = 0.064 \, \text{cm}^3 \]**Calculate Density**:Plug the mass and volume into the density formula:\[\text{Density} = \frac{0.064 \, \text{g}}{0.064 \, \text{cm}^3} = 1.00 \, \text{g/cm}^3\]

Key concepts

Qualitative Observations

In the realm of scientific study, qualitative observations play a crucial role. They describe non-numeric, observable qualities and characteristics. When examining iron pyrite, also known as fool's gold, qualitative observations might refer to its "shiny golden metallic appearance" and the "perfect cube forms" of its crystals. These observations help us understand the visual and physical traits of the material, without involving measurements or quantities. Such characteristics provide essential initial insights into what the substance might be and are the foundation of categorizing it apart from other materials.

Quantitative Observations

Unlike qualitative observations, quantitative observations involve numbers and measurements. They quantify the material, which can be vital for scientific analysis and comparison. Looking at iron pyrite, the quantitative observations include measurements such as a cube having sides of 0.40 cm and its mass being 0.064 g.

• The cube’s side measurement gives us a precise dimension that's essential for calculating values like the volume.
• The mass provides the amount of matter present in the sample.

Together, these observations allow us to perform further calculations, such as determining density, and offer a precise, numeric perspective that complements the descriptive nature of qualitative observations.

Extensive Properties

The properties of a material can be divided into different types to help us understand how these properties behave. Extensive properties are those that change when the amount of matter changes. For iron pyrite, both mass and volume fall into this category.

• Mass: With a mass of 0.064 g in our exercise, this property will increase if we have more of the substance.
• Volume: Computed from side measurements (0.40 cm), the volume will also change if the amount of substance increases or decreases.

Understanding extensive properties is important because they help determine how quantity alters a substance's total characteristics. More quantity generally results in more mass and volume.

Intensive Properties

Unlike extensive properties, intensive properties do not change with the amount of material. They remain consistent, regardless of the quantity. For iron pyrite, intensive properties include the "shiny golden metallic appearance" and density. These properties characterize the substance itself rather than the size of the sample.

• Appearance keeps its golden shine whether you have a small sample or a large one.
• Density, calculated in the next section, remains constant irrespective of sample size.

Intensive properties are crucial in identifying a substance, as they offer a consistent measure that doesn’t vary with the sample size or quantity.

Density Calculation

Density is a pivotal intensive property that describes how much mass is contained in a given volume. It is calculated using the formula \[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]For our iron pyrite cube, each side is 0.40 cm, so the volume is\[(0.40 \, \text{cm})^3 = 0.064 \, \text{cm}^3\].
With a mass of 0.064 g, the density is:\[\text{Density} = \frac{0.064 \, \text{g}}{0.064 \, \text{cm}^3} = 1.00 \, \text{g/cm}^3\]This calculation shows that even small samples of iron pyrite maintain the same density, helping to identify and differentiate it from other materials. Density is a powerful tool in material science, allowing for comparison across different substances and helping to predict how materials will behave in different situations.