Problem 15 - Chemistry and Chemical Reactivity

Question

A piece of turquoise is a blue-green solid; it has a density of \(2.65 \mathrm{g} / \mathrm{cm}^{3}\) and a mass of \(2.5 \mathrm{g}.\) (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 volume of the piece of turquoise?

Step-by-Step Solution

Answer

Qualitative: color and state; Quantitative: density, mass. Density is intensive; mass is extensive. Volume: \(0.943 \, \mathrm{cm}^3\).

Step 1: Identify Qualitative Observations

Qualitative observations describe the qualities or characteristics of an object. In this exercise, the phrase "a blue-green solid" is a qualitative observation. The color and state (solid) are descriptive traits and do not include numerical measurements.

Step 2: Identify Quantitative Observations

Quantitative observations involve numerical data. In this exercise, "density of \(2.65 \, \mathrm{g/cm}^3\)" and "mass of \(2.5 \, \mathrm{g}\)" are quantitative observations. Both involve numerical measurements and units.

Step 3: Differentiate Between Intensive and Extensive Properties

Intensive properties do not depend on the amount of substance. Density (\(2.65 \, \mathrm{g/cm}^3\)) is an intensive property because it remains the same regardless of the sample size. Extensive properties depend on the amount of substance. Mass (\(2.5 \, \mathrm{g}\)) is an extensive property as it varies with the amount of substance.

Step 4: Calculate the Volume of the Turquoise

To find the volume, use the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Rearrange to solve for volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \). Substitute the known values: \( \text{Volume} = \frac{2.5 \, \mathrm{g}}{2.65 \, \mathrm{g/cm}^3} \approx 0.943 \mathrm{cm}^3\).

Key Concepts

Qualitative Observation

Qualitative observations help describe the features or properties of an object without using numbers.
These observations are based on what we see, hear, touch, or sometimes smell and taste. For instance, in the provided exercise, the description of turquoise as a "blue-green solid" is a qualitative observation.
This is because it refers to the color and state of the material without providing any numerical data. Understanding qualitative observations is crucial in scientific research, as they allow for descriptions that can help in classifying and comparing different substances.

Quantitative Observation

Quantitative observations are all about numbers. These observations help provide measurable or countable data about an object.
In this context, the density (given as 2.65 g/cm³) and the mass (2.5 g) of the turquoise are examples of quantitative observations.
They include specific measurements and units, allowing scientists to perform calculations like finding the object's volume.
Using quantitative data, scientists can verify and compare results consistently, making these observations fundamental in experiments and data analysis.

Intensive Property

Intensive properties are characteristics of a substance that do not change with the amount of material present.
For example, density is an intensive property.
Whether you have a large or small piece of turquoise, its density remains constant at 2.65 g/cm³.
Intensive properties are incredibly useful for identifying substances because they are consistent regardless of sample size.

• Other examples of intensive properties include temperature, color, and melting point.
• These traits do not vary with the quantity of the sample.

Extensive Property

Unlike intensive properties, extensive properties depend on the amount of substance present. As an example, consider the mass of turquoise given as 2.5 g.
If you were to take only half of the original piece, the mass would reduce accordingly, demonstrating its dependence on quantity.
Understanding extensive properties is essential for processes involving scaling quantities, such as chemical reactions and production.

• Examples include volume, weight, and total charge.
• These properties scale with the size or amount of the material.

Density Calculation

Density is a handy physical property when trying to determine the volume of an object, especially if its shape is irregular.
The formula for density is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). By rearranging this formula, we can find the volume if the mass and density are known: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
In the original exercise, using the mass of turquoise (2.5 g) and its density (2.65 g/cm³), the volume can be calculated as \( \frac{2.5 \text{ g}}{2.65 \text{ g/cm}^3} \), which equals approximately 0.943 cm³.
This calculation helps in determining how much space the object occupies, which can be vital for various practical applications in chemistry and materials science.