Exploring Density: A Case Study of an Unknown Metal

When faced with the discovery of an unknown metal, one fundamental question arises: How dense is it? In this article, we will delve into a detailed analysis of a piece of unknown metal with a mass of 0.008 kg and a volume of 7 × 105 cm3. By working through the steps to calculate its density, we will uncover unique insights about this metal's properties and its behavior in different environments.

Understanding Density

Density is a fundamental physical property that describes how tightly packed the components of a substance are. It is defined as the mass per unit volume and is typically measured in units like grams per cubic centimeter (g/cc) or kilograms per cubic meter (kg/m3). Calculating density is essential for identifying materials, understanding their behavior in various environments, and comparing them to known substances.

Calculating the Density of the Unknown Metal

Let's start by converting the given mass and volume into more familiar units.

Mass

The problem provides the mass of the metal as 0.008 kg. To make it easier to work with, we can convert this to grams, remembering that 1 kg 1000 g:

0.008 kg 0.008 × 1000 g 8 g

Volume

The volume is given in cubic centimeters (cm3):

7 × 105 cm3 700,000 cm3

Calculating Density

Density is calculated using the formula:

density mass / volume

Substituting the values we have:

density 8 g / 700,000 cm3 ≈ 0.0001143 g/cm3

Considering significant figures (1 sigfig), the density is approximately:

density ≈ 0.0001143 g/cm3 ≈ 1.1×10-4 g/cm3

Comparing the Metal's Density to Other Substances

To better understand the implications of this density, let's compare it to the densities of water and air.

Comparing to Water

The density of water is 1 g/cm3. Since the metal has a much lower density (0.0001143 g/cm3), it is approximately 8,736 times less dense than water. This means that the metal would float on water, given its light weight relative to the volume it occupies.

Comparing to Air

The density of air is much lower than water, at approximately 0.0012 g/cm3. The metal is about 1 g/cm3 / 0.0012 g/cm3 833 times more dense than air. While it is dense enough to sink in air, it is relatively lightweight for its volume, making it easy for air currents to lift and move it.

Unit Conversion and Dimensional Analysis

One of the key skills used in solving density problems is unit conversion and dimensional analysis. By multiplying by appropriate unit factors, we can convert units and cancel out unwanted units. Let's perform the calculation to convert the density from g/cm3 to kg/m3:

0.0001143 g/cm3 × (1 kg / 1000 g) × (100 cm / 1 m) × (100 cm / 1 m)  1.143×10-4 kg/m3

Adjusting for significant figures, the density in kg/m3 is approximately:
1.1×10-4 kg/m3
By mastering these techniques, you can easily solve similar problems and ensure accuracy in your calculations.
Conclusion
The density of the unknown metal is extremely low, highlighting its unique properties. It is lighter than both water and air, which makes it interesting in various scientific and engineering contexts. Understanding how to calculate and compare densities is crucial for a wide range of applications, from material science to environmental studies.
Related Keywords:
density calculation
relative density
unit conversion