Question

4\. Density of a substance in SI units is (a) \(\mathrm{mol} \mathrm{L}^{-1}\) (b) \(\mathrm{kg} \mathrm{m}^{-3}\) (b) \(\mathrm{gL}^{-1}\) (d) \(\mathrm{g} \mathrm{cm}^{-3}\)

Short answer

The correct answer is (b) \(kg/m^3\). This is the SI unit for density.

Step-by-step solution

Understanding the Concept of Density

Density is a measure of mass per unit volume. In the International System of Units (SI), the unit of mass is the kilogram (kg), and the unit of volume is the cubic meter (m³). Therefore, the SI unit of density is kilogram per cubic meter (\(kg/m^3\)).

Identification of the Correct SI Unit

Looking at the options, only option (b) represents the SI unit of density, which is \(kg/m^3\). The other options represent density units in other systems or contain units of substance amount (mol) or length (cm) that are not part of the SI definition of density.

Conclusion

Therefore, the correct answer is option (b). In the International System of Units (SI), the unit of density is kilogram per cubic meter (\(kg/m^3\)). The other options do not represent the correct SI unit for density.

Key concepts

Mass Per Unit Volume

Understanding density begins with grasping the concept of 'mass per unit volume.' This fundamental idea is used to describe how much mass is present in a given volume of a material. Think of it like this: if you have a box full of cotton and a box of the same size full of lead, the box with lead will be much heavier because lead has more mass in the same amount of space.

Mass is a measure of the amount of matter in an object, typically quantified in kilograms or grams. Volume, on the other hand, is the amount of space that an object occupies, measured in cubic meters or liters. Therefore, when we talk about mass per unit volume, we're essentially discussing the concentration of matter within a certain space, resulting in what is commonly known as density. This concept is very important in various fields, from materials science to fluid dynamics, as it influences the physical and chemical properties of substances.

SI Unit of Density

In scientific contexts, using standard units is crucial for clarity and consistency. The SI unit of density plays a critical role in this standardization. The SI, short for Système International d'Unités, is a universally adopted system for measuring physical quantities. When we measure density according to SI standards, we do so in kilograms per cubic meter (\(kg/m^3\)).

This unit explicitly combines the SI's basic units for mass (kilograms) and volume (cubic meters). The value in \(kg/m^3\) tells us exactly how many kilograms of a substance are present in one cubic meter of space. When students encounter this unit, it acts as a common language, which allows scientists, engineers, and educators worldwide to discuss and compare material properties without misunderstandings caused by differing units of measurement.

Kilogram Per Cubic Meter

The SI unit 'kilogram per cubic meter' is at the heart of measuring density. It's the standard unit that allows for an internationally recognized method of reporting a material's density. This precision is necessary for comparing substances across different studies and applications globally.

To imagine what a kilogram per cubic meter looks like, envision a cube with sides measuring exactly one meter. If this cube was filled with a substance that has a density of \(1 kg/m^3\), then the entire cube’s contents would weigh one kilogram. Knowing the density of substances is essential in many practical scenarios, such as in engineering where material strength and buoyancy are critical, or in meteorology where air density affects weather patterns.

Always remember, while a kilogram is a static measure of mass, the cubic meter part of \(kg/m^3\) is volumetric and will always depend on the space the material occupies, which can change with temperature and pressure.