How to Calculate Density with Mass and Volume ?

Density is a key concept that shows how much "stuff" is packed into a certain amount of space. In everyday terms, it's what makes objects heavy or light for their size. For example, a rock feels much heavier than a sponge of the same size because the rock has a higher density. Here, we will explore various methods of measuring density and the application of density.

What is Density?

Density is a measure that compares the amount of matter in an object to the space it occupies. An object with more matter packed into a given volume has a higher density.

When two materials are mixed, density determines which one rises and which one sinks. This principle explains why objects sink or float and why a cold front sinks below a warm front in the atmosphere.

The density of an object can be calculated using the equation:

Density = Mass/Volume

or

ρ = m/v

Where, ρ is the density, m is the mass and V is the volume.

SI Unit Of Density

Every substance has its own unique density. Typically, the density of water, around 1 gram per cubic centimeter, is used as a reference point when calculating the density of other materials. However, the standard unit of density in the International System of Units (SI) is kilograms per cubic meter (kg/m³).

There are several other units commonly used to measure density :

1. Grams per cubic centimeter (g/cm³) – It is used for solids and liquids.
2. Grams per milliliter (g/mL) – Equivalent to g/cm³, commonly used for liquids.
3. Pounds per cubic foot (lb/ft³) – A common unit used in the United States, especially for materials like wood or construction materials.
4. Pounds per gallon (lb/gal) – Used in some industries, such as for liquids like oil or chemicals.

Also Read,

• Unit of Work
• Unit of Energy

Methods to Calculate Density

There are following methods to calculate density:

Direct Measurement Methods

• This method involves directly measuring the mass and volume of an object to calculate its density.
• For solids, mass can be measured using a scale or balance, while the volume can be determined using geometric calculations (for regular shapes) or displacement methods (for irregular shapes).
• For liquids, volume is typically measured using a graduated cylinder, and mass is measured with a balance.
• Once both mass and volume are determined, density can be calculated by dividing mass by volume.

Archimedes' Principle Method

• Archimedes' principle is used to determine the volume and density of irregular objects that cannot be easily measured using conventional methods.
• This method involves immersing the object in a liquid (usually water) and measuring the amount of liquid displaced.
• The volume of the displaced liquid is equal to the volume of the object. To calculate density, first measure the mass of the object, then divide it by the volume of displaced liquid (which gives you the object's volume).
• Density is calculated using the formula density = mass / volume of displaced liquid.

Hydrometer Method

• A hydrometer is a simple instrument used to measure the density (or specific gravity) of liquids, commonly in applications like brewing, winemaking, and chemical analysis.
• The hydrometer consists of a graduated stem and a bulb filled with liquid, allowing it to float in the liquid being tested.
• When placed in a liquid, the level to which the hydrometer sinks correlates with the density of the liquid.
• The deeper it sinks, the less dense the liquid is; the higher it floats, the denser the liquid.
• Density is determined by reading the scale on the hydrometer, which gives the specific gravity or relative density compared to water.

Pycnometer Method

• A pycnometer is a small, precisely calibrated glass vessel used to measure the density of liquids and fine powders.
• The pycnometer has a known volume, and it is typically used to measure the density of substances that are difficult to measure by other methods.
• To use the pycnometer, first, the substance (liquid or powder) is placed in the pycnometer, and its mass is measured.
• The volume is already known based on the pycnometer’s design. For liquids, the pycnometer is filled, and the liquid’s density is calculated. For powders, the substance is weighed and then the volume is measured by displacement.
• Density is then calculated using the formula density = mass /volume.

Gas Displacement Method

• The Gas Displacement Method is used to measure the concentration or density of a gas by replacing a known volume of one gas with the gas of interest.
• In this method, the volume and mass of the displaced gas are measured, and the density of the gas can be calculated based on the conditions (such as pressure and temperature).
• The ideal gas law, or other relevant gas laws, can be applied to determine the gas's density using the formula=mass of gas/volume of gas.

X-ray Crystallography Method

• X-ray crystallography is a technique used to determine the atomic structure of a material by analyzing how X-rays diffract through a crystal.
• When X-rays pass through a crystal, they scatter in specific patterns. By studying these diffraction patterns, scientists can determine the precise positions of atoms within the crystal lattice.
• This method provides valuable information about the material's atomic arrangement and density, offering insights into its properties and structure.

Ultrasonic Method

• Ultrasonic densitometers use high-frequency sound waves to measure the density of liquids and solids.
• By sending sound waves through a material and measuring the speed at which the sound travels, the density of the material can be calculated.
• This is based on the known relationship between the speed of sound, density, and temperature.
• The method is particularly useful for measuring the density of fluids or materials that are difficult to handle or sample directly, providing quick and non-destructive results.

Applications of Density in Real Life

The real life applications of density is given below:

• Food and Beverage: Used to determine sugar content in drinks, ensuring product quality and consistency.

• Oil and Gas: Helps geologists identify and extract resources by analyzing the density of rock formations.

• Archaeology and Geology: Used to date fossils, study rocks, and understand Earth's geological history.

• Construction and Engineering: Ensures soil and asphalt compaction for the stability of roads, buildings, and infrastructure.

• Aerospace: Guides design and performance of aircraft and spacecraft by analyzing material density.

• Oceanography and Marine Biology: Studies ocean currents, salinity, and marine life distribution, helping to understand ecosystems and climate.

• Forensic Science: Assists in analyzing evidence, such as objects from crime scenes, and verifying authenticity.

• Manufacturing and Materials Science: Evaluates material quality and strength, ensuring proper application in industries like automotive and construction.

Solved Examples

Example 1. Calculate the density of water if it has a mass of 1160kg and a volume of 1m³?

Solution:

Given,

Mass = 1160kg

Volume = 1m³

Density is given by the formula:

Density = Mass / Volume

ρ = 1160/1 = 1600 kg/m³

Example 2. A block of wood has a mass of 1200 grams and a volume of 600 cubic centimeters. Calculate the density of the wood block in grams per cubic centimeter.

Solution:

Given,

Mass = 11200 grams

Volume = 600 cubic centimeters

Formula: Mass/Volume

Substitute the given values into the formula

Density = 1200 grams/ 600 cubic centimeters

Density = 2 grams/ cubic centimeter

The density of the wood block is 2 grams per cubic centimeter.

Example 3. A liquid has a density of 0.8g/mL and a volume of 100 mL. Calculate the mass of the liquid in grams.

Solution:

Given,

Density = 0.8g/mL

Volume = 100mL

The formula for calculating mass using density and volume is:

Mass = Density × Volume

Substitute the given values into the formula:

Mass = 0.8g/mL × 100mL

Mass = 80 grams

The mass of the liquid is 80 grams.

Related Reads,

• Relative Density
• How to calculate Energy Density?
• What is the Density of Water?