Define density. Describe methods to determine the densities of regular and irregular-shaped solids, liquids, and gases.

Definition of Density:

Density is defined as the mass of an object per unit volume. It is mathematically expressed as:

Density=Mass/Volume​

The standard unit of density is typically grams per milliliter (g/mL) for liquids and solids, and kilograms per cubic meter (kg/m³) for gases.

Methods to Determine the Densities of Different Substances:

1. Regular-Shaped Solids:

For objects with regular geometric shapes (like cubes, spheres, or cylinders), density can be determined using the formula:

Density=Mass/Volume​

• Mass: Measure the mass using a balance or scale.
• Volume: Calculate the volume based on the shape. For example:
  • For a cube: Volume = side³
  • For a sphere: Volume = 4/3πr³
  • For a cylinder: Volume = πr²h, where $r$ is the radius and $h$ is the height.

2. Irregular-Shaped Solids:

For irregularly shaped objects, volume can be determined by displacement of water (Archimedes’ principle):

• Mass: Measure the mass using a balance.
• Volume: Submerge the object in a known volume of water. The change in water level gives the volume of the object. The volume of the displaced water is equal to the volume of the object.

Density is then calculated using the formula:

Density=Mass/Volume (displaced water)​

3. Liquids:

To determine the density of a liquid:

• Mass: Measure the mass of the liquid using a balance.
• Volume: Measure the volume using a graduated cylinder or volumetric flask.

Then, use the formula:

Density=Mass/Volume​

4. Gases:

To determine the density of a gas:

• Mass: Measure the mass of the gas (often done by weighing a container before and after filling it with gas).
• Volume: Measure the volume of the gas using a gas syringe or another device that can hold and measure gas.

For gases, the density is often calculated at standard temperature and pressure (STP) and can be related to the molar mass using the ideal gas law.

Density=Mass/Volume or Density=P⋅M/R⋅T​

where $P$ is pressure, $M$ is the molar mass of the gas, $R$ is the gas constant, and T is temperature in Kelvin.