How Were Densities of Different Substances Determined?

The densities of different substances are determined by measuring their mass and volume and then calculating the density using the formula: Density = Mass / Volume (D = m/v).

Here's a breakdown of the process:

Steps for Determining Density

1. Measure the Mass:

   • Use a balance or scale to accurately measure the mass of the substance. The mass is typically measured in grams (g) or kilograms (kg).

2. Determine the Volume:

   • For Regularly Shaped Objects: Measure the dimensions (length, width, height, radius, etc.) and use the appropriate geometric formula to calculate the volume. For example:
     • Cube: Volume = side³
     • Rectangular prism: Volume = length × width × height
     • Cylinder: Volume = π × radius² × height
   • For Irregularly Shaped Objects (Solids): Use the water displacement method.
     • Partially fill a graduated cylinder with a known volume of liquid (usually water). Record the initial volume.
     • Carefully submerge the object in the liquid.
     • Record the new volume of the liquid.
     • The volume of the object is the difference between the final and initial volumes. This is based on Archimedes' principle.
   • For Liquids: Use a graduated cylinder or a volumetric flask to directly measure the volume.

3. Calculate the Density:

   • Divide the mass by the volume to obtain the density. The density is typically expressed in units of grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). For example:
     • Density (ρ) = Mass (m) / Volume (V)

Considerations and Examples

• Accuracy: Precise measurements of both mass and volume are critical for accurate density determination.
• Temperature: Density is temperature-dependent, as volume changes with temperature. Therefore, it's important to specify the temperature at which the density is measured.
• Example: To find the density of a rock, you would first weigh it on a scale (e.g., 150 grams). Then, using water displacement, you determine that the rock displaces 50 mL of water (which is equal to 50 cm³). The density is calculated as 150 g / 50 cm³ = 3 g/cm³.

Factors Affecting Density

Density is influenced by:

• Atomic Mass: Heavier atoms generally contribute to higher densities.
• Atomic Arrangement: How closely atoms are packed together impacts density. Substances with tightly packed atoms tend to be denser.
• Interatomic Spacing: Smaller interatomic distances lead to higher density.

In summary, the density of a substance is experimentally determined by carefully measuring its mass and volume and applying the formula Density = Mass/Volume, taking into account factors like temperature and the shape of the substance.