7.2 MEASURING DENSITIES OF DIFFERENT SUBSTANCES

To measure the densities of liquids, solids (regular shaped or irregular shape), we will follow some steps in each case, which we will explain below:

Density of Liquids

  1. Place the empty measuring cylinder on balance and measure its mass.
  2. Add liquid in the measuring cylinder and measure its volume.
  3. Subtract mass of empty cylinder from the mass of cylinder and liquid (measured in step 2).
  4. Measure volume of liquid from the measuring cylinder.
  5. To calculate the density of liquid, divide mass of liquid by its volume.

EXAMPLE 7.2: DENSITY OF LIQUID

Mass of empty measuring cylinder is 145 g. We add a 60 mL liquid in it. Now, its mass becomes 205 g. Find density of the liquid?

Given:
Mass of empty cylinder = 145 g
Mass of measuring cylinder and added liquid = 205 g
Volume of liquid = 60 mL

Required: Density of the liquid ρ?

Solution:
Mass of liquid is calculated by:
Mass of liquid = Mass of measuring cylinder and liquid - Mass of empty cylinder
Mass of liquid = 205 g - 145 g = 60 g
Density of liquid is calculated by:
ρ = Mass of liquid / Volume of liquid
Putting values:
ρ = 60 g / 60 mL = 1 g/mL
Density of liquid is 1 gram per milliliter. As this is the density of water (at 4°C), so our liquid in the measuring cylinder is water.

7.2.1 DENSITY OF REGULARLY SHAPED SOLIDS

To find density of regularly shaped solids (like solid cubes, solid cuboids, solid sphere etc.), we will follow these steps:

  1. Find mass of the solid regular shaped object using balance.
  2. Calculate the volume of object using formula according to shape of the object.
    For example:
    • Volume of cuboid = Length x Width x Height
    • Volume of cube = (side length)³
    • Volume of sphere = 4/3 πr³
  3. Finally, calculate its density by using the formula:
    Density of Solid = Mass of Solid / Volume of Solid

EXAMPLE 7.3: DENSITY OF BRICK

Find the density of a solid brick of mass 3.30 kg as shown in the figure.

Given:
Mass of brick = 3.30 kg
Length of brick = 21.6 cm = 0.216 m
Width of brick = 10.2 cm = 0.102 m
Height of brick = 6.35 cm = 0.0635 m

Required: Density of the solid object ρ = ?

Solution:
First, we calculate the volume of regular brick by:
Volume = Length x Width x Height
Putting values:
Volume = 0.216 m × 0.102 m × 0.0635 m = 0.00140 m³
Now, we will find density of the brick using formula:
Density of brick = Mass of brick / Volume of brick
Putting values:
ρ = 3.3 kg / 0.00140 m³ ≈ 2358.773 kg/m³ ≈ 2360 kg/m³

7.2.2 DENSITY OF IRREGULAR SHAPED OBJECT (DISPLACEMENT METHOD)

We can find the density of irregular shaped solid objects like stones which can sink in the water. We need a graduated measuring cylinder to measure volume and balance to measure mass of object. We will follow these steps to find its density:

  1. Find the mass of the irregular shaped stone.
  2. Add some water in measuring cylinder and measure its initial volume (Vi).
  3. Tie a thread with the irregular shaped object (e.g., stone) and lower it in the measuring cylinder.
  4. Water will rise (i.e., displace) in the measuring cylinder; measure final volume (Vf). This final volume reading is the sum of the volume of water and volume of object.
  5. Subtract initial volume (Vi) from final volume (Vf) to get the volume of the object.
    Volume of object = Vf - Vi
  6. To find density of objects, divide the mass of object by its volume.
    Density of Solid = Mass of Solid / Volume of Solid

EXAMPLE 7.4: VOLUME AND DENSITY OF IRREGULAR SHAPE

Mass of a rock is 80.52 grams. It was immersed in a measuring cylinder containing water. From the figure, find the initial and final volumes of water. Use this data to find volume of object and density.

Given:
Mass of rock = 80.52 g
Initial volume of water = 18 mL
Final volume of water = 46 mL

Required:
Volume of object = final volume - Initial volume
Volume of object = 46 mL - 18 mL = 28 mL = 28 cm³

Density of irregular shaped stone is:
Density of object = Mass of object / Volume of object
Putting values:
ρ = 80.52 g / 28 cm³ ≈ 2.88 g/cm³