How is density measured experimentally?

Density is experimentally measured by determining an object's mass and volume, then dividing the mass by the volume. A common method, especially for irregularly shaped objects, involves using an auxiliary liquid of known density.

Steps for Experimental Density Measurement

Here's a detailed breakdown of the method using an auxiliary liquid:

1. Mass Measurement:

   • First, the mass of the sample is measured using a balance. This is the mass of the sample required for the density calculation.

2. Volume Determination Using an Auxiliary Liquid:

   • An auxiliary liquid with a known density is used.
   • The liquid's container is weighed. This is the initial mass of the container with the liquid.
   • The sample is carefully immersed in the liquid. This increases the liquid level which is equivalent to the sample's volume.
   • The container with liquid and the immersed sample is weighed again. This is the mass of the container with the liquid and sample
   • The mass difference (the difference between the weight of liquid and container after and before immersing the sample) is noted. A tare can also be used to get the difference directly.
   • Using the known density of the auxiliary liquid, and the mass difference measured, the volume of the sample can be determined. The volume is determined using the following relationship:
   • Volume of sample = Mass difference / Density of auxiliary liquid

3. Density Calculation:

   • Once both the mass of the sample and volume of the sample are known, the density can be calculated using the formula:
   • Density = Mass of Sample / Volume of Sample

Example

Let's illustrate with an example:

• Imagine we want to determine the density of a small rock.
• We weigh the rock and find that it has a mass of 100 grams.
• We use water as our auxiliary liquid. The density of water is approximately 1 g/cm³.
• We weigh a container with water and note the mass.
• We then immerse the rock into the water. We note that the mass of the container, water, and rock together is 105g. Therefore, the increase of 5g mass is due to the immersion of the rock. This mass is also equivalent to the mass of displaced water.
• The displaced water has a volume of 5 cm³ using the water density of 1 g/cm³ and the relationship Volume = Mass / Density.
• Therefore, the rock has a volume of 5 cm³ (since the rock displaces the same volume as its own).
• The density of the rock is thus: Density = 100g / 5 cm³ = 20 g/cm³.

Key Considerations

• Accuracy: For accurate measurements, it's crucial to use precise balances and carefully note volume changes.
• Liquid Choice: The auxiliary liquid should be chosen so that it does not react with the sample. It must have a known density and be able to completely surround the sample.
• Taring: Tare can be used to measure the mass differences directly. This improves the experimental workflow and reduces chance of error.
• Sample Immersion: Ensure the sample is fully immersed in the auxiliary liquid and that no air bubbles are trapped.
• Irregular Shapes: This method is particularly valuable for measuring the volume of irregularly shaped objects, for which direct geometric calculations aren't possible.