How do you find the capacity of a density bottle?

To find the capacity of a density bottle, you essentially determine the volume it can hold. This is typically done by weighing the bottle empty and then full of a liquid of known density, usually water.

Steps to Determine the Capacity

Here's a step-by-step guide:

1. Weigh the Empty, Dry Density Bottle: Clean and thoroughly dry the density bottle, including the stopper. Weigh it accurately using a balance. Let's denote this mass as m₁.

2. Fill the Density Bottle with a Liquid of Known Density: Carefully fill the density bottle completely with a liquid whose density is accurately known. Distilled water is commonly used because its density is well-established at various temperatures. Ensure there are no air bubbles. Insert the stopper, which will displace any excess liquid. Wipe the outside of the bottle dry.

3. Weigh the Density Bottle Filled with the Liquid: Weigh the filled density bottle accurately. Let's denote this mass as m₂.

4. Calculate the Mass of the Liquid: Subtract the mass of the empty bottle (m₁) from the mass of the bottle filled with liquid (m₂) to find the mass of the liquid. This is: m_liquid = m₂ - m₁.

5. Calculate the Volume (Capacity): Use the density of the liquid (ρ) and the mass of the liquid (m_liquid) to calculate the volume using the formula:

   Volume (V) = Mass / Density or V = m_liquid / ρ

   If you're using water, you'll need to know the density of water at the temperature at which you performed the experiment. For example, the density of water at approximately 20°C is 0.9982 g/mL. You can find more precise values in standard reference tables.

Example

Let's say:

• m₁ (mass of empty density bottle) = 20.00 g
• m₂ (mass of density bottle filled with water) = 70.00 g
• Density of water (ρ) at the experimental temperature = 0.9982 g/mL

Then:

1. m_liquid = 70.00 g - 20.00 g = 50.00 g
2. V = 50.00 g / 0.9982 g/mL ≈ 50.09 mL

Therefore, the capacity of the density bottle is approximately 50.09 mL.

Important Considerations

• Temperature: The density of liquids, especially water, varies with temperature. Be sure to use the correct density value for the temperature at which you are working.
• Accuracy: Accurate weighing is crucial. Use a balance with sufficient precision.
• Cleanliness: A clean and dry density bottle is essential for accurate results.