How do you measure density by specific gravity bottle?

Specific gravity bottles, also known as pycnometers, measure liquid density by comparing the mass of a substance to the mass of an equal volume of water. Here's a detailed look at the process:

Understanding the Principles

The specific gravity bottle method is based on a few key principles:

• Volume Consistency: Specific gravity bottles are designed to hold a very precise volume when filled to a marked line.
• Mass Measurement: The difference in mass between the bottle when empty and when filled with a liquid tells us the mass of the liquid sample.
• Specific Gravity: By comparing the liquid's mass to the mass of an equal volume of water, we find its specific gravity, which is the ratio of the substance's density to that of water. The density of water at a known temperature can then be used to derive the liquid's absolute density.

Steps for Measuring Density

Here's how to measure density using a specific gravity bottle:

1. Weigh the Empty Bottle: First, clean and dry the specific gravity bottle thoroughly. Then, weigh it using an accurate balance. Note the weight; we'll call this M_empty.
2. Fill with Liquid: Fill the bottle completely with the liquid you want to measure, ensuring no air bubbles are trapped. The meniscus of the liquid should precisely align with the marked line on the bottle.
3. Weigh the Filled Bottle: Weigh the bottle filled with liquid, again using the accurate balance. Record this as M_filled.
4. Determine Liquid Mass: Subtract the empty bottle's weight from the filled bottle's weight to find the mass of the liquid. That is M_liquid = M_filled - M_empty.
5. Repeat with Water: Empty and clean the specific gravity bottle. Now fill it with distilled water up to the mark and weigh it again. Note this mass as M_water. Determine the mass of water: M_water - M_empty.
6. Calculate Specific Gravity: According to the reference, the specific gravity is calculated by dividing the mass of the liquid sample by the mass of the same volume of water. Therefore, specific gravity = M_liquid / (M_water - M_empty).
7. Calculate Density: Once you have the specific gravity, you can calculate the density of the liquid. Density = specific gravity * density of water at the temperature of your measurement (usually 1 g/mL or 1000 kg/m³ at around 4°C).

Example Calculation

Let's say:

• Mass of empty bottle (M_empty) = 25 g
• Mass of bottle with liquid (M_filled) = 50 g
• Mass of bottle with water (M_water) = 50g

Then:

• Mass of liquid (M_liquid) = 50 g - 25 g = 25 g
• Mass of water = 50g - 25g = 25 g
• Specific gravity = 25 g/25 g = 1
• Density = Specific gravity Density of water = 1 1 g/mL = 1 g/mL.

Practical Insights

• Temperature Control: Density is affected by temperature; ensure your measurements are taken at a controlled temperature or record the temperature of the measurement.
• Accuracy: The accuracy of the measurement depends on the precision of the balance and the careful filling of the bottle to the mark.
• Cleaning: Always ensure the specific gravity bottle is thoroughly cleaned and dried between uses to avoid errors.

In summary, specific gravity bottles measure density by finding the ratio of a liquid's mass to the mass of an equal volume of water. This ratio is known as specific gravity, and the liquid density can then be derived.