1. Density Measurement
1.1 Principle of Measurement
The basic principle of density measurement is based on Archimedes’ Law, which states that an object submerged in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.
1.2 Measuring Instruments and Materials
1.2.1 Precision Balance
The precision balance should have a weighing range up to 10g with a mass tolerance of ±0.1mg. For samples above 10g, the accuracy should be ±0.001%.
1.2.2 Container
A beaker is typically used as the container. The size should be chosen so that when the sample is immersed in the liquid, the rise in liquid level does not exceed 2.5 mm.
1.2.3 Pycnometer
A pycnometer with a volume of 10 mL is recommended for accurate measurements.
1.2.4 Liquid
1.2.4.1 For density measurements, distilled or deionized water is commonly used. The density values at different temperatures are listed in Table 1 below:
Table 1: Density of Distilled or Deionized Water at Different Temperatures in Air
Temperature, °C | Density, g/cm³ | Temperature, °C | Density, g/cm³ |
10.0 | 0.99970 | 20.0 | 0.99820 |
15.0 | 0.99910 | 25.0 | 0.99704 |
10.5 | 0.99965 | 20.5 | 0.99810 |
15.5 | 0.99902 | 25.5 | 0.99691 |
11.0 | 0.99960 | 21.0 | 0.99799 |
16.0 | 0.99894 | 26.0 | 0.99678 |
11.5 | 0.99955 | 21.5 | 0.99788 |
16.5 | 0.99886 | 26.5 | 0.99665 |
12.0 | 0.99949 | 22.0 | 0.99777 |
17.0 | 0.99877 | 27.0 | 0.99651 |
12.5 | 0.99943 | 22.5 | 0.99765 |
17.5 | 0.99868 | 27.5 | 0.99637 |
13.0 | 0.99937 | 23.0 | 0.99754 |
18.0 | 0.99859 | 28.0 | 0.99623 |
13.5 | 0.99931 | 23.5 | 0.99742 |
18.5 | 0.99850 | 28.5 | 0.99609 |
14.0 | 0.99924 | 24.0 | 0.99729 |
19.0 | 0.99840 | 29.0 | 0.99594 |
14.5 | 0.99917 | 24.5 | 0.99717 |
19.5 | 0.99830 | 29.5 | 0.99580 |
1.2.4.2 The temperature of the liquid must be balanced with the ambient temperature during the measurement to ensure consistency and accuracy.
1.2.5 Thermometer
A thermometer with an accuracy of ±0.5°C is required to monitor the temperature of the liquid during the process.
1.2.6 Fine Wire
The wire used for suspending the sample should have a diameter no more than 0.25 mm to minimize any impact on the measurement results.
1.3 Sample Preparation
1.3.1 The surface of the sample should be clean, smooth, and free from oil or contaminants. If there is a coating, it should be removed before testing to avoid interference.
1.3.2 The sample volume should be greater than 0.5 cm³. If the sample is too small, multiple samples can be combined to meet the minimum volume requirement.
1.3.3 The temperature of the sample should be adjusted to match the ambient temperature before starting the measurement.
1.4 Procedure for Density Measurement
1.4.1 Large Volume Samples (Volume > 0.5 cm³)
1.4.1.1 Weigh the dry and clean sample in air to determine its mass (mâ‚€).
1.4.1.2 For water-absorbing samples, apply a thin layer of paraffin or Vaseline to the surface to prevent moisture absorption. Then, weigh the treated sample in air (mâ‚).
1.4.1.3 Suspend the sample in water using a fine wire, ensuring it is at least 10 mm away from the surface. Remove any air bubbles and weigh the sample in water (mâ‚‚).
1.4.1.4 Weigh the wire alone in water to determine its mass (m₃).
1.4.1.5 Measure the temperature (t) of the liquid during the process.
1.4.1.6 Calculations
The density of non-absorbent samples is calculated using formula (1):
……………………………………… (1)
The density of water-absorbing samples is calculated using formula (2):
……………………………………… (2)
In formulas (1) and (2):
D = Density of the sample, g/cm³;
D₀ = Density of the liquid at temperature t, g/cm³;
mâ‚€ = Mass of the sample in air, g;
mâ‚ = Mass of the water-absorbing sample after treatment, g;
mâ‚‚ = Mass of the sample in water (including wire), g;
m₃ = Mass of the wire in water, g.
The final result should be rounded to two decimal places.
1.4.2 Small Volume Samples (Volume ≤ 0.5 cm³)
1.4.2.1 Weigh the dry and clean sample in air to obtain mâ‚€.
1.4.2.2 Treat water-absorbing samples using the method described in 1.4.1.2, then weigh them in air (mâ‚).
1.4.2.3 Weigh the pycnometer filled with liquid to get mâ‚‚.
1.4.2.4 Place the sample into the pycnometer, remove any air bubbles, and weigh the total mass (m₃).
1.4.2.5 Measure the temperature (t) of the liquid.
1.4.2.6 Calculations
The density of non-absorbent samples is calculated using formula (3):
.............................................(3)
The density of water-absorbing samples is calculated using formula (4):
.............................................(4)
In formulas (3) and (4):
D = Density of the sample, g/cm³;
D₀ = Density of the liquid at temperature t, g/cm³;
mâ‚€ = Mass of the sample in air, g;
mâ‚ = Mass of the water-absorbing sample after treatment, g;
mâ‚‚ = Mass of the pycnometer filled with liquid, g;
m₃ = Mass of the pycnometer containing the sample and liquid, g.
All results should be presented with two decimal places for clarity and precision.
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