Density (chemistry): Difference between revisions
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For a homogeneous solid object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate [[Weighing scale|weighing scale or balance]] and the volume may be measured directly (from the geometry of the object) or by the displacement of a liquid. | For a homogeneous solid object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate [[Weighing scale|weighing scale or balance]] and the volume may be measured directly (from the geometry of the object) or by the displacement of a liquid. | ||
One of the many statements attributed to the [[Archimedes principle]] is that an object immersed in a fluid apparently loses weight by an amount equal to the weight of the fluid displaced.<ref>[http://www.csudh.edu/oliver/satcoll/archmede.htm California State University Dominguez Hills]</ref> That principle makes it possible to determine of the density of a solid object that is denser than water and is so irregular in shape that its volume cannot be measured directly. | |||
First, the object's dry weight in air, <math>W_d</math>, is measured. Next, the weight of the object while submerged in water, <math>W_s</math>, is measured. Then the submerged object is removed from the water, the excess surface water is removed and the wet weight in air, <math>W_w</math>, is measured.<ref>{{cite book|author=American Society of Composites|title=American Society of Composites, Ninth International Conference Proceedings|edition=|publisher=CRC Press|year=1994|pages=page 539|id=1-56676-220-0}}</ref> The density of the object, <math>\rho_o</math>, is then obtained from: | |||
:<math>\rho_o = \frac{m}{V} = \frac{W_d}{(W_w - W_s)/\rho_{water}} = \frac{W_d \cdot \rho_{water}}{W_w - W_s}</math> | |||
and the volumetric [[porosity]] fraction, <math>p</math> can be obtained from: | |||
:<math>p = \frac{W_w - W_d}{W_w - W_s}</math> | |||
If the object has no porosity (i.e., a porosity fraction of zero), then <math>W_w</math> and <math>W_d</math> will be equal. | |||
A very simple and commonly used instrument for directly measuring the density of a liquid is the [[hydrometer]]. A less common device for measuring fluid density is a pycnometer and a similar device for measuring the absolute density of a solid is a gas pycnometer. | A very simple and commonly used instrument for directly measuring the density of a liquid is the [[hydrometer]]. A less common device for measuring fluid density is a pycnometer and a similar device for measuring the absolute density of a solid is a gas pycnometer. | ||
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:'''''L''''' is [[Loschmidt]] or [[Avogadro's constant]] | :'''''L''''' is [[Loschmidt]] or [[Avogadro's constant]] | ||
:'''''a''''', '''''b''''', '''''c''''' are the [[lattice parameters]] | :'''''a''''', '''''b''''', '''''c''''' are the [[lattice parameters]] | ||
==Density of gases== | ==Density of gases== |
Revision as of 14:53, 12 June 2008
Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. The higher an object's density, the higher its mass per volume. The density of an object equals its total mass divided by its total volume. An object made of a denser material (such as iron) will have less volume than an equal mass of some less dense substance (such as water). The SI unit of density is the kilogram per cubic metre (kg/m3)
where:
- ρ is the object's density (measured in kilograms per cubic metre)
- m is the object's total mass (measured in kilograms)
- V is the object's total volume (measured in cubic metres)
Under specified conditions of temperature and pressure, the density of a fluid is defined as described above. However, the density of a solid material can be defined in several ways. Porous or granular materials have a density of the solid material, as well as a bulk density, which can be variable. For example, if you gently fill a container with sand, and divide the mass of sand by the container volume you get a value termed loose bulk density. If you took this same container and tapped on it repeatedly, allowing the sand to settle and pack together, and then calculate the results, you get a value termed tapped or packed bulk density. Tapped bulk density is always greater than or equal to loose bulk density. In both types of bulk density, some of the volume is taken up by the spaces between the grains of sand. The density of the sand grains, exclusive of the air between the grains, will be higher than the bulk density.
In candy making, density is affected by the melting and cooling processes. Loose granular sugar, like sand, contains a lot of air and is not tightly packed, but when it has melted and starts to boil, the sugar loses its granularity and some entrained air and becomes a fluid. When molded to make a smaller, compacted shape, the syrup tightens up and loses more air. As it cools, it contracts and gains moisture, making the already heavy candy even more dense.
Other units
Density in terms of the SI base units is expressed in kilograms per cubic meter (kg/m3). Other units fully within the SI include grams per cubic centimetre (g/cm3) and megagrams per cubic metre (Mg/m3). Since both the litre and the tonne or metric ton are also acceptable for use with the SI, a wide variety of units such as kilograms per litre (kg/L) are also used. Imperial units or U.S. customary units, the units of density include pounds per cubic foot (lb/ft³), pounds per cubic yard (lb/yd³), pounds per cubic inch (lb/in³), ounces per cubic inch (oz/in³), pounds per gallon (for U.S. or imperial gallons) (lb/gal), pounds per U.S. bushel (lb/bu), in some engineering calculations slugs per cubic foot, and other less common units.
The maximum density of pure water at a pressure of one standard atmosphere is 999.861 kg/m3; this occurs at a temperature of about 3.98 °C (277.13 K).
From 1901 to 1964, a litre was defined as exactly the volume of 1 kg of water at maximum mass, and the maximum density of pure water was 1.000 000 kg/L (now 0.999 972 kg/L). However, while that definition of the litre was in effect, just as it is now, the maximum density of pure water was 0.999 972 kg/dm3. During that period students had to learn the esoteric fact that a cubic centimetre and a millilitre were slightly different volumes, with 1 mL = 1.000 028 cm³. (often stated as 1.000 027 cm³ in earlier literature).
Measurement of density
For a homogeneous solid object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate weighing scale or balance and the volume may be measured directly (from the geometry of the object) or by the displacement of a liquid.
One of the many statements attributed to the Archimedes principle is that an object immersed in a fluid apparently loses weight by an amount equal to the weight of the fluid displaced.[1] That principle makes it possible to determine of the density of a solid object that is denser than water and is so irregular in shape that its volume cannot be measured directly.
First, the object's dry weight in air, , is measured. Next, the weight of the object while submerged in water, , is measured. Then the submerged object is removed from the water, the excess surface water is removed and the wet weight in air, , is measured.[2] The density of the object, , is then obtained from:
and the volumetric porosity fraction, can be obtained from:
If the object has no porosity (i.e., a porosity fraction of zero), then and will be equal.
A very simple and commonly used instrument for directly measuring the density of a liquid is the hydrometer. A less common device for measuring fluid density is a pycnometer and a similar device for measuring the absolute density of a solid is a gas pycnometer.
Another instrument used to determine the density of a liquid or a gas is the digital density meter, based on the oscillating U-tube principle.
For some crystalline materials, density can be calculated based on crystallographic information and molecular mass:
where:
- M is molecular mass
- N is the number of atoms in a unit cell
- L is Loschmidt or Avogadro's constant
- a, b, c are the lattice parameters
Density of gases
From the ideal gas law, the density of an ideal gas may be expressed as:
and the density of a real gas (as differentiated from an ideal gas) may be expressed as:
where is the compressibility factor, is the molar gas constant, is the pressure, is the molecular mass, and is the absolute temperature.
Thus, at an atmospheric pressure of 101.325 kPa, an absolute temperature of 273.15 K ( 0 °C ) and using as 8.314472 m3·Pa·K-1·mol-1, the density of a real gas in kg/m3 is given by:
At atmospheric pressure and 0 °C, most gases may be considered to be ideal and therefore the compressibility factor, , can be taken to be 1. At other conditions of temperature and pressure, where a gas may deviate from ideal gas behavior, the compressibility factor may be calculated using the van der Waals equation (see Compressibility factor (gases)#The van der Waals equation).
Density of various substances
Perhaps the highest density known is reached in neutron star matter (see neutronium). The singularity at the centre of a black hole, according to general relativity, does not have any volume, so its density is undefined.
Substance | Density (kg/m³) |
Substance | Density (kg/m³) | |
---|---|---|---|---|
Iridium | 22,650 | Diamond | 3,500 | |
Osmium | 22,610 | Basalt | 3,000 | |
Platinum | 21,450 | Granite | 2,700 | |
Gold | 19,300 | Aluminum | 2,700 | |
Tungsten | 19,250 | Graphite | 2,200 | |
Uranium | 19,050 | Magnesium | 1,740 | |
Mercury | 13,580 | Polyvinylchloride (PVC) | 1,300 | |
Palladium | 12,023 | Seawater (15 °C) | 1,025 | |
Lead | 11,340 | Water | 1,000 | |
Silver | 10,490 | Ice (0 °C) | 917 | |
Copper | 8,960 | Polyethylene | 910 | |
Iron | 7,870 | Ethyl alcohol | 790 | |
Steel | 7,850 | Gasoline | 730 | |
Tin | 7,310 | Liquid Hydrogen | 68 | |
Titanium | 4,507 | Aerogel | 3 |
The densest naturally occurring substance on Earth is iridium, at about 22,650 kg/m3. Aerogel is the world's lightest solid. Also, note the low density of aluminium compared to most other metals. For this reason, aircraft are made of aluminium.
Temperature ( °C ) |
Density ( kg/m³ ) |
---|---|
- 10 | 1.341 |
- 5 | 1.316 |
0 | 1.293 |
+ 5 | 1.269 |
+ 10 | 1.247 |
+ 15 | 1.225 |
+ 20 | 1.204 |
+ 25 | 1.184 |
+ 30 | 1.164 |
The effect of temperature on the density of solids and fluids
The relation between temperature and the density of solids and fluids can be expressed as:
where:
- C is the coefficient of cubic expansion.
- ↑ California State University Dominguez Hills
- ↑ American Society of Composites (1994). American Society of Composites, Ninth International Conference Proceedings. CRC Press, page 539. 1-56676-220-0.