The specific weight (also known as the unit weight) is the weight per unit volume of a material. The symbol of

specific weight is γ (the Greek letter Gamma).

A commonly used value is the specific weight of water on Earth at 5°C which is 62.43 lbf/ft3 or 9807 N/m3. [1]

The terms specific gravity, and less often specific weight, are also used for relative density.

Mathematically: Density = Mass Divided By Volume

where:

ρ (rho) is the density,

m is the mass,

V is the volume.

Different materials usually have different densities, so density is an important concept

regarding buoyancy, metal purity and packaging.

In some cases density is expressed as the dimensionless quantities specific gravity (SG)

or relative density (RD), in which case it is expressed in multiples of the density of some

other standard material, usually water or air/gas.

Relative density, or specific gravity,[1][2] is the ratio of the density (mass of a unit volume) of a substance to the

density of a given reference material. Specific gravity usually means relative density with respect to water. The term

"relative density" is often preferred in modern scientific usage.

If a substance's relative density is less than one then it is less dense than the reference; if greater than 1 then it is

denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the

two substances have the same mass. If the reference material is water then a substance with a relative density (or

specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will

float. A substance with a relative density greater than 1 will sink.

Temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always

1 atm equal to 101.325 kPa. Where it is not, it is more usual to specify the density directly. Temperatures for both

sample and reference vary from industry to industry. In British brewing practice the specific gravity as specified above

is multiplied by 1000.[3]Specific gravity is commonly used in industry as a simple means of obtaining information about

the concentration of solutions of various materials such as brines, sugar solutions (syrups, juices, honeys,

brewers wort, must, etc.) and acids.

DENSITY Applications 

with Liquids and Solids

 DENSITY is a physical property of matter, as each element and compound has a unique density associated with it. Density defined in a qualitative manner as the measure of the relative "heaviness" of objects with a constant volume. For liquids the density may also vary with the temperature.

Density Comparison to Water: In chemistry, the density of many substances is compared to the density of water. Does an object float on water or sink in the water? If an object such as a piece of wood floats on water it is less dense than water vs. if a rock sinks, it is more dense than water.

 Liquid Density examples based upon differences in mass or weight per unit volume.

Density of a liquid with a constant volume, varies according to the weight. The higher the weight, the higher the density.

Layers of Liquids Demonstrations:In this series of demonstrations the theme is that a variety of liquids have different physical properties as shown by their densities. The most dense liquids will be found on the bottom, the least dense liquid is on the top. See Table below.Layers of Liquids - Demonstrations with Density

Any objects placed in the liquids will seek their own level depending upon the density. If an object has a density that is intermediate in value, the object will float between two layers.Floating objects in

water

Floating Spheres:In the case of the floating spheres, the water is the most dense and hence on the bottom. If the alcohol is very carefully added to the water with only a minimal mixing, the alcohol will layer on the top of the water since it is less dense. The oil drops that are added are more dense than the alcohol so will fall through the alcohol, but will remain on top of the water. The oil is less dense than the water.See Table below.Floating Spheres - Demonstrations with Density

Lava Lamp: The lava lamp in this demo does not actually work on the principle of original electric lava lamp. In this case, a cylinder is prepared with water on the bottom and oil floating on the top. Small amounts of salt are added. Since salt has a high density of 2.16 g/mL, it forms a coat around some of the oil and causes it to sink, since it now has a higher density than water. As the salt

covered oil drop rests on the bottom of the water, the salt dissolves into the water. When all of the salt has dissolved, the oil drop again rises to the top since it is now again less dense than the water. See Table below.Lava Lamp - Demonstrations with Density

Other Demonstration Examples:Nylon Rope: The adipylchloride or (acid) solution is dissolved in hexane. The hexane is less dense than the the lower water solution and thus floats on top of the water. The chemical reaction occurs right between the two layers. See Table below.

Deep Purple Magic: In this demo, dichloromethane is added to water that contains iodine. The density of the dichloromethane is greater than that of the water, therefore it sinks to the bottom. During the demo, the iodine is extracted from the water into the dichloromethane and gives a very deep purple color.

 

 

 Density examples based upon differences in liquids and solids. The solid has a constant density, but the density of the liquids varies to give various effects.

Ice cubes in different liquids:In this demo ice cubes are placed into two clear liquids which appear to be identical. One liquid is water and the ice cube floats. The other liquid is ethyl alcohol and the ice cube sinks. The ice cube has a constant density, but its behavior changes because of the different densities of the liquids. See Table below.

Mysterious Ice - Demonstrations with Density

Eggs in different liquids:

Again in this demo, the egg has a constant density, but the liquids have different densities. If the egg is more dense than the liquid it will sink as in plain water. If the liquids is more dense than the egg, it will float as in the case of the salt water. See Table below.Egg Densities - sugar water/oilFloating Eggs - sugar and water - Demonstrations with Density

In one case, the egg floats in hydrochloric acid because the bubbles of carbon dioxide attach to the side of the egg and make it less dense than the water so that it floats.Smart Eggs - salt water and acid

- Demonstrations with Density

Liquid Density examples based upon differences in temperature.

There are a number of changes to the structure of water or any other liquid that occurs with increasing temperature. The water molecules gain energy which is used to bend and break the hydrogen bonds. On raising the temperature, the size of ordered clusters of water molecules decreases, the number of smaller clusters increases, the number of hydrogen bonds decreases and the average distance between the water molecules increases.

Underwater Volcano Demonstration: What makes hot water rise? As stated above, the hot water has less hydrogen bonds and the spaces between water molecules increases. The net effect is to have less mass per unit volume. This translates into a lower density. The lower density water floats on top of the denser cold water. In the photo, the hot water is colored with red dye to make it more visible.

 Demonstrations with Density

Mysterious IceLayers of LiquidsEgg Densities - sugar water/oilSmart Eggs - salt water and acid

Floating Eggs - sugar and waterFloating SpheresLava LampUnderwater Smoke StackFloating objects in water

 

 

 Densities of Common

Compounds

 Substance

 Density

grams per mL

Hexane 0.66

0

Ethyl Alcohol 

0.789

 Rubbing Alcohol

 0.79

 Ice  0.92 

Corn oil  0.93

 Water  1.00

 Sea Water (3%)

 1.03

25% Salt water

1.25

Dichloromethane

1.3 

 Corn Syrup

 1.38

 Salt  2.16

 Density of water and iceFor most substances, the solid form of the substance is more dense than the liquid phase; thus, a block of pure solid substance will sink in a tub of pure liquid substance. But, by contrast, a block of common ice will float in a tub of water

because solid water is less dense than liquid water. This is an extremely important characteristic property of water. At room temperature, liquid water becomes denser with lowering temperature, just like other substances. But at 4 °C, just above freezing, water reaches its maximum density, and as water cools further toward its freezing point, the liquid water, under standard conditions, expands to become less dense. The physical reason for this is related to the crystal structure of ordinary ice, known as hexagonal ice Ih. Water, gallium, bismuth, acetic acid, antimony and silicon are some of the few materials which expand when they freeze; most other materials contract. It should be noted however, that not all forms of ice are less dense than liquid water. For example HDA and VHDA are both more dense than liquid phase pure water. Thus, the reason that the common form of ice is less dense than water is a bit non-intuitive, and relies heavily on the unusual properties inherent to the hydrogen bond.

Generally, water expands when it freezes because of its molecular structure, in tandem with the unusual elasticity of the hydrogen bond and the particular lowest energy hexagonal crystal conformation that it adopts under standard conditions. That is, when water cools, it tries to stack in a crystalline lattice configuration that stretches the rotational and vibrational components of the bond, so that the effect is that each molecule of water is pushed further from each of its neighboring molecules. This effectively reduces the density ρ of water when ice is formed under standard conditions.

The importance of this property cannot be overemphasized for its role on the ecosystem of Earth. For example, if water were more dense when frozen, lakes and oceans in a polar environment would eventually freeze solid (from top to bottom). This would happen because frozen ice would settle on the lake and riverbeds, and the necessary warming phenomenon (see below) could not occur in summer, as the warm surface layer would be less dense than the solid frozen layer below. It is a significant feature of nature that this does not occur naturally in the environment.

Nevertheless, the unusual expansion of freezing water (in ordinary natural settings in relevant biological systems), due to the hydrogen bond, from 4 °C above freezing to the freezing point offers an important advantage for freshwater life in winter. Water chilled at the surface increases in density and sinks, forming convection currents that cool the whole water body, but when the temperature of the lake water reaches 4 °C, water on the surface decreases in density as it chills further and remains as a surface layer which eventually freezes and forms ice. Since downward convection of colder water is blocked by the density change, any large body of fresh water frozen in winter will have the coldest water near the surface, away from the riverbed or lakebed. This accounts for various little known phenomena of ice characteristics as they relate to ice in lakes and "ice falling out of lakes" as described by early 20th century scientist Horatio D. Craft.

The following table gives the density of water in grams per cubic centimeter at various temperatures in degrees Celsius:

Temp (°C) Density (g/cm3) 30 0.9957 20 0.9982 10 0.9997 0 0.9998 −10 0.9982 −20 0.9935 −30 0.9839 

The values below 0 °C refer to supercooled water.

Which is more dense - Ice or Liquid Water?

DENSITY is defined in a qualitative manner as the measure of the relative "heaviness" of objects with a constant volume. To understand the properties of ice, we need to think in terms of a change in volume with a constant weight or mass.

Density Comparison to Water: In chemistry, the density of many substances is compared to the density of water. Does ice float on water or sink in the water?

Everyone knows what happens in the case of ice cubes in a glass of water.

Look at the graphic on the left.

Why does ice float?

What other observations or facts are known?

Because ice floats, we can infer that ice must be less dense than water.

If water is frozen in a glass jar, the glass jar breaks.

If a pop can freezes, it will also burst. From both of the above we infer that the

volume of the ice has increased.

Conclusion: The volume of ice must be greater than the same mass of liquid water. Why does the volume increase?

 Molecular basis for the Volume Increase of Ice:

The normal pattern for most compounds is that as the temperature of the liquid increases, the density decreases as the molecules spread out from each other. As the temperature decreases, the density increases as the molecules become more closely packed. This pattern does not hold true for ice as the exact opposite occurs.

In liquid water each molecule is hydrogen bonded to approximately 3.4 other water molecules. In ice each each molecule is hydrogen bonded to 4 other molecules.

Compare the structures of Liquid Water and Solid Ice - Graphic Notice the empty spaces within the ice structure, as this translates to a more open or expanded structure. The ice structure takes up more volume than the liquid water molecules, hence ice is less dense than liquid water.

Chime: Ice/Water - structures from Martin Chaplin

 Mathematical Definition of Density

The formal definition of density is mass per unit volume. Usually the density is expressed in grams per mL or cc. Mathematically a "per" statement is translated as a division. cc is a cubic centimeter and is equal to a mL Therefore,

 Density =

 mass =   g/mL

    volume  

 What is the exact change in volume of the water when it freezes as ice?

Comparison of:

 Liquid water

 Ice

 Mass = 100 g

 Mass = 100 g

 Volume = 100 mL

 Volume = ? mL

 Density = 1.0 g/mL

Density = 0.92 g/mL

Example: Calculate the volume in a 100 g ice cube with a density of 0.92 g per mL.

Solution: The density translated as a conversion factor is: 

0.92 g = 1 mL - "per" is equivalent to an equal sign.

 100 g x

 1.0 mL =

 108.7 mL

 0.92

g 

The increase in volume of ice is about 9%. This increase causes enough force to break most rigid containers. This is the same force, repeated on a daily basis, that creates "pot holes" in the roads in the winter time.

An important property of any gas is its density. Density is defined as the mass of an object divided by its volume, and most of our experiences with density involve solids. We know that some objects are heavier than other objects, even though they are the same size. A brick and a loaf of bread are about the same size, but a brick is heavier--it is more dense. Among metals, aluminum is less dense than iron. That's why airplanes and rockets and some automobile parts are made from aluminum. For the same volume of material, one metal weighs less than another if it has a lower density.

For solids, the density of a single element or compound remains fairly constant because the molecules are bound to one another. For example, if you found a pure gold nugget on the earth or you found a pure gold nugget on the moon, the measured density would be nearly the same. But for gases, the density can vary over a wide range because the molecules are free to move. Air at the surface of the earth has a very different density than air 50 kilometers above the earth. An interactive simulator allows you to study how air density varies with altitude. Understanding density and how it works is fundamental to the understanding of rocket aerodynamics.

There are two ways to look at density: (1) the small scale action of individual air molecules or (2) the large scale action of a large number of molecules. Starting with the small scale action, from the kinetic theory of gases, a gas is composed of a large number of molecules that are very small relative to the distance between molecules. The molecules are in constant, random motion and frequently collide with each other and with the walls of a container. Because the molecules are in motion, a gas will expand to fill the container. Since density is defined to be the mass divided by the volume, density depends directly on the size of the container in which a fixed mass of gas is confined. As a simple example, consider Case #1 on our figure. We have 26 molecules of a mythical gas. Each molecule has a mass of 20 grams (.02 kilograms), so the mass of this gas is .52 kg. We have confined this gas in a rectangular tube that is 1 meter on each side and 2 meters high. We are viewing the tube from the front, so the dimension into the slide is 1 meter for all the cases considered. The volume of the tube is 2 cubic meters, so the density is .26 kg/cubic meter. This corresponds to air density at about 13 kilometers altitude. If the size of our container were decreased to 1 meter on all sides, as in Case #3, and we kept the same number of molecules, that density would increase to .52 kg/cubic meter. Notice that we have the same amount of material; it is just contained in a smaller volume. How we decrease the volume is very important for the final value of pressure andtemperature. You can explore the variations in pressure and temperature at the animated gas lab.

Turning to the larger scale, the density is a state variable of a gas and the change in density during a process is governed by the laws of thermodynamics. Actual molecules of a gas are incredibly small. In one cubic meter the number of molecules is about ten to the 23rd power. (That's 1 followed by 23 zero's !!!) For a static gas, the molecules are in a completely random motion. Because there are so many molecules, and the motion of each molecule is random, the value of the density is the same throughout the container. Density is a scalar quantity; it has a magnitude but no direction associated with it. As an example, consider Case #1, in which the mass is .52 kg, the volume is 2 cu m, and the density is .26 kg/cu m. If we sample a smaller volume of 1 meter on a side as in Case #2, we will obtain the same density. The volume of the blue box in Case #2 is only 1 cu m, but the number of molecules in the box is 13 at .2 kg per molecule; and the density is .26 kg/cu m. (This example REALLY works only for a very large number of molecules moving at random. Case #2 is just an illustration.) Another way to obtain the same density for a smaller volume is to remove molecules from the container. In Case #4, the container is the same size as in Case #3, but the number of molecules (the mass) has been decreased to only 13 molecules. The density is .26 kg/cubic meter, which is the same density seen in the blue box of Case #2 and throughout Case #1. A careful study of these four cases will help you understand the meaning of gas density.

These rather simple examples help explain a fundamental effect that we see in nature. Between Cases #3 and #4, the number of molecules in a given volume decreased, and the corresponding density decreased. In the atmosphere, air molecules near the surface of the earth are held together more tightly than the molecules in the higher atmosphere because of the gravitational pull of the earth on all the molecules above the surface molecules. The higher up you go in the atmosphere, the fewer the

molecules there are above you, and the lower the confining force. So in the atmosphere, density decreases as you increase altitude; there are fewer molecules.

Gas density is defined to be the mass of gas divided by the volume confining the gas. There is a related state variable called the specific volume which is the reciprocal of the density r. The specific volume v is given by:

v = 1 /r

Specific volume is often used when solving static gas problems for which the volume is known, while density is used for moving gas problems. They are equivalent state variables.

DENSITY Applications with Gases DENSITY is a physical property of matter, as each element and compound has a unique density associated with it. Density defined in a qualitative manner as the measure of the relative "heaviness" of objects with a constant volume. For gases the density may vary with the number of gas molecules in a constant volume.

Density Comparison to Air: The density of several gases is compared to the density of air. Does an object float in air or sink in the air? If an object containing a gas floats on air, it is less dense than air vs. if it sinks, it is more dense than air.

Gas Density examples based upon differences in molecular weight.

Density of a gas with a constant number of molecules in a constant volume, varies according to the molecular weight. The higher the molecular weight the higher the density.

Helium balloon: Compare the behavior of a helium filled balloon with that of an air filled balloon. Even taking into account the weight of the rubber balloon, the helium balloon floats on the air and is less dense than the air. The air filled balloon sinks because the weight of the rubber balloon makes is slightly heavier and thus more dense. Table of Densities

Applications: Mylar balloons, Goodyear blimp. Exit Vchembook site

Hydrogen balloon: Compare the densities of hydrogen, helium, and air to predict what will happen to a hydrogen balloon. In the hydrogen balloon demonstration -  Demonstrations with Density usually not enough hydrogen fills the balloon to overcome the weight of the balloon. Sometimes you can almost see the effect of the hydrogen filled balloon attempting to float. Table of Densities

Application: Hindenburg Exit Vchembook site

Carbon Dioxide: Did you ever see the effect of having dry ice (which is solid carbon dioxide) in a punch bowl at a party? The dry ice is vaporizing to the gaseous state, as well as condensing some water vapor in the air to produce a white fog that sinks in the air. This shows that the carbon dioxide and cold water vapor are more dense than air. Table of Densities

Application: Fire extinguisher demonstration -  Demonstrations with Density

In this case, the carbon dioxide produced by the vinegar and baking soda reaction sinks to the bottom of the beaker. In the process, the air which is less dense is pushed up and out of the beaker. As the oxygen in the air is pushed out of the beaker by the denser carbon dioxide, the candles go out one by one.

Application: Floating Flame

In this demonstration graphic ( graphic in new window ) the first picture shows that the container is filled with carbon dioxide gas. The white cloud that you see is condensed water

vapor, but carbon dioxide gas is mixed in as well. In the second picture, the red glow on the bottom is caused by by red light sticks placed at the level of the gas delivery jet. The more dense carbon dioxide gas has filled the container. Natural gas, methane, is less dense than the carbon dioxide, so it floats to the top of the more dense carbon dioxide. At the level just above the layer of carbon dioxide, there is sufficient air and methane to support combustion - so the flame appears to float on top of the white cloud.

Gas Density examples based upon differences in temperature.

The density of gases depends upon the temperature. The higher the temperature, the more the molecules are spread out and the lower the density as shown in the graphic on the left. The result is that warm gases rise and cool gases sink. The same concept helps to explain the weather resulting in high and low pressures. High pressure means high density, cooler, sinking air. Low pressure means low density, warmer, rising air.

Hot Air Balloon: What makes a hot air balloon rise? As air is heated, it becomes less dense than the surrounding cooler air. The less dense hot air has enough lifting power to cause the balloon to float and rise into the air.

Hot Air Balloon Demonstration Exit Vchembook site

 Cold Water Vapor: What causes a cloud to sink to the earth surface and we call it fog. Tiny droplets of water are present in clouds and fog. If the surrounding warm air is cooled it sinks since it is more dense, and at the same time the water as a gas is condensed into tiny droplets of water.

Application: Liquid Nitrogen DemonstrationThe white fog coming from the liquid nitrogen container (graphic in new window ) is having the same effect as described above.

 

 Mathematical Definition of Density

The formal definition of density is mass per unit volume. Usually the density is expressed in grams per mL or cc. Mathematically a "per" statement is translated as a division. cc is a cubic centimeter and is equal to a mL Therefore,

 Density =

 mass =   g/mL

    volume  

 Demonstrations with Density

Mysterious IceLayers of LiquidsEgg Densities - sugar water/oilSmart Eggs - salt water and acidFloating Eggs - sugar and waterFloating SpheresLava LampUnderwater Smoke StackFloating objects in water

 

 Densities of Common Elements

and Compounds

 Substance

 Densitygrams per mL

 Hydroge 0.000089

n gas

 Helium gas

0.00018

 Air  0.00128

 Carbon Dioxide

 0.001977

Water  1.00

:>>>The specific gravity of a material is defined as the ratio of its density to the density of some standard material, such as water at a specified temperature, for example, 60°F (15°C), or (for gases) air at standard conditions of temperature and pressure. Specific gravity is a convenient concept because it is usually easier to measure than density, and its value is the same in all systems of units.