So what is the volume of 18 g of water when you measure it directly? If you measure out 18 g of water in a graduated cylinder, its volume will be 18 mL. Try measuring the mass of 0 mL, 20 mL, 40 ml, 60 mL, 80 mL, and 100 mL of water.

water
volume (mL)	mass (g)
0.0	0.0
20.0	20.0
40.0	40.0
60.0	60.0
80.0	80.0
100.0	100.0

What do you notice about the relationship between the volume and the mass of water? They are directly proportional to each other. Which only makes sense… if you double the volume of water, then you would expect the mass to double as well. In the case of water, each milliliter of water adds one gram of mass to the total. Therefore, we say that the “density” of water is 1 g/mL (or 1 g/cm3). The density of a material is defined as its mass per unit volume, and the density can be calculated by dividing a material’s mass by its volume.

Drilling down to the molecular scale once again, the density of a material is determined by the mass of its molecules and how closely packed together those molecules are. The mass of a water molecule is 18 u (2.99 × 10-23 g). At 20 °C and standard atmospheric pressure, the average distance between water molecules in the liquid state is 3.85 × 10-8 cm and there are 3.34 × 1022 water molecules packed into 1 cm3 of space. Meanwhile, the mass of an ethanol molecule is 46 u (7.65 × 10-23 g). At 20 °C and standard atmospheric pressure, the average distance between ethanol molecules in the liquid state is 5.7 × 10-8 cm and there are 1.0 × 1022 ethanol molecules packed into 1 cm3 of space.

The average distance between molecules and the average amount of space a molecule occupies depends on the size and shape of the molecule, the attraction between molecules, and the temperature of and pressure on the molecule. The stronger the attraction between molecules and the higher the pressure, the closer together the molecules will become. The higher the temperature, the faster the molecules will be moving, the more space the molecules will occupy. So we would expect the density of a material to increase if the attraction between molecules becomes stronger and when the pressure increases. And we would expect the density of a material to decrease when the temperature increases.

Density of Liquid Water at 4 °C

You may have found it an odd coincidence that liquid water has a density of 1.00 g/cm3 (actually, 0.9982 g/cm3 at 20 °C and standard atmospheric pressure), but it is not a coincidence at all. The gram was first defined as the mass of 1 cm3 of liquid water at 0 °C. This definition was later revised to the mass of 1 cm3 of liquid water at 4 °C when it was discovered that liquid water is densest at 4 °C, and then to 1/1000 of the mass of a platinum-iridium cylinder [known as the international prototype kilogram (IPK)] stored in France. Using the latest definition of a gram, the density of liquid water at 4 °C is 0.9999720 g/cm3.

Density of Ice and Liquid Water at 0 °C

Most pure substances are slightly denser in the solid state than in the liquid state. Water is one of the few exceptions. At 0 °C (the freezing point of water), liquid water is actually slightly denser than ice. This is why ice floats and bodies of water freeze from the top down. This is an important feature of Earth’s biosphere. If ice were denser than liquid water, many organisms would not be able to survive the cold.

In the liquid state, a water molecule is able to form intermolecular bonds with up to four other water molecules. These intermolecular bonds are created by the electromagnetic attraction between the negative (−) oxygen atoms and the positive (+) hydrogen atoms in water molecules. The force of this attraction is what pulls water molecules so close together in the liquid state, giving it a relatively high density.

As water molecules begin to enter the solid state, they begin to form a system of repeating, hexagonal crystals. While this hexagonal structure is very stable, the large hexagonal rings leave almost enough empty space for another water molecule to fit inside them. This is why solid ice is less dense than liquid water.

When molecules enter a crystalline solid state, they form a regular geometric pattern. This geometric pattern must be capable of tessellating three-dimensional space. The crystal structures that molecules form depend on the properties of the molecules and the conditions under which solidification occurs. Cubic and hexagonal structures are common. For example, carbon atoms can form a crystalline solid known as graphite. Graphite has a hexagonal structure and a density of 2.1 g/cm3. It is black, soft, and often used as the “lead” in pencils. Meanwhile, carbon atoms can also form another crystalline solid known as diamond under extreme pressures and temperatures deep in the Earth’s mantle. Diamond has an isometric-hexoctahedral (cubic) structure and a density of 3.5 g/cm3. It is transparent, extremely hard, and often used as the gem for wedding rings.

Intermolecular Bonds and Chemical Bonds

If liquid water is denser than solid ice, why is solid ice “harder” than liquid water? Why is it easier to push your finger through liquid water than through solid ice? This gets back to the common misconception about states of matter that we discussed earlier. Solids are not solid because they are denser than liquids. Solids are solid because, except at the surface, the intermolecular bonds holding molecules in place are stable… they are not constantly being broken and re-formed. The intermolecular bonds holding water molecules together in solid ice prevent you from easily separating water molecules and pushing your finger through an ice cube. Liquids are fluid not because they lack intermolecular bonds. Liquids are fluid because those intermolecular bonds are constantly being broken and re-formed. Individual water molecules are constantly breaking away from one cluster and joining another. You can push your finger through a fluid because individual molecules are breaking away, flowing, and re-forming in clusters around your finger. You are not actually breaking any intermolecular bonds with your finger; intermolecular bonds are breaking on their own.

So far, we have only talked about intermolecular bonds. Intermolecular bonds are bonds that are created by the attraction between molecules. Intermolecular means “between molecules.” The specific bonds formed between water molecules are known as hydrogen bonds. These bonds form because of the attraction between the negative (−) oxygen atom of one molecule and the positive (+) hydrogen atom of another molecule. Later in this unit, you will be learning about chemical bonds. Chemical bonds are the bonds that form between atoms within a molecule. In a water molecule (H2O) there are two chemical bonds, one between each of the two hydrogen atoms and the oxygen atom. To avoid confusion, I will always refer to bonds as either intermolecular bonds (between molecules) or chemical bonds (within molecules).

Intermolecular bonds and chemical bonds are very similar. Both types of bonds are electromagnetic in nature, and some bonds even blur the line between the two. In general, chemical bonds are much stronger and harder to break than intermolecular bonds. However, the primary difference is that chemical bonds alter the physical and chemical properties of a substance while intermolecular bonds do not. If you have two water molecules and break or form intermolecular bonds between them, you still have water, maybe just in a different state. But if you take two water molecules and break and re-form the chemical bonds between oxygen and hydrogen atoms, you will have completely new substances. You may form hydrogen (H2) molecules, oxygen (O2) molecules, or hydrogen peroxide (H2O2) molecules. Hydrogen is a highly flammable gas. Oxygen is a gas and a key component of air that many organisms breathe in and use in cellular respiration. Hydrogen peroxide is a clear liquid like water, but you would not want to drink it. It is often used as a bleach or coloring agent.

Density is a characteristic property of a pure substance. At 100 °C and standard atmospheric pressure, water vapor will always have a density of 0.0006 g/cm3. At 20 °C and standard atmospheric pressure, liquid water will always have a density of 0.9982 g/cm3. And at 0 °C and standard atmospheric pressure, solid ice will always have a density of 0.9167 g/cm3. The density of a pure substance only depends on the mass, size, and shape of the molecules, the attraction between molecules, and the temperature of and pressure on the molecules. So if you are dealing with water and water molecules, except for the temperature and pressure, those properties are never going to change.

We say that density is a “characteristic” property of a pure substance because it can be used to identify the pure substance. If you had a glass of water (H2O) and a glass hydrogen peroxide (H2O2), you could identify which was water by measuring the densities of the two liquids. At 20 °C and standard atmospheric pressure, liquid water has a density of 0.9982 g/cm3 while liquid hydrogen peroxide has a density of 1.450 g/cm3. (You cannot say a liquid is water just because it has a density of 0.9982 g/cm3. Many liquids may have the same density. But if a liquid does not have a density of 0.9982 g/cm3, you can definitely say that a liquid is not water.)

When I referred to density as a characteristic property, I used the term “pure substance.” A pure substance is a substance that is made up of only one type of molecule. If you could examine every molecule in a glass of pure water, you would find that they are all water molecules (H2O… two hydrogen atoms chemically bonded to one oxygen molecule). On the other hand, if you could examine every molecule in a bottle of air, you would find many different types of molecules. You would find mostly nitrogen (N2) and oxygen (O2) molecules; some argon (Ar) atoms, carbon dioxide (CO2) molecules and water (H2O) molecules; and a handful of other molecules. There is no such thing as an “air” molecule… air is a mixture, not a pure substance.

Now if you went to your kitchen sink and drew a glass of water from the tap, you would not have a pure substance. Tap water is a mixture of water molecules and other dissolved minerals and gasses. When you make ice cubes from tap water, the ice cubes are often cloudy because of these impurities. If you were to make ice cubes from boiled, distilled water (boiling will drive out many of the dissolved gasses that even distilled water can contain), you would have crystal clear ice cubes. This, again, is an issue between scientific language and everyday language.

For example, your local pharmacy will carry products that are called, in everyday language, isopropyl alcohol, hydrogen peroxide, and ammonia. None of those products are pure substances; they are all mixtures. Isopropyl alcohol, hydrogen peroxide, and ammonia all exist as pure substances. There is an isopropyl alcohol molecule (C3H8O), a hydrogen peroxide molecule (H2O2), and an ammonia molecule (NH3). At your local pharmacy, all three of those substances are sold in a diluted (mixed with water) form. Rubbing alcohol is often 70% or 91% isopropyl alcohol, with the remaining 30% or 9% being water. Hydrogen peroxide is usually sold in concentrations of 3-6% and ammonia in concentrations of 5-10%. So when we talk about “water,” we need to be clear whether we are using everyday language or scientific language.

Density is not a characteristic property of a mixture for obvious reasons. Consider salt water: a mixture of salt (NaCl) and water (H2O). Because you have a mixture, salt water can have many different concentrations of salt. As the concentration of salt increases, the density of the salt water also increases.

If you look at the table of densities for different materials at the top of this page, you will see that some of the densities are given as approximations (≈). Gasoline, oak, polypropylene, honey, and granite are all mixtures that can have different compositions that can affect their densities. Air is also a mixture, but when we say “air,” we are referring to the specific composition that makes up the Earth’s atmosphere. The composition of air has changed over the millennia, but dry air currently contains roughly 78% nitrogen (N2), 21% oxygen (O2), argon (Ar), carbon dioxide (CO2), and small amounts of other gases. We would not say that a mixture that is 60% nitrogen and 40% oxygen is air. You will learn much more about pure substances and mixtures later in this unit.