Is it a coincidence that the density of water is 1 g/cm3?
No, the density of “one” comes from the way metric units were originally defined. The metric system was invented in the late 1700s because people were looking for a simpler way to define and describe measurements. Before that time, people around the world used “customary” units that were often complex because of the way they had developed through historical accident. For example, inches, feet, and miles (still used today in the United States) are all customary units that date back to ancient times, but they are difficult to use because the relationships among them are complex (such as 12 inches in 1 foot and 5,280 feet in 1 mile).
The metric system was designed to make calculations easier by always having relationships that are factors of 10 (such as 10 millimeters in a centimeter, 100 centimeters in a meter). The inventors of the metric system also tried to give their units some physical meaning. For example, the inventors originally based their definition of the meter on their best estimate of the distance from the equator to the north pole. (More specifically, they defined the meter to be 1/10,000,000 (one ten-millionth) of that distance.) Once the meter was defined, the powers of 10 nature of the system automatically defined other lengths such as millimeters, centimeters, or kilometers.
The metric inventors also needed to come up with basic units for volume and mass. Volume was easy, since “cubing” a length gives a volume; that is, a cubic centimeter or cubic meter is a volume. For convenience, they also defined a separate volume unit, the liter, to be the same as 1,000 cubic centimeters.
That left mass, and the metric inventors decided to define mass based on the weight of a known volume of water. They chose a volume of 1 cubic centimeter, and then defined the mass of 1 cubic centimeter of water to be 1 gram. In other words, the metric inventors first decided that water would have a density of 1 g/cm3, then used this choice as their way of defining the meaning of 1 gram of mass.
Note that, although the inventors in the late 1700s could not measure precisely enough to realize it, we now know that the density of water actually varies slightly with temperature and pressure. This fact is important not only for chemistry but for human civilization: As we’ll discuss in Chapter 7, global warming is causing the temperature of the oceans to rise, and higher temperature causes water to become slightly less dense. As a result, the oceans are expanding slightly, and this is one of the reasons why sea level has been rising, leading to damages to many coastal communities.