Knowing exactly what amount of a given substance is present as part of assessing that substance's physical and chemical properties is central to science. Quantities matter – a lot! You're probably thinking, "Okay, let's move past the obvious stuff" at this point, but consider the question of what "amount" means. If someone asked you *how much of you is there*, what would you tell her?

Most of us would probably interpret this question as "How much do you weigh?" or possibly "How tall are you?" There are, however, a lot of equally plausible answers. For example, how much volume (say, in liters) does your body occupy? How many individual atoms or cells does it contain?

Mass is one way to keep track of "stuff" in the universe, and it refers to how much matter is present; this is independent of volume, which simply describes amounts of three-dimensional space. The ratio of these two quantities, called density, is naturally of interest, as is a close cousin, termed *specific gravity*. Specific gravity measurement is included in the physics toolbox mainly to account for the universal nature of water, as you'll soon learn.

## The Fundamentals of Matter

At some point, one simply runs out of words to describe a concept, and so it is with matter. One way to think of matter is that it is anything gravity acts on, and you could theoretically hold any sort of matter with your hands if your hands were tiny enough, and see it with your own eyes if you had supernaturally powerful vision.

Matter consists of one or more *elements*, of which 92 occur in nature. Elements cannot be further broken down into other parts and still retain their properties; the smallest complete unit of an element is an *atom*. A large chunk of matter can consist of trillions of atoms of a single element, such as a pound of pure gold. More often, different elements combine to form compounds, such as hydrogen (H) and oxygen (O) combining to form water (H_{2}O).

## Mass Versus Weight

Mass and weight are similar but distinct units of measure. Mass simply describes the amount of matter present regardless of external factors, and the SI (International System, or metric) unit of mass is the kilogram (kg). In physics problems involving specific gravity, the gram (g), which is 1/1,000 of a kilogram, is used.

The weight of an object depends on the gravity to which its mass is subjected, and has units of force, which in the SI system is the newton (N). On Earth, this value does not change perceptibly, so mass and weight are often used interchangeably. But on the moon, were gravity is less strong, your mass would be the same but your weight (mass *m* times gravity *g*) would be proportionally weaker.

## Volume and Its Applications

Volume refers to an amount of three-dimensional space. It is the cube of length, and the SI unit is the liter (L). One liter is represented by a cube 10 centimeters, or cm (0.1 meters, or m) on a side. You're likely familiar with this volume selection generally because of the number of 1-L beverage bottles made.

By itself, "volume" is just a mathematically defined space, perhaps waiting to be occupied by matter, perhaps not waiting. When matter occupies that space, however, the resulting effects will be different, when different amounts of matter are placed into that same amount of space. You know this intuitively; when you carry around a box of packing peanuts and air, your job is easier than it was when the same box held a shipment of textbooks moments earlier.

The ratio between mass and volume, otherwise known as "the division mass by volume," is called density. But the unique relationship of water to everything mentioned so far has yet to be described.

## Density Defined

Density does not have its own unit in physics, not does it really require one, given that it is derived from one fundamental physical quantity (mass) and one easily derived from another (volume has cubed units of length). It is normally represented by the Greek letter rho, or ρ:

You can see that density has units of kg/L in the SI system, but in physics problems, the unit g/mL is often employed. (Since the latter represents the former with both the mass and the volume divided by 1,000, kg/L and g/mL are actually equivalent.)

You'll find that most living things and many common substances that participate in biochemical reactions have densities similar to that of water; this follows from the fact that most living things consist largely or primarily of H_{2}O.

## Why "Specific Gravity" at All?

This exploration has hammered away at the fact that water is everywhere not to dispel fears of a drought, but because physicists and chemists have come up with an easy way to account for small changes in the density of the *same* type of matter: Specific gravity, a dimensionless number that is just the ratio of that fluid's density to that of water – with a twist.

By definition, 1 mL of unadulterated water has a mass of 1 g. A liter was originally chosen to be the amount of water that had a mass of exactly 1 kg. The problem with this is that, as more modern researchers learned, the specific gravity of water actually varies with temperature even across small, everyday ranges (more on this later). But while density of water is almost always simply rounded to "exactly" 1 for everyday purposes, this is not actually a constant.

- Note that the word "gravity" can be confusing, since gravity in physics has units of acceleration and is independent of this discussion.

## Archimedes' Principle

Before diving fully into specific gravity, a demonstration of the importance and elegance of density is in order – Archimedes' principle. Simply, this states that the upward-acting (buoyant) force exerted on a body immersed in a fluid (usually water) is equal to the weight of the fluid displaced by the body: **F _{B}=w**

_{f}.

This explains why ships are mostly hollow. The materials used to make them are denser than water, meaning that if these materials were compressed, the "ship" would displace its own volume in water and have sufficient weight to make it sink. But if the ship's volume is increased by putting a hollow hull at its base, the overall density decreases, and the ship remains afloat.

## How to Calculate Specific Gravity

The device most often use to determine the specific gravity of a fluid when its value is unknown is called a *hydrometer*. These come in a number of forms, but the basic construct is a tube weighted at the bottom so that it will sink to a certain point in the test fluid, which rests in a graduated cylinder to measure volume.

From knowing the volume of fluid the weighted tube displaces and the weight of the immersed portion, along with the temperature of the room to determine the true density of water under these conditions, the density and specific gravity of the fluid can be determined from Archimedes' principle.

## Variation of Specific Gravity With Temperature

A glance at the graph in the Resources reveals that the specific gravity of water remains very close to 1.000 in the range of 0 to 10 degrees Celsius, but it then declines at a more or less constant rate to about 0.960 as temperature approaches water's boiling point of 100 C. When substances such as medications are often measured and prepared in micrograms, it is vital to be able to account in practice for such seemingly trivial differences.