# A bit of chemistry. 0007. Physical magnitudes. Derived units of measure.

The **basic** or **fundamental** SI (International System of Units) **units** are used to obtain the **derived units** of other magnitudes. These derived units come from the **relationship** between the appropriate basic physical magnitudes as a result of the equation defining the derived physical magnitude.

For example, the **speed** of a body is defined as “the **ratio** of the **distance** traveled by the body and the **time** taken to cover”. Thus, the SI unit for speed is the basic unit of distance (length) “**m**”, divided by the basic unit of time “**s**” whose result is the **derived unit** “**m/s**” (read “meters per second”).

As we move forward we will find many **derived units** used to measure derived magnitudes as: pressure, force, potential energy, etc.

Because of its usefulness in chemistry, now we will focus on how it is defined and measured the volume and density of bodies. The **volume** of a cube is calculated with the cube of its **length** (length)^{3}. Therefore, the SI unit of volume is the unit length “m” of SI cubed. The **cubic meter**, or “**m ^{3}**” is the derived unit of measurement of volume equal to the volume of a cube that is 1 m on each side. Another unit of volume widely used in chemistry is the

**liter “L”**which is equivalent to a cubic decimeter dm

^{3}. The liter is a unit of ancient Metric System, it is not a unit of the International System, but it is still in use. In one liter are 1,000 milliliters (mL) and each milliliter has the same volume as one cubic centimeter:

**1 mL = 1 cm**. Both terms, milliliter and cubic centimeter are equivalent in volume.

^{3}To measure volumes, there are a number of **devices** frequently used in a chemical laboratory like pipettes, syringes or burettes that are more accurate than the graduated cylinders. The most accurate devices are the volumetric flasks, which are **calibrated** for a given volume of liquid.

**Density** is a property of matter widely used to **characterize** a substance. It is defined as “**the amount of substance in a unit of volume**.”

The densities of the solids and liquids are usually expressed in grams per cubic centimeter, “**g/cm ^{3}**” or grams per milliliter “

**g/mL**”.

**Water** density is 1.00 g/mL because the gram was originally defined as the mass of 1 mL of water at a particular temperature. In fact, the density is a quantity which depends on **temperature** because the volume of many substances changes – dilates or contracts – when they are heated or cooled. Therefore, when densities are described, it must be specified the temperature at which it was measured. If not specified, it is assumed that the temperature is **25 °C**, near room temperature.

The terms **density** and **weight** are sometimes confused.

A simple example is when someone says that iron is heavier than air, it usually means that **it has a higher density**.

1 kg of air has the **same mass** as 1 kg of iron, but iron occupies a **smaller volume**, so it has a **higher density** [recall that the density equals mass divided by the volume occupied or density = mass / volume].

If two liquids do not mix with each other is due to the difference in density. For example oil and water: oil is the least dense of the two liquids, and therefore floats on the denser (water).