#### Learning Objective

- Recognize the relationship between derived and base SI units

#### Key Points

- The International System of Units (SI) is the basis of the modern metric system. All SI units can be derived from the seven fundamental SI units.
- Ranges of specific units are indicated by positive or negative multiples of powers of ten (e.g. 10
^{2}, 10^{-2}, etc.). - Pressure—the effect of a force applied to a surface—is a derived unit, obtained from combining base units.
- The unit of pressure in the SI system is the pascal (Pa), defined as a force of one Newton per square meter.
- The conversion between atm, Pa, and torr is as follows: 1 atm = 101325 Pa = 760 torr.
- A standardized prefix system indicates fractions and multiples of metric units (e.g. milli-, mega-).

#### Terms

- barometeran instrument for measuring atmospheric pressure
- PressureThe amount of force applied over a given area divided by the size of the area.
- pascalin the International System of Units, the derived unit of pressure and stress, equal to one newton per square meter; symbol: Pa
- Newtonin the International System of Units, the derived unit of force; the force required to accelerate a mass of one kilogram by one meter per second per second; symbol: N
- International System of Unitsthe basis of the metric system; SI, from the French Système international d’unités; metric measurements derive from seven base units and multiples of ten

## SI Units

The International System of Units (abbreviated SI from the French Système International d’Unités) is the basis of the metric system. The SI was established in 1960 and is based on the metre-kilogram-second system rather than the centimetre-gram-second system. The units are divided into two classes: base units and derived units. There are seven base units, each representing a different kind of physical quantity.

## Derived Units

Derived units are unlimited in number and are formed by multiplying and dividing the seven base units and other derived units; for example, the SI derived unit of speed is meters per second, m/s. Some derived units have special names; for example, the unit of resistance, the ohm (Ω), is uniquely defined by the following relation:

[latex]\Omega = {m}^{2}\cdot kg\cdot {s}^{3}\cdot {A}^{2}[/latex]

This follows the definition of electrical resistance.

Pressure, the effect of a force applied to a surface, is a derived unit. The unit of pressure in the SI system is the pascal (Pa), defined as the force of one newton per square meter:

[latex]1Pa=1{N} \cdot {m}^{-2}[/latex]

In chemistry, it is more common to express pressures in units of atmospheres or torr:

1 atm = 101325 Pa = 760 torr [latex]\approx[/latex] 760 mm Hg

Torr and millimeters of mercury (mm Hg, defined as a one millimeter difference in the height of a mercury barometer at 0°C) are nearly equivalent. Another unit of pressure used in meteorology is the bar:

1 bar = 105 N/m^{2} = 750.06 torr = 0.987 atm.

Since the quantities measured can have such a wide range, a standardized prefix system has been set in place.

This allows us to easily write out very small and very large numbers, such as 1 mPa (millipascal, 10^{-3}) or 1 GPa (gigapascal, 10^{9}, e.).

Pressure can be represented by many different units and prefixes. When performing pressure calculations, it is important to ensure that all dimensions are in the same unit system.

## Example 1

On a given day, the atmospheric pressure is 770 mm Hg. What is the pressure in pascals?

[latex]\text {770 mm Hg} \times \frac {\text{101.3 Pa}}{\text{760 mm Hg}}=\text{102.6 Pa}[/latex]

The pressure is 102.6 pascals.