Chemistry · Ch 1 — Some Basic Concepts of Chemistry

The International System of Units (SI)

1.3.3

The International System of Units (SI)

Science depends on measurement, and measurement depends on a consistent system of units. Before 1960, different countries used different systems — the British Imperial system, the CGS (centimetre-gram-second) system, the FPS (foot-pound-second) system — which made it difficult to compare scientific results across borders. The need for a single, coherent, universally accepted system led to the creation of the International System of Units, universally abbreviated as SI (from the French Le Système International d'Unités).

The SI system was formally established by the 11th General Conference on Weights and Measures (CGPM, from Conférence Générale des Poids et Mesures). The CGPM is an intergovernmental treaty organisation created by the Metre Convention, a diplomatic treaty signed in Paris in 1875. India is a signatory to this treaty, and the responsibility for maintaining measurement standards in India lies with the National Physical Laboratory (NPL) in New Delhi, which serves as the country's National Metrology Institute (NMI). The NPL realises the base and derived units and periodically compares its standards with those at other NMIs around the world and at the International Bureau of Standards in Paris.

The SI system is built on seven base units, each corresponding to a fundamental physical quantity that cannot be expressed in terms of any other quantity. All other physical quantities — speed, volume, density, force, pressure, energy — are derived from these seven base units.

Table 1.1(table)Base Physical Quantities and their Units

Base Physical Quantity	Symbol for Quantity	Name of SI Unit	Symbol for SI Unit
Length	$l$	metre	m
Mass	$m$	kilogram	kg
Time	$t$	second	s
Electric current	$I$	ampere	A
Thermodynamic temperature	$T$	kelvin	K

The Seven Base Quantities and Their SI Units

The following table lists the seven base physical quantities, their symbols, the names of their SI units, and the symbols for those units. This is the foundation upon which all other units in physics and chemistry are built.

Base Physical Quantity	Symbol for Quantity	Name of SI Unit	Symbol for SI Unit
Length	$l$	metre	m
Mass	$m$	kilogram	kg
Time	$t$	second	s
Electric current	$I$	ampere	A
Thermodynamic temperature	$T$	kelvin	K
Amount of substance	$n$	mole	mol
Luminous intensity	$I_v$	candela	cd

Important

Memorise this table. Every SI unit you will ever use — newton, joule, pascal, hertz, volt — is a combination of these seven base units.

Definitions of the SI Base Units

The definitions of the base units have been refined over time as measurement technology has improved. The modern definitions (as of the 2019 redefinition of the SI) are based on fixing the numerical values of fundamental physical constants. This means the units are now defined in terms of invariant constants of nature, not physical artefacts (like the old prototype kilogram kept in Paris).

Table 1.2(table)Definitions of SI Base Units

Unit	Name	Definition
Unit of length	metre	The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit m s⁻¹, where the second is defined in terms of the caesium frequency Δν(Cs).
Unit of mass	kilogram	The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10⁻³⁴ when expressed in the unit J s, which is equal to kg m² s⁻¹, where the metre and the second are defined in terms of c and Δν(Cs).
Unit of time	second	The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency Δν(Cs), the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s⁻¹.
Unit of electric current	ampere	The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10⁻¹⁹ when expressed in the unit C, which is equal to A s, where the second is defined in terms of Δν(Cs).
Unit of thermodynamic temperature	kelvin	The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380649×10⁻²³ when expressed in the unit J K⁻¹, which is equal to kg m² s⁻² K⁻¹, where the kilogram, metre and second are defined in terms of h, c and Δν(Cs).
Unit of amount of substance	mole	The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076×10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, Nₐ, when expressed in the unit mol⁻¹, and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

1. Metre (m) — The SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum, $c$ , to be $299\,792\,458$ when expressed in the unit $\text{m s}^{-1}$ , where the second is defined in terms of the caesium frequency $\Delta \nu_{\text{Cs}}$ .

Note

This means the metre is now defined as the distance light travels in $1/299\,792\,458$ of a second. The speed of light is no longer a measured quantity; it is a fixed constant.

2. Kilogram (kg) — The SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant, $h$ , to be $6.626\,070\,15 \times 10^{-34}$ when expressed in the unit $\text{J s}$ , which is equal to $\text{kg m}^2 \text{s}^{-1}$ , where the metre and the second are defined in terms of $c$ and $\Delta \nu_{\text{Cs}}$ .

Watch out

The kilogram is the only base unit with a prefix (kilo-) built into its name. When forming multiples and submultiples of the kilogram, the prefixes are attached to the word "gram" (e.g., milligram, not microkilogram).

3. Second (s) — The SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency $\Delta \nu_{\text{Cs}}$ , the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be $9\,192\,631\,770$ when expressed in the unit Hz, which is equal to $\text{s}^{-1}$ .

Tip

A caesium atomic clock works by counting the oscillations of the radiation emitted when a caesium-133 atom transitions between two specific hyperfine energy levels. One second is exactly $9\,192\,631\,770$ such oscillations.

4. Ampere (A) — The SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge, $e$ , to be $1.602\,176\,634 \times 10^{-19}$ when expressed in the unit C, which is equal to $\text{A s}$ , where the second is defined in terms of $\Delta \nu_{\text{Cs}}$ .

Note

$1 \text{ coulomb} = 1 \text{ A s}$ . So the ampere is defined such that the charge of a single electron is exactly $1.602\,176\,634 \times 10^{-19}$ coulombs.

5. Kelvin (K) — The SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant, $k$ , to be $1.380\,649 \times 10^{-23}$ when expressed in the unit $\text{J K}^{-1}$ , which is equal to $\text{kg m}^2 \text{s}^{-2} \text{K}^{-1}$ , where the kilogram, metre, and second are defined in terms of $h$ , $c$ , and $\Delta \nu_{\text{Cs}}$ .

Important

The kelvin is a unit of thermodynamic temperature. A change of $1 \text{ K}$ is exactly equal to a change of $1^\circ \text{C}$ , but the zero point is different: $0 \text{ K} = -273.15^\circ \text{C}$ (absolute zero).

6. Mole (mol) — The SI unit of amount of substance. One mole contains exactly $6.022\,140\,76 \times 10^{23}$ elementary entities. This number is the fixed numerical value of the Avogadro constant, $N_A$ , when expressed in the unit $\text{mol}^{-1}$ , and is called the Avogadro number. The amount of substance, $n$ , of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle, or a specified group of particles.

1 \text{ mol} = 6.02214076 \times 10^{23} \text{ elementary entities}

Watch out

The mole is a counting unit, like a dozen (12) or a gross (144). It is not a unit of mass. One mole of carbon-12 atoms has a mass of exactly 12 grams, but one mole of oxygen molecules ( $\text{O}_2$ ) has a mass of approximately 32 grams.

7. Candela (cd) — The SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency $540 \times 10^{12} \text{ Hz}$ , $K_{\text{cd}}$ , to be 683 when expressed in the unit $\text{lm W}^{-1}$ , which is equal to $\text{cd sr W}^{-1}$ , or $\text{cd sr kg}^{-1} \text{m}^{-2} \text{s}^3$ , where the kilogram, metre, and second are defined in terms of $h$ , $c$ , and $\Delta \nu_{\text{Cs}}$ . …

Table 1.3(table)Prefixes used in the SI System

Multiple	Prefix	Symbol
$10^{-24}$	yocto	y
$10^{-21}$	zepto	z
$10^{-18}$	atto	a
$10^{-15}$	femto	f
$10^{-12}$	pico	p
$10^{-9}$	nano	n
$10^{-6}$	micro	μ
$10^{-3}$	milli	m
$10^{-2}$	centi	c
$10^{-1}$	deci	d
$10$	deca	da
$10^{2}$	hecto	h
$10^{3}$	kilo	k
$10^{6}$	mega	M
$10^{9}$	giga	G
$10^{12}$	tera	T

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