# SI Units Introductory Chemistry Tutorial

## Key Concepts

⚛ There are 7 base SI units.

· metre (m)^{(1)}

· kilogram (kg)

· second (s)

· ampere (A)

· kelvin (K)

· mole (mol)

· candela (cd)

⚛ All other SI units are derived from these 7 base SI units. Examples include:

· cubic metre (m^{3})

· joule (J, kg m^{2} s^{-2})

· pascal (Pa, N m^{-2})

· volt (V)

⚛ Some derived SI units have acceptable non-SI alternatives. Examples include:

· minute (min)

· litre (L or l)

· electronvolt (eV)

⚛ Prefixes are used to indicate multiples or submultiples of SI units.

Some common prefixes |

Multiples |
Submultiples |

Multiple |
Name |
Symbol |
Submultiple |
Name |
Symbol |

×10^{3} |
kilo |
k |
×10^{-3} |
milli |
m |

×10^{6} |
mega |
M |
×10^{-6} |
micro |
μ |

⚛ In general,

(i) The symbol of the quantity being measured is written in italics (sloped).

(ii) The symbol of an SI unit of measurement is written:

(a) upright (not in italics)

(b) in lowercase letters (not Capital Letters) unless the unit has been named after a person (with the exception of the symbol for the litre, L or l)

(iii) There is a space between the number and the units of measurement.

(iv) There is no space between a prefix and the unit of measurement.

(v) There is a space between the symbols for each unit of measurement in a derived SI unit.

Some examples |

in words |
in symbols |

time equals 3 seconds |
*t* = 3 s |

time equals 10 milliseconds |
*t* = 10 ms |

volume equals 1.25 litres |
*V* = 1.25 L |

volume equals 500 microlitres |
*V* = 500 μL |

speed equals 3 millimetres per second |
*ν* = 3 mm s^{-1} |

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## Introduction: What are SI units?

SI units is the abbreviation for Système Internationale d'Unités or the International System of Units.
It is a unified version of the metric system agreed upon by the 11^{th} General Conference of Weights and Measures (CGPM) in 1960 and is used world-wide.

There are 7 base SI units. By multiplying or dividing these base SI units we arrive at units referred to as derived SI units.

Base SI units and derived SI units can be modified by prefixes.

Since 2019 the base SI units been defined in terms of defined constants and universal physical constants.
The definitions of each SI base unit are given below:

⚛ metre (m)

the fixed numerical value of the speed of light in vacuum is taken to be 299 792 458 when expressed in m s^{-1}

⚛ kilogram (kg)

the fixed numerical value of the Planck constant is taken to be 6.626 070 15×10^{-34} when expressed in J s or kg m^{2} s^{-1}

⚛ second (s)

the fixed numerical frequency, the unperturbed ground-state hyperfine transition of the caesium-133 atom, taken to be 9 192 631 770 when expressed in Hertz which is equal to s^{-1}

⚛ ampere (A)

the fixed numerical value of the elementary charge *e* taken to be 1.602 1176 634×10^{-19} when expressed in C which is equal to A s

⚛ kelvin (K)

the fixed numerical value of the Boltzmann constant *k* taken to be 1.380 649×10^{-23} when expressed in J K^{-1} which is equal to kg m^{2} s^{-2} K^{-1}

⚛ mole (mol)

(1) the fixed numerical value of the Avogadro constant *N*_{A} when expressed in mol^{-1}. 1 mole of elementary entities contains exactly 6.022 140 76×10^{23} elementary entities, or the Avogadro number of elementary entities.

(2) the elementary entities must be specified and may be atoms, molecules, ions, electrons, or other particles, or specified groups of such particles

⚛ candela (cd)

the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540×10^{12} Hertz taken to be 683 when expressed in lm W^{-1} which is equal to cd sr W^{-1} or cd sr kg^{-1} m^{-2} s^{3}

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## Base SI Units

There are 7 base SI units^{(2)}: metre, kilogram, second, ampere, kelvin, mole and candela.

These units correspond to base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.

The symbol given to a base SI unit is always a lowercase letter, unless the symbol is derived from the name of a person in which case it is a capital letter.
The letters used to represent a unit are always Roman (upright, not sloped or italic).

The letters used to represent a physical quantity are sloped (in italics).

Base quantity |
SI base unit |

Name |
Symbol |
Name |
Symbol |

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^{(3)} |
n |
mole |
mol |

luminous intensity |
*I*_{v} |
candela |
cd |

Symbols for SI units remain unchanged when used in the plural and are NOT followed by a full stop UNLESS they occur at they end of a sentence.

For example, the symbol for the SI units of length are m NOT ms NOR m. (unless it is at the end of a sentence)

For example, the symbol for the SI units of amount of substance are mol NOT mols NOR mol. (unless it is at the end of a sentence)

When a number is followed by the base unit, there is a space between the number and the unit.

For example, if a chemical reaction takes 12.69 seconds to go to completion we would write the t for time in italics, *t*, and there is a space between the number of seconds and the SI base units, s (lowercase and NOT in italics):

*t* = 12.69 s

NOT *t* = 12.69 *s*

NOT *t* = 12.69s NOR *t* = 12.69*s*

NOT t = 12.69 s NOR t = 12.69 *s*

NOT t = 12.69s NOR t = 12.69*s*

When the quantity being measured is the amount of substance, the symbol for the quantity is immediately followed by the chemical formula for the substance being measured, not in italics, enclosed in round brackets^{(4)}.

For example, if 0.75 moles of helium atoms, He, are present in a balloon then the quantity of atoms is represented by an n in italics, *n*, followed by the symbol for the elementary entities being measured enclosed in round brackets, (He), and there is a space between the number of entities and the base SI unit which is NOT in italics:

*n*(He) = 0.75 mol

NOT *n* = 0.75 mol

NOT *n*(He) = 0.75mol nor *n* = 0.75mol

NOT n(He) = 12.69 mol nor n = 12.69 mol

NOT n(He) = 12.69mol nor n = 12.69mol

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## Derived SI Units

Base SI units can be multiplied or divided to give us derived units.

For example, the volume of a rectangular prism is its length multiplied by its breadth multiplied by its height.
The base SI unit for length, breadth and height is the metre, m, so the derived SI unit for volume is m×m×m = m^{3}, metre cubed or cubic metre.

m^{3} is a derived SI unit.

For example, the density of a substane is its mass divided by its volume.
The base SI unit for mass is the kilogram, kg, and the derived SI unit for volume is m^{3} so the derived unit for density is kg/m^{3} or kg m^{-3}, kilogram per cubic metre.

Note: if a solidus, /, is used, then there is no space between the number and the solidus

kg/m^{3} NOT kg / m^{3}

m/s NOT m / s

Note: if the solidus is not used then there is a space between two units^{(5)}:

kg m^{-3} NOT kgm^{-3}

m s^{-1} NOT ms^{-1}

Some derived SI units have been given their own name and symbol.

For example, the quantity of energy has the derived SI units of kg m^{2} s^{-2} but this unit is referred to as the joule and has the symbol J.

The table below lists some derived SI units that a High School chemistry student should be aware of.

Derived quantity |
SI derived unit |

Name |
Symbol |
Units |
Symbol |

area |
*A* |
square metre |
m^{2} |

volume |
*V* |
cubic metre |
m^{3} |

frequency |
*ν* or *ƒ* |
Hertz |
Hz or s^{-1} |

speed |
*ν* |
metre per second |
m s^{-1} |

density |
*ρ* |
kilogram per cubic metre |
kg m^{-3} |

energy |
*E* |
Joule |
J |

potential energy |
*E*_{p} |
Joule |
J |

kinetic energy |
*E*_{k} |
Joule |
J |

power |
*P* |
Watt |
W |

pressure |
*p* or *P* |
Pascal |
Pa or N m^{-2} |

viscosity |
*η or **μ* |
Pascal second |
Pa s |

electric charge quantity of electricity |
*Q* |
Coulomb |
C |

electric potential |
*V* |
Volt |
V |

electromotive force |
*E* |
Volt |
V |

## Prefixes

When the quantity measured is very large, we can use a prefix to indicate its magnitude. The table below lists prefixes to be used with SI units:

Multiple |
Prefix |

Name |
Symbol |

10^{1} |
deca |
da |

10^{2} |
hecto |
h |

10^{3} |
kilo |
k |

10^{6} |
mega |
M |

10^{9} |
giga |
G |

10^{12} |
tera |
T |

10^{15} |
peta |
P |

10^{18} |
exa |
E |

10^{21} |
zetta |
Z |

10^{24} |
yotta |
Y |

When a prefix is attached to the name of the SI unit there is no space between them:

For example: kilometre NOT kilo metre

For example: megamole NOT mega mole

Similarly, when a prefix is attached to the symbol of the SI unit there is no space between them:

For example: km NOT k m

For example: Mmol NOT M mol

For example, standard pressure is 100 000 pascal or, in scientific notation, 100×10^{3} Pa. Since 10^{3} can be represented by the prefix kilo (symbol k) we can write:

(i) 100 kilopascal

(ii) 100 kPa

Chemists commonly use kilopascal (kPa) to record gas pressure.

Similarly, 100 000 pascal could be written in scientific notation as 1000×10^{2} Pa. Since 10^{2} corresponds to the prefix hecto (symbol h) we can write:

(i) 1 000 hectopascal

(ii) 1 000 hPa

Meteorologists often use hectopascal (hPa) to record atmosperic pressure.

Note that the SI unit for mass is the kilogram, 1000 gram or 10^{3} gram.

That is, the SI unit for mass already contains a prefix, kilo.

1 000 kilograms = 1 000×10^{3} g but we cannot use two prefixes, we cannot write kilokilogram.

Instead we could write 10^{6} gram, 10^{6} g. Since 10^{6} corrresponds to the prefix mega (symbol M) we can write:

(i) 1 megagram

(ii) 1 Mg

Although 1 Mg and 1 000 kg are equivalent, a chemist is probably more likely to record this mass as 1 000 kg, or, in scientific notation, 1×10^{3} kg (or 1.000×10^{3} kg if all the figures are significant).

If the measured quantity is very small, we can attach a prefix to the name and symbol of the unit to indicate its magnitude.
The table below lists the prefixes for these submultiples.

Submultiple |
Prefix |

Name |
Symbol |

10^{-1} |
deci |
d |

10^{-2} |
centi |
c |

10^{-3} |
milli |
m |

10^{-6} |
micro |
μ |

10^{-9} |
nano |
n |

10^{-12} |
pico |
p |

10^{-15} |
femto |
f |

10^{-18} |
atto |
a |

10^{-21} |
zepto |
z |

10^{-24} |
yocto |
y |

When a prefix is attached to the name of the SI unit there is no space between them:

For example: millisecond NOT milli second

For example: micromole NOT micro mole

Similarly, when a prefix is attached to the symbol of the SI unit there is no space between them:

For example: ms NOT m s

For example: μmol NOT μ mol

For example, 0.005 mole of helium atoms is much smaller than the SI unit of mole (mol) so we could use a prefix. The following are 3 acceptable ways to express the amount of helium atoms:

(i) as a decimal: n(He) = 0.005 mol

(ii) in scientific notation: n(He) = 5×10^{-3} mol

(iii) using a prefix: n(He) = 5 mmol (5 millimole)

For example, the radius of an atom is of the order of 10^{-10} metre, or 10^{-9} ÷ 10 which is 1 nanometre divided by 10, or, 1 nanometre multiplied by 0.1. The following are acceptable ways to express the radius of the atom:

(i) as given: 10^{-10} m

(ii) as a decimal and a prefix: 0.1 nm (0.1 nanometre)

(iii) scientific notation and a prefix: 10^{-1} nm (10^{-1} nanometre)

Note that the SI unit for mass, kilogram (kg), already includes a multiplier so the submultiple is calculated on the basis of gram (g) NOT kilogram.

For example, a mass of 0.000002 kg = 0.000002 kg × 1000 g/kg = 0.002 g (0.002 gram) or 2×10^{-3} g.

10^{-3} corresponds to the prefix milli, so we could write 2 milligram, or 2 mg

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## Acceptable non-SI Units

Chemists regularly use units that are not SI units but are acceptable alternatives to SI units.
The table below lists the acceptable non SI units a student is likely to encounter.

Physical quantity |
Acceptable non-SI unit |

Name |
Symbol |
Value in SI units |

time |
minute |
min |
60 s |

hour |
h |
3600 s |

volume |
litre |
L or l |
1 dm^{3} = 10^{-3} m^{3} |

mass |
tonne |
t |
1 Mg = 10^{3} kg |

dalton |
Da |
1.660 5538 782×10^{-27} kg |

unified atomic mass unit |
u |
= 1 Da |

energy |
electronvolt |
eV |
1.602 176 487×10^{-19} J |

Note that the symbol for the litre, L, is the exception to the rule that unit symbols are always lowercase letters unless they are derived from a person's name.
The uppercase L is commonly used in order to avoid confusing it with the number 1.

SI prefixes may be attached to these non SI units.

For example, the volume of a solution may be given as 250 millilitre, 250 mL (or 250 ml).

For example, the volume of a solution may be given as 100 microlitre, 100 μL (or 100 μl).

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## Sample Question: SI Units

Select the row of the table that gives the correct symbols for a base SI unit and a derived SI unit.

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Footnotes:

(1) metre or meter? IUPAC uses metre as the unit of length.

(2) Refer to Quantities, Units and Symbols in Physical Chemistry, third edition, International Union of Pure and Applied Chemistry, 2007

(3) The term "number of moles" should be discouraged when referring to the amount of substance.

For example, we should refer to the amount of sodium chloride NOT to the number of moles of sodium chloride.

In Australian High School Chemistry exams the question often asks for "the amount in moles" so there can be no confusion.

Note: the term "enplethy" has been suggested for international usage.

(4) This is not the only acceptable convention but it is the one most commonly used in Australian High School Chemistry courses.

It is also acceptable to use a subscript, for example n_{He} = 0.75 *mol*

(5) dot products may also be used

for example: kg m^{-3} can also be written as a dot product kg·m^{-3}

for example: m s^{-1} can also be written as a dot product m·s^{-1}

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