Guide for the Use of the International System of Units (SI)

Quantity in numerator 
Amount of Substance 
Symbol:
n 
SI unit:
mol 
Volume 
Symbol:
V
SI unit:
m
3
Mass 
Symbol:
m
SI unit:
kg 
Amount of Substance 
Symbol:
n 
SI unit:
mol
amount-of-substance 
fraction 
n
n
x
B
B
=
SI unit:
mol/mol = 1 
molar volume 
n
V
V
=
m
SI unit:
m
3
/mol 
molar mass 
n
m
M
=
SI unit:
kg/mol 
Volume 
Symbol:
V
SI unit:
m
3
amount-of-substance 
concentration 
V
n
c
B
B
=
 
SI unit:
mol/mol
3
volume fraction 
*
A
m,
A
*
B
m,
B
B
V
x
V
x
∑
=
ϕ
SI unit:
m
3
/m
3
= 1
mass density 
V
m
=
ρ
 
SI unit:
kg/m
3
Q
u
an
ti
ty
 in den
omina
to
r 
Mass 
Symbol:
m
SI unit:
kg 
molality 
A
B
B
m
n
b
=
 
SI unit:
mol/kg 
specific volume 
m
V
=
υ
 
SI unit:
m
3
/kg 
mass fraction 
m
m
w
B
B
=
SI unit:
kg/kg = 1 
(a)
Adapted 
from 
Canadian Metric Practice Guide 
(see Ref. [6], note 2; the book cited in Ref. [6], note 3, may also be consulted). 
Notes: 
1. This quantity is commonly called “mole fraction of B” but this Guide prefers the name “amount-
of-substance fraction of B,” because it does not contain the name of the unit mole (compare 
kilogram fraction to mass fraction). 
2. For a mixture composed of substances A, B, C, . . . ,
∑
≡
+
+
+
A
A
C
B
A
...
n
n
n
n
3. A 
related 
quantity 
is 
amount-of-substance ratio of B (commonly called “mole ratio of solute B”), 
symbol r
B
. It is the ratio of the amount of substance of B to the amount of substance of the solvent 
substance: r
B
= n
B
/n
S
. For a single solute C in a solvent substance (a one-solute solution), 
r
C
= x
C
/(1 − x
C
). This follows from the relations n = n
C
+ n
S
, x
C
= n
C 
/ n, and r
C
= n
C 
/ n
S
, where the 
solvent substance S can itself be a mixture. 
8.6.3 Molar volume 
 
Quantity symbol: V
m
.
SI unit: cubic meter per mole (m
3
/mol). 
Definition: volume of a substance divided by its amount of substance: V
m
= V/n. 
Notes: 
1. The word “molar” means “divided by amount of substance.” 
 
26 

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Guide for the Use of the International System of Units (SI) 
 
27 
2. For a mixture, this term is often called “mean molar volume.” 
3. The amagat should not be used to express molar volumes or reciprocal molar volumes. (One 
amagat is the molar volume V
m
of a real gas at p = 101 325 Pa and T = 273.15 K and is 
approximately equal to 22.4 × 10
−3
m
3
/mol. The name “amagat” is also given to 1/V
m
of a real gas 
at p = 101 325 Pa and T = 273.15 K and in this case is approximately equal to 44.6 mol/m
3
.) 
 
8.6.4 Molar mass 
 
Quantity symbol: M. 
SI unit: kilogram per mole (kg/mol). 
Definition: mass of a substance divided by its amount of substance: M = m/n. 
Notes: 
1. For a mixture, this term is often called “mean molar mass.” 
2. The molar mass of a substance B of definite chemical composition is given by M(B) = 
M
r
(B) × 10
−3
kg/mol = M
r
(B) kg/kmol = M
r
g/mol, where M
r
(B) is the relative molecular mass of 
B (see Sec. 8.4). The molar mass of an atom or nuclide X is M(X) = A
r
(X) × 10
−3
kg/mol = 
A
r
(X) kg/kmol = A
r
(X) g/mol, where A
r
(X) is the relative atomic mass of X (see Sec. 8.4). 
8.6.5 Concentration of B; amount-of-substance concentration of B 
 
Quantity symbol: c
B
.
SI unit: mole per cubic meter (mol/m
3
). 
Definition: amount of substance of B divided by the volume of the mixture: c
B
= n
B
/V. 
Notes: 
1. This Guide prefers the name “amount-of-substance concentration of B” for this quantity because it 
is unambiguous. However, in practice, it is often shortened to amount concentration of B, or even 
simply to concentration of B. Unfortunately, this last form can cause confusion because there are 
several different “concentrations,” for example, mass concentration of B, 
ρ
B
= m
B
/V; and 
molecular concentration of B, C
B
= N
B
/V, where N
B
is the number of molecules of B. 
2. The term normality and the symbol N should no longer be used because they are obsolete. One 
should avoid writing, for example, “a 0.5 N solution of H
2
SO
4
” and write instead “a solution 
having an amount-of-substance concentration of c [(1/2)H
2
SO
4
]) = 0.5 mol/dm
3
” (or 0.5 kmol/m
3
or 0.5 mol/L since 1 mol/dm
3
= 1 kmol/m
3
= 1 mol/L). 
3. The term molarity and the symbol 
M
should no longer be used because they, too, are obsolete. One 
should use instead amount-of-substance concentration of B and such units as mol/dm
3
, kmol/m
3
, 
or mol/L. (A solution of, for example, 0.1 mol/dm
3
was often called a 0.1 molar solution, denoted 
0.1 
M
solution. The molarity of the solution was said to be 0.1 
M
.)