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1.3.8 Chemical thermodynamics
Name Symbol Definition SI unit Notes
heat q, Q J (1)
work w, W J (1)
internal energy U ∆U = q + w J (1)
enthalpy H H = U + pv J
thermodynamic T K
temperature
Celsius temperature θ, t θ / °
C = T /K - 273.
C (2)
entropy S d S = d q rev
/ T J K
Helmholtz energy, A A = U - TS J (3)
(Helmholtz function)
Gibbs energy G G = H - TS J
(Gibbs function)
surface tension γ, σ γ = ( ∂
G /
A
s
T, p
J m
, N m
molar quantity X X m
X
) X
m
= X/n (varies) (4),(5)
specific quantity X x x = X/m (varies) (4),(5)
(1) Both q > 0 and w > 0 indicate an increase in the energy of the system; ∆ U = q + w. The
given equation is sometimes written as d U =
d
q +
d
w , where
d
denotes an inexact
differential.
(2) This quantity is sometimes misnamed ‘centigrade temperature'.
(3) It is sometimes convenient to use the symbol F for Helmholtz energy in the context of
surface chemistry, to avoid confusion with A for area.
(4) The definition applies to pure substance. However, the concept of molar and specific
quantities (see section 2) may also be applied to mixtures.
(5) X is an extensive quantity. The unit depends on the quantity. In the case of molar
quantities the entities should be specified.
Example molar volume of B, V m
(B) = V/n B
pressure coefficient β β = ( ∂
p / ∂
T )
V
Pa K
relative pressure α p
α p
= (1/ p )( ∂
p / ∂
T )
V
K
coefficient
compressibility,
isothermal κ T
κ T
= -(1/ V )(
V /
p ) T
Pa
isentropic κ S
κ S
= -(1/ V )(
V /
p ) S
Pa
linear expansion α l
α l
= (1/ l )( ∂
l / ∂
T ) K
coefficient
cubic expansion α, α V
, γ α = (1/ V )( ∂
V /
T )
p
K
coefficient
heat capacity,
at constant pressure C p
C
p
H /
T )
p
J K
at constant volume C V
C
V
U /
T )
V
J K
ratio of heat capacities γ, (κ) γ = C p
/C
V
Joule-Thomson coefficient μ, μ JT
μ = ( ∂
T /
p ) H
K Pa
virial coefficient,
second B pV m
= RT (1 + B/V
m
m
3
mol
third C + C/V m
2
m
m
6
mol
van der Waals a ( p + a/V m
2
)( V
m
3
mol
coefficients b m
3
mol
compression factor, Z Z = pV m
/ RT 1
(compressibility factor)
(6) This quantity is also called the coefficient of thermal expansion, or the expansivity
coefficient.
(7) For a gas satisfying the van der Waals equation of state, given in the definition, the
second virial coefficient is related to the parameters a and b in the van der Waals
equation by B = b - a/RT
standard reaction Gibbs
energy (function) ∆ r
G
r
G
B
B B
ν μ J mol
affinity of reaction A, ( ) A = -( ∂
G /
ξ ) p, T
J mol
B
B B
ν μ
standard reaction
enthalpy ∆ r
H
r
H
B
B B
ν H J mol
standard reaction
entropy ∆ r
S
r
S
B
B B
ν S J mol
K
reaction quotient Q Q = ∏
B
B
B
ν
a
1 (15)
equilibrium constant K °
, K K
= exp (-∆ r
G
/ RT) 1 (10),(13),(16)
(12) The symbol r indicates reaction in general. In particular cases r can be replaced by
another appropriate subscript, e.g. ∆ f
H
denotes the standard molar enthalpy of
formation.
(13) The reaction must be specified for which this quantity applies.
(14) Reaction enthalpies (and reaction energies in general) are usually quoted in kJ mol
In older literature kcal mol
is also common, where 1 kcal = 4.184 kJ.
(15) This quantity applies in general to a system which is not in equilibrium.
(16) This quantity is equal to the value of Q in equilibrium, when the affinity is zero. It is
dimensionless and its value depends on the choice of standard state, which must be
specified.
equilibrium constant,
pressure basis K p
K
p
B
B
B
ν
p
Pa
Σ
v
concentration basis K c
K
c
B
B
B
ν
c
(mol m
Σ
v
molality basis K m
K
m
B
B
B
ν
m
(mol kg
Σ
v
fugacity f,~p f B
λ B
p → 0
lim
( p B
/ λ B
T
Pa (9)
fugacity coefficient φ φ B
= f B
/ p B
Henry's law constant k H
k H,B
lim
B
x
( f B
/ x B
) Pa (9), (18)
f B
x B
x B
=
(17) These quantities are not in general dimensionless. One can define in an analogous way
an equilibrium constant in terms of fugacity K f
, etc. At low pressures K p
is
approximately related to K °
by the equation K ° ≈
K
p
/( p °
Σ
v
, and similarly in dilute
solutions K c
is approximately related to K °
by K ° ≈
K
c
/( c °
Σ
v
; however the exact
relations involve fugacity coefficients or activity coefficients.
The equilibrium constant of dissolution of an electrolyte (describing the equilibrium
between excess solid phase and solvated ions) is often called a solubility product,
denoted K sol
or K s
(or K sol°
or K s°
as appropriate). In a similar way the equilibrium
constant for an acid dissociation is often written K a
, for base hydrolysis K hidr
and for
water dissociation K w
(18) Henry's law is sometimes expressed in terms of molalities or concentrations and then the
corresponding units of the Henry's law constant are Pa kg mol
or Pa m
3
mol
respectively.
Other symbols and conventions in chemical thermodynamics
(i) Symbols used as subscripts to denote a chemical process or reaction
These symbols should be printed in roman (upright) type, without a full stop (period).
vaporization, evaporation (liquid →
gas) vap
sublimation (solid →
gas) sub
melting, fusion (solid → liquid) fus
transition (between two phases) trs
mixing of fluids mix
solution (of solute in solvent) sol
dilution (of a solution) dil
adsorption ads
displacement dpl
immersion imm
reaction in general r
atomization at
combustion reaction c
formation reaction f
(ii) Recommended superscripts
standard
θ
pure substance *
infinite dilution ∞
ideal id
activated complex, transition state ‡
excess quantity E
(iii) Examples of the use of these symbols
The subscripts used to denote a chemical process, listed under (i) above, should be used as
subscripts to the ∆ symbols to denote the change in an extensive thermodynamic quantity
asocciated with the process.
Example ∆ vap
H = H (g) - H (l), for the enthalpy of vaporization, an extensive quantity
proportional to the amount of substance vaporized.
