inÜnitely high. In van der Waals’s
equation, proposed by the Dutch
physicist J. D. van der Waals (1837–
1923),
k = n^2 a/V^2 ,where a is a constant. This equation
more accurately reÛects the behav-
iour of real gases; several others have
done better but are more complicated.
equatorial1.See ring conforma-
tions. 2.See apical.
equilibriumA state in which a sys-
tem has its energy distributed in the
statistically most probable manner; a
state of a system in which forces,
inÛuences, reactions, etc., balance
each other out so that there is no net
change. A body is said to be in ther-
mal equilibrium if no net heat ex-
change is taking place within it or
between it and its surroundings. A
system is in *chemical equilibrium
when a reaction and its reverse are
proceeding at equal rates (see also
equilibrium constant). These are
examples of dynamic equilibrium, in
which activity in one sense or direc-
tion is in aggregate balanced by com-
parable reverse activity.
equilibrium constant For a re-
versible reaction of the type
xA + yB ˆzC + wDchemical equilibrium occurs when
the rate of the forward reaction
equals the rate of the back reaction,
so that the concentrations of prod-
ucts and reactants reach steady-state
values. It can be shown that at equi-
librium the ratio of concentrations
[C]z[D]w/[A]x[B]yis a constant for a given reaction and
Üxed temperature, called the equilib-
rium constant Kc(where the c indi-
cates concentrations have been used).
Note that, by convention, the prod-
ucts on the right-hand side of the re-
action are used on the top line of the
expression for equilibrium constant.
This form of the equilibrium con-
stant was originally introduced in
1863 by C. M. Guldberg and P. Waage
using the law of *mass action. They
derived the expression by taking the
rate of the forward reaction
kf[A]x[B]y
and that of the back reaction
kb[C]z[D]w
Since the two rates are equal at equi-
librium, the equilibrium constant Kc
is the ratio of the rate constants kf/kb.
The principle that the expression is a
constant is known as the equilibrium
lawor law of chemical equilibrium.
The equilibrium constant shows
the positionof equilibrium. A low
value of Kcindicates that [C] and [D]
are small compared to [A] and [B]; i.e.
that the back reaction predominates.
It also indicates how the equilibrium
shifts if concentration changes. For
example, if [A] is increased (by
adding A) the equilibrium shifts to-
wards the right so that [C] and [D] in-
crease, and Kcremains constant.
For gas reactions, partial pressures
are used rather than concentrations.
The symbol Kpis then used. Thus, in
the example above
Kp= pCzpDw/pAxpBy
It can be shown that, for a given re-
action Kp= Kc(RT)∆ν, where ∆νis the
difference in stoichiometric coefÜ-
cients for the reaction (i.e. z + w – x –
y). Note that the units of Kpand Kcde-
pend on the numbers of molecules
appearing in the stoichiometric equa-
tion. The value of the equilibrium
constant depends on the tempera-
ture. If the forward reaction is
exothermic, the equilibrium constant
decreases as the temperature rises; if
endothermic it increases (see also
van’t hoff’s isochore).
The expression for the equilibrium
constant can also be obtained by209 equilibrium constant
e