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 behaviour of real gases; several others have
done better but are more complicated.
equatorial 1. See ring conformations. 2. See apical.
equilibrium A state in which a system 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 thermal equilibrium if no net heat exchange 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 direction is in aggregate balanced by comparable reverse activity.
equilibrium constant For a reversible reaction of the type
xA + yB ˆ zC + wD
chemical equilibrium occurs when
the rate of the forward reaction
equals the rate of the back reaction,
so that the concentrations of products and reactants reach steady-state
values. It can be shown that at equilibrium the ratio of concentrations
[C]
z [D]
w /[A]
x
[B]
y
is a constant for a given reaction and
Üxed temperature, called the equilibrium constant K c (where the c indicates concentrations have been used).
Note that, by convention, the products on the right-hand side of the reaction are used on the top line of the
expression for equilibrium constant.
This form of the equilibrium constant 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
k f [A]
x [B]
y
and that of the back reaction
k b [C]
z [D]
w
Since the two rates are equal at equilibrium, the equilibrium constant K c
is the ratio of the rate constants k f /k b .
The principle that the expression is a
constant is known as the equilibrium
law or law of chemical equilibrium.
The equilibrium constant shows
the position of equilibrium. A low
value of K c indicates 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 towards the right so that [C] and [D] increase, and K c remains constant.
For gas reactions, partial pressures
are used rather than concentrations.
The symbol K p is then used. Thus, in
the example above
K p = p C
z p D
w /p A
x
p B
y
It can be shown that, for a given reaction K p = K c (RT)
∆ν , where ∆ν is the
difference in stoichiometric coefÜcients for the reaction (i.e. z + w – x –
y). Note that the units of K p and K c depend on the numbers of molecules
appearing in the stoichiometric equation. The value of the equilibrium
constant depends on the temperature. 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 by
209
equilibrium constant
e
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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 behaviour of real gases; several others have
done better but are more complicated.
equatorial 1. See ring conformations. 2. See apical.
equilibrium A state in which a system 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 thermal equilibrium if no net heat exchange 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 direction is in aggregate balanced by comparable reverse activity.
equilibrium constant For a reversible reaction of the type
xA + yB ˆ zC + wD
chemical equilibrium occurs when
the rate of the forward reaction
equals the rate of the back reaction,
so that the concentrations of products and reactants reach steady-state
values. It can be shown that at equilibrium the ratio of concentrations
[C]
z [D]
w /[A]
x
[B]
y
is a constant for a given reaction and
Üxed temperature, called the equilibrium constant K c (where the c indicates concentrations have been used).
Note that, by convention, the products on the right-hand side of the reaction are used on the top line of the
expression for equilibrium constant.
This form of the equilibrium constant 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
k f [A]
x [B]
y
and that of the back reaction
k b [C]
z [D]
w
Since the two rates are equal at equilibrium, the equilibrium constant K c
is the ratio of the rate constants k f /k b .
The principle that the expression is a
constant is known as the equilibrium
law or law of chemical equilibrium.
The equilibrium constant shows
the position of equilibrium. A low
value of K c indicates 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 towards the right so that [C] and [D] increase, and K c remains constant.
For gas reactions, partial pressures
are used rather than concentrations.
The symbol K p is then used. Thus, in
the example above
K p = p C
z p D
w /p A
x
p B
y
It can be shown that, for a given reaction K p = K c (RT)
∆ν , where ∆ν is the
difference in stoichiometric coefÜcients for the reaction (i.e. z + w – x –
y). Note that the units of K p and K c depend on the numbers of molecules
appearing in the stoichiometric equation. The value of the equilibrium
constant depends on the temperature. 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 by
209
equilibrium constant
e
www.AzShimi.ir www.AzShimi.com