Chapter # 1
Chemical
Equilibrium
For Class X
(According to New Syllabus 2022)
1.1
Introduction to Reversible Reaction and Chemical Equilibrium
Generally, we presume that most chemical and physical changes proceed to completion. A complete reaction is one in which all reactants have been converted into products.
However, most chemical reactions do not go to completion because products react themselves to form the reactants. As a result, after sometime no further change takes place. Quantities of reactants and products remain unchanged and it seems that the reaction has stopped. In fact, these reactions do not stop; rather they take place on both directions at equal rate and attain the equilibrium state. Such reactions are called reversible reactions. Many examples of physical and chemical equilibrium are found in nature.
We owe our existence to equilibrium phenomenon taking place in atmosphere. We inhale oxygen and exhale carbon dioxide, while plants consume carbon dioxide and release oxygen. This natural process is responsible for the existence of life on the Earth.
Many environmental systems depend for their
existence on delicate equilibrium phenomenon.
For example, concentration of gases in lake
water is governed by the principles of equilibrium. The lives of aquatic plants
and animals are indirectly related to concentration of dissolved oxygen in
water.
1.2 Reversible Reactions (Both
Way/Bi-Directional Reactions)
Definition of Irreversible Reactions
Definition of Reversible Reactions
Such reactions are never proceed to completion i.e. the reactants are not completely changed into products but they apparently come to rest after leaving behind a considerable amount of reactants. In reversible reactions, reactants are not completely changed into products and never run to completion because as soon as the products are formed, they start reacting and regenerating the reactants.
Reversible Reaction is carried out in closed flask.
Representation
General Example of Reversible Process
The characteristics of system at equilibrium are better understood if we
examine some physical processes. The most familiar examples are phase
transformation processes.
conversion of ice
into water by melting and conversion of water into ice by freezing is an
example of reversible change.
Direction
of Reversible Reactions
reversible reactions proceed in both ways, i.e., they consist of two reactions; forward and reverse.
1. Forward Reaction; It is the direction in which reactants are converted into products.
2. Backward
Reaction; It is
the direction in which products are converted into reactants again.
Examples
of Reversible Reactions
Difference between reversible and irreversible reactions
Explanation of Reversible Reaction through
Manufacture Of Ammonia from Its Constituent Elements
Let us discuss a reaction between hydrogen and nitrogen to manufacture
ammonia.
N2(g) + 3H2(g) → 2NH3(g)
When 1 mole of nitrogen gas reacts with 3 moles of hydrogen gas, it gives 2 moles of ammonia gas. This is known as forward reaction.
N2(g) + 3H2(g) ← 2NH3(g)
On the other hand, two moles of ammonia gas may also be changed into one
mole of nitrogen and 3 moles of hydrogen. This reaction is reverse of the
above. Therefore, it is called as reverse reaction.
When both of these reactions are written together as a reversible reaction, they are represented as:
N2(g) + 3H2(g) ⇌ 2NH3(g)
Explanation of REVERSIBLE REACTION through
hydrogen iodide formation
Let us discuss a reaction between hydrogen and iodine. Because one of
the reactants, iodine is purple, while the product hydrogen iodide is
colourless, proceedings of the reaction are easily observable. On heating,
hydrogen and iodine.
Vapours in a closed flask,
hydrogen iodide is formed. As a result, purple colour of iodine fades as it
reacts to form colourless hydrogen iodide. This reaction is called as forward
reaction.
On the other hand, when only hydrogen iodide is heated in a closed
flask, purple colour appears because of formation of iodine vapours. Such as In
this case, hydrogen iodide acts as reactant and produces hydrogen and iodine
vapours. This reaction is reverse of the above. Therefore, it is called as reverse
reaction.
When both of these reactions are written together as a reversible
reaction, they are represented as:
explanation of reversible reaction through calcium
carbonate formation
Let us have another example, when calcium oxide and carbon dioxide
react, they produce calcium carbonate:
On the other hand, when CaCO3 is heated in an open flask, it decomposes to form calcium oxide and carbon dioxide. CO2 escapes out and reaction goes to completion:
In these two reactions, decomposition is reverse to combination or vice
versa. When calcium carbonate is heated in a closed flask, so that CO2
cannot escape out. Initially only decomposition take place on (forward
reaction), but after a while CO2 starts combining with CaO to form
CaCO3 (reverse reaction). In the beginning, forward reaction is fast
and reverse reaction is slow. But eventually, the reverse reaction speeds up
and both reactions go on at the same rate. At this stage, decomposition and
combination take place at the same rate but in opposite directions, as a result
amounts of CaCO3, CaO and CO2 do not change. It is
written as
1.3 Chemical Equilibrium
Under given set of conditions if a reversible process or chemical reaction is carried out in a closed container, a constancy in some observable properties like colour intensity, pressure, density, is observed. Such a state is referred to as an equilibrium state.
Equilibrium means no change
in state of body which may be in rest or motion
If a body is in rest and in rest = static
equilibrium (may be stable or unstable)
If a body is in motion and in motion = dynamic
equilibrium
Definition
of Chemical Equilibrium
Chemical Equilibrium is the state of a
reversible reaction (in a closed vessel) at which there is no
observable change in the concentrations of reactants and products with time and rate of forward reaction is
exactly equal to the rate of reverse reaction i.e. it an apparent state of rest in a reversible chemical reaction where the
rate of forward reaction becomes equal to the rate of reverse reaction. Thus at
equilibrium state:
Rate of forward reaction = Rate
of backward reaction
Equilibrium represents the state of a
process in which the measurable properties like T, P, colour, concentration of the
system do not show any change with the passage of time. Chemical systems
at equilibrium have constant observable properties. Nothing appears to be
happening because the internal movement involves entities that are too small to
see.
Different
Definition of Chemical Equilibrium
1. Stated differently, a reversible reaction is said to be in equilibrium when the rate of transformation of reactants into products is just equal to the rate of transformation of products into reactants (i.e. two opposing reactions occur at the same rate) and the concentrations of reactants and products do not change with the passage of time and becomes constant.
2. An equilibrium is said to have been
established when velocities of opposing reactions become equal.
Conditions
Necessary for Equilibrium
1. Must
have a closed system
2. Must
have a constant temperature
3. Activation
energy is low enough to allow a reaction
Graphical Representation of attainment
of dynamic equilibrium
In a reversible reaction, dynamic
equilibrium is established before the completion of reaction. The rate of both
forward and reverse reaction becomes equal upon reaching the equilibrium point.
The following graph which is of concentration vs time, shows that the
concentrations of both reactants and products becomes constant at equilibrium.
Explanation
Rate of forward reaction = Rate of backward reaction
Thus, when the rate of the forward reaction is the same as the rate of
reverse reaction, the composition of the reaction mixture remains constant, it
is called a chemical equilibrium state.
Establishing Equilibrium
At equilibrium state there are two possibilities.
1. When reaction ceases to proceed, it is called static equilibrium. This happens mostly in physical phenomenon. For example, a building remains standing rather than falling down because all the forces acting on it are balanced. This is an example of static equilibrium.
2. When reaction does not stop, only the rates of forward and reverse reactions become equal to each other but take place in opposite directions. This is called dynamic equilibrium state. Dynamic means reaction is still continuing. At dynamic equilibrium state:
Rate
of forward reaction = Rate of reverse reaction
For example, in case of reaction between hydrogen and iodine vapours, some of the molecules react with each other to give hydrogen iodide.
At the same time, some of the hydrogen iodide molecules decompose back
to hydrogen and iodine.
In the beginning, as the concentration of the reactants is higher than
that of the products, the rate of the forward reaction is faster than the
reverse reaction. As the reaction proceeds, the concentration of reactants will
gradually decrease while that of product will increase, consequently the rate
of the forward reaction will go on decreasing and the reverse reaction will go
on increasing and ultimately the two rates will become equal to each other.
Thus, the equilibrium will set up and concentration of various species (H2,
I2,HI) becomes constant. It is represented as
1.It is always
directed from left to right in a chemical reaction.
2. Reactants
produce products (reactants → products)
3. Initially
rate is fast but gradually slows down.
Macroscopic Characteristics of Reverse Reactions
1. It is always directed from right to left in a chemical reaction
2. Products produce reactants (Reactants ←products)
3. Initial rate
is low but gradually speeds up.
Macroscopic characteristics
of forward and reverse Reactions
Macroscopic characteristics
of dynamic equilibrium
1. Achievement
of Equilibrium in a closed system
2. The rates of opposing changes are equal
3. constant Concentrations of reactants
and products/ constant observable (macroscopic) properties of a system
4. Approaching
Equilibrium from either direction
5. Changing
equilibrium state by changing concentration, pressure and temperature.
6. change in free energy i.e. ∆G = 0.
7. change in microscopic properties
A few important characteristic features of dynamic equilibrium are given
below:
1. Achievement of Equilibrium in a
closed system
Equilibrium can only be reached in a closed system. An equilibrium is achievable only in a closed system (in which substances can neither leave nor enter).
2. The rates of opposing changes are equal
Equilibrium is achieved in reversible process when opposing changes to a closed system occur simultaneously at the same rate i.e. the rates of opposing changes are equal. Equilibrium is a dynamic process (A close system is a system that may exchange energy but not matter with its surroundings).
At equilibrium state, a reaction does not stop. Forward and reverse reactions keep on taking place at the same rate but in opposite direction.
3.constant observable (macroscopic) properties
of a system
The observable (macroscopic)
properties of a system at equilibrium are constant (e.g. temperature, pressure,
colour, mass, density, pressure, pH, concentration etc.) i.e. When a chemical
system is at equilibrium, there are no visible changes in the system. The
concentrations of reactants and products are constant (Not equal!)
At equilibrium state, the amount (concentration) of reactants and products remains constant.
4.Approaching Equilibrium from
either direction
Equilibrium can be established
from either direction i.e. equilibrium can be approached from both sides. An equilibrium
state is attainable from either way, i.e. starting from reactants or from
products.
5. change in microscopic properties
It is a microscopic property. When chemical equilibrium is established even then minute changes continuously take place. These changes are called microscopic properties.
6. Factors Disturbing State of Equilibrium
An equilibrium state can be disturbed and again achieved under the given conditions of concentration, pressure and temperature.
7. Effect of Catalyst on EQUILIBRIUM
The state of equilibrium is not affected by the presence of catalyst. It only helps to attain the equilibrium state in less or more time.
8 change in free energy i.e. ∆G = 0.
Thermodynamically, at equilibrium the Gibb’s free energy (G) is minimum and any change occurring at equilibrium proceeds without change in free energy i.e. ∆G = 0.
9. Equilibrium can be attained in homogenous and heterogeneous system.
Dynamic
Equilibrium
It is an equilibrium involving constant interchange of
activated particles in motion. The chemical equilibrium is said to be in Dynamic State because
it involves constant
and continuous interchange (exchange) of activated (dynamic) molecules of
reacting substances (reactants
and products) in motion i.e. forward and reverse reactions occur at equal rates in opposite
directions (reaction is continuously going
on in the forward and reverse directions with equal rates).
A system at equilibrium is dynamic on the
molecular level; no further net change is observed because changes in one
direction are balanced by changes in the other.
Apparently, it appears that the
equilibrium is dead or static and the reaction seems to be cease but the
equilibrium is dynamic and the molecules are still changing from reactants to
products and from products to reactants but with no net change in their
concentrations.
Although the concentrations of the substances remain unchanged (as indicated by the term “equilibrium”), there is still activity going on; both forward and backward reactions are continually occurring (as indicated by the term “dynamic”) but since they proceed at the same rate, each species is formed as fast as it is consumed, resulting in a constant concentration term.
In a reversible reaction, dynamic equilibrium is established before the
completion of reaction.At initial stage, the rate of forward reaction is very
fast and reverse reaction is taking place at a negligible rate. But gradually
forward reaction slows down and reverse reaction speeds up. Eventually, both
reactions attain the same rate, it is called a dynamic equilibrium state.
Activated
or Dynamic Molecules
The small fractions of reacting molecules
that successfully collide to form products are called Activated or dynamic
Molecules.
Equilibrium
Mixture
A mixture of various substances at
equilibrium in a closed vessel is called equilibrium mixture. It is a mixture
of various species in which the chemical equilibrium exists. It is a mixture of
reactants and products in the equilibrium state.
Equilibrium
Concentration
The concentrations of reactants and
products at equilibrium state are called Equilibrium Concentration.
1.4 Law of Mass Action/Law of
Equilibrium (Guldberg-Waage Law)
Introduction
Law of Mass Action gives a quantitative relationship between the rate of reaction and the active masses (molar concentration) of reacting substances. In 1869 (1864), two Norwegian
chemists Cato
Maximillian (C.M) Guldberg (1836–1902)
and Peter (P)
Waage (1833–1900) put
forward law of mass
action or equilibrium law.
Statement
of LMA
The rate at which a
substance reacts is directly proportional to its active mass and the rate of
a chemical reaction is directly proportional to the product of the active
masses (molar
concentrations in mole/dm3) of its reacting substances
raised to power equal to their number of moles in the balanced chemical
equation of the reaction at constant temperature.
Rate of reaction α Active mass of reacting substance
Active Mass
The Molar Concentration in mole/dm3 or mol dm−3 (mole/litre) of substances is termed as active
mass which represented by square brackets; [ ]. While writing expression for equilibrium
constant, symbol for phases (s, l, g) are generally ignored.
1.5 Derivation
of Equilibrium Constant (Kc) Expression for General Reversible
Reaction
Let us apply the law of Mass Action to derive equilibrium constant (Kc),
for a
general reversible reaction in which reactants A and B combine to form products C and D. At
equilibrium state, the concentrations of A, B, C and D become constant. Let
[A], [B], [C] and [D] are the active masses or molar concentrations in mole/dm3
of A, B, C and D at equilibrium state respectively.
\
According to Law of Mass Action, rate of forward reaction and backward reactions are given as:
Rate of forward reaction α [A]a [B]b
OR
Rf = Kf [A]a[B]b
(Kf=specific rate
constants for forward reaction)
Rate of reverse reaction α [C]c[D]d
OR
Rr=Kr [C]c[D]d
(Kr=specific
rate constants for reverse reaction)
Where Kf and Kr are
the proportionality constants known as the specific rate constants for forward
reaction and specific rate constants for reverse reaction respectively. Their values
depend upon the nature of reactants and products.
Since, at the equilibrium state:
(on re-arranging i.e. By taking the constants on L.H.S side and
the variables on R.H.S of the equation, the above equation becomes)
(Where a, b, c and d are the number of moles (co-efficient) of A, B, C and D respectively in the balanced equation).
The ratio Kf/Kr is a
constant quantity at any specific temperature, which is known as Equilibrium
Constant for the Reaction denoted by Kc (or simply K) where
subscript ‘c’ indicates concentrations in mole/dm3.
The above expression is known as Equilibrium Constant Expression or Kc–Expression or Law of Mass Action Expression or LMA-Expression, which is written by
placing the active masses of products in the numerator and active masses of
reactants in the denominator with each concentration term raised to a power
equal to the coefficient of the substance in the balanced equation.
1.6 Equilibrium Constant (Kc)
and Its Unit
The equilibrium constant (Kc) of
a reversible reaction is a constant ratio of Kf/Kr (specific rate constant for forward
reaction/specific rate constant for reverse reaction) at constant temperature.
Equilibrium constant is a ratio of the product of the
molar concentrations (active masses) of products to the product of molar concentrations
(active
masses) of reactants with each concentration term raised to the power of
coefficient as expressed in the balanced chemical equation at constant temperature.
Thus Kc is directly proportional to molar equilibrium concentrations (active
masses) of products and inversely proportional to molar equilibrium
concentrations (active masses) of reactants.
Characteristics of Equilibrium Constant
1. Expression for
equilibrium constant is applicable only when concentrations of the reactants and products have attained constant value at equilibrium state.
2. Kc for any given reaction
at a particular temperature always has the same value.
3. The value Kc is
determined by experiment.
Importance
of Kc
Kc determines which in greater
concentration at equilibrium – the products or the reactants. In general:
Kc > 102 (1); equilibrium lies to
the right and favours the product.
Kc < 10-2
(1); equilibrium
lies to the left and favours the reactants.
If Kc is very large, the
equilibrium mixture will contain mostly products while if Kc is very
small, the equilibrium mixture will contain mostly reactants.
Unit of Kc
For the reaction in which the number of moles of reactants and products are not equal in the balanced chemical equation, Kc has some unit.
1. Kc
has no units in
reactions with equal number of moles on both sides of the equation. This is
because concentration units cancel out in the expression for Kc.
e.g.
For the reaction; CO2(g) + H2(g)
⇌ CO2(g) + H2O(l),
the unit of Kc is derived as
For the reaction; H2(g) + I2(g)
⇌ 2HI(g), the unit of Kc
is derived as
2. Kc has units for those reactions when the number of moles of reactants and product are not equal
e.g.
For the reaction; N2(g) + 3H2(g)
⇌ 2NH3(g); the unit of Kc
is derived as
Factors that does not affect Equilibrium
Constant
1. The value of equilibrium constant is independent of initial concentrations of the reacting species (reactants and products) i.e. it does not depend on the initial concentrations of the reactants and the products.
2. Kc is independent of the number of intermediate steps in the reaction mechanism.
3. The
equilibrium constant is independent of the presence of a catalyst.
Factors affecting Equilibrium Constant
The value of Kc depends only on temperature i.e. Kc changes with
change in temperature having one unique value for a particular reaction. The
effect of temperature change on Kc depends on the sign of DH for the reaction. The Kc for an
exothermic reaction (negative DH) decreases as the
temperature increases while Kc for an endothermic reaction (positive
DH) increases with the rise in
temperature.
Rules
for writing Kc– Expression
1.In writing Kc– Expression, the active masses (molar concentrations) of products appear in numerator and active masses (molar concentrations) of reactants appear in denominator.
2.The number of moles of reactants and products
(i.e. their coefficients in the balanced equation) appear as the power of
active mass (molar concentrations).
1.7 Importance of Equilibrium Constant
Knowing the numerical value of equilibrium constant of a chemical
reaction, direction as well as extent of the reaction can be predicted.
1. Predicting Direction of a Reaction
Direction of a reaction at a particular moment can be predicted by inserting the concentration of the reactants and products at that particular moment in the equilibrium expression. The reaction quotient Qc is useful because it predicts the direction of the reaction by comparing the value of Qc with Kc .
Thus, we can make the following generalization about the direction of
the reaction.
Consider the gaseous reaction of hydrogen with iodine.
H2(g)
+ I2(g) ⇌ 2HI(g), Kc = 57.0 at 700K
We withdraw the samples from the reaction mixture and determine the concentrations of H2(g), I2(g) and HI(g) . Suppose concentrations of the components of the mixture are:
[H2]t = 0.10 mol dm−3
[I2]t =
0.20 mol dm−3
[HI]t = 0.40 mol dm−3
The subscript ‘t’ with the concentration symbols means that the concentrations mare measured at some time t, not necessarily at equilibrium. When we put these concentrations into the equilibrium constant expression, we obtain a value called the reaction quotient Qc. The reaction quotient for this reaction is calculated as:
As the numerical value of Qc (8.0) is less than Kc
(57.0), the reaction is not at equilibrium. It requires more concentration of
product. Therefore, reaction will move in the forward direction.
2. Predicting Extent of a Reaction
Numerical
value of the equilibrium constant predicts the extent or scope of a chemical reaction.
It indicates to which extent reactants are converted to products. In fact, it
measures how far a reaction proceeds before establishing equilibrium state.
In general,
there are three possibilities of predicting extent of reactions as magnitude of
Kc may be very high, very low or moderate, so can be extent of
reaction
(a) Large numerical value of Kc
The large value of Kc indicates that at equilibrium position the
reaction mixture consists of almost all products and reactants are negligible. Reactions with high Kc values
are virtually complete. High Kc indicates maximum product
concentration and minimum reactant t concentration. The reaction has
almost gone to completion. This type of
reaction is known as forward reaction.
For example, oxidation of carbon monoxide goes to completion at 1000 K.
Similarly, reaction between hydrogen and oxygen has almost gone to completion
at 227oC
2CO(g) + O2(g) ⇌ 2CO2(g), Kc = 2.2 x 1022
2H2(g) + O2(g) ⇌ 2H2O (g), Kc = 2.4 x 1047 At 227oC
H2(g) + Br2(g) ⇌ 2HBr(g) Kc = 5.4 x 1018 at 300K
H2(g) + Cl2(g) ⇌ 2HCl(g) Kc = 4.0 x 1031 at 300K
2O3(g) ⇌ 3O2(g) Kc = 1 x 1055 at 25°C
(b) Small numerical value of Kc
When the Kc value of reaction is small, it indicates that the equilibrium has established with a very small conversion of reactants to products. At equilibrium position, almost all reactants are present but amount of products is negligible. Reactions with low Kc value never finish. Low Kc indicates maximum reactant concentration and minimum product concentration. These are called reverse or backward responses. Such type of reactions never go to completion. Such type of reactions never go to completion.
2NH3(g) ⇌ N2(g) + 3H2(g), Kc = 3.0 x 10-9
F2(g)⇌ 2F(g), Kc = 7.4 x 10-13 At 227oC
2H2O ⇌ 2H2(g) + O2(g) Kc = 4.1 x 10-48
N2(g) + O2(g) ⇌ 2NO(g) Kc = 10-30
(c) Numerical value of Kc is neither small nor large.
Such reactions have comparable amounts of reactants and products at equilibrium position. Reactions which have moderate value of Kc are considered to be at equilibrium. The concentration of reactants and products is almost same
For example:
N2O4(g) ⇌ 2NO2(g) , Kc = 0.3 At 25oC
N2(g) +3H2(g) ⇌ 2NH3(g) Kc = 10 at 300°C
H2(g) + I2(g)⇌ 2HI (g) Kc = 57 at 700K
Solved Questions
Writing Equilibrium Constant
Expression for Reaction along with Rate of forward and reverse Reactions
Q1.For
the reversible reaction of sulphur dioxide with oxygen to form sulphur
trioxide, the Equilibrium Constant expression is
derived as follows:
2SO2(g) + O2(g) ⇌ 2SO3(g)
The rate of forward reaction = Rf = Kf [SO2]2[O2]
The rate of reverse reaction = Rr = Kr [SO3]2
Q2.For the reversible reaction of nitrogen
with oxygen to form nitrogen monoxide, the Equilibrium Constant expression is derived as follows:
N2(g) + O2(g) ⇌ 2NO(g)
The rate of forward reaction = Rf
= Kf [N2][O2]
The rate of reverse reaction = Rr = Kr [NO]2
Q3.For
the reversible reaction of nitrogen with hydrogen to form ammonia, the
Equilibrium Constant expression
is derived as follows:
N2(g) +3H2(g) ⇌ 2NH3(g)
The rate of forward reaction = Rf = Kf [N2][H2]3
The rate of reverse reaction = Rr = Kr [NH3]2
Q4.For
the reversible reaction of combination of nitrogen dioxide into its dimer
dinitrogen tetraoxide,the Equilibrium
Constant expression is derived as follows:
2NO2(g) ⇌ N2O4(g)
The rate of forward reaction = Rf
= Kf [NO2]2
The rate of reverse reaction = Rr = Kr [N2O4]
Writing Equilibrium Constant
Expression for Reaction
Q. Write down the equilibrium constant expression or Kc equation for given reactions
(i) H2(g) + I2(g) ⇌ 2HI(g)
(ii) S(s) + O2(g) ⇌ SO2(g)
(iii) 2SO2(g)+ O2(g) ⇌ 2SO3(g)
(iv) PCl3(g) + Cl2(g) ⇌ PCl5(g)
(v) N2 + 2O2(g) ⇌ 2NO2(g)
(vi) N2 + 3H2(g) ⇌ 2NH3(g)
(vii) H2 + Br2(g) ⇌ 2HBr(g)
(viii) SO2(g) + NO2(g) ⇌ NO(g) + SO3(g)
(ix) CO(g) + 3H2(g) ⇌ CH4(g) + H2O(g)
(x) NH4Cl(s) ⇌ NH3(g) + HCl(l)
Answer
(i) H2(g) + I2(g) ⇌ 2HI(g)
(ii) S(s) + O2(g) ⇌ SO2(g)
(iii) 2SO2(g)+ O2(g) ⇌ 2SO3(g)
(iv) PCl3(g) + Cl2(g) ⇌ PCl5(g)
(v) N2 + 2O2(g) ⇌ 2NO2(g)
(vi) N2 + 3H2(g) ⇌ 2NH3(g)
(vii) H2 + Br2(g) ⇌ 2HBr(g)
(viii) SO2(g) + NO2(g) ⇌ NO(g) + SO3(g)
(ix) CO(g) + 3H2(g) ⇌ CH4(g) + H2O(g)
(x) NH4Cl(s) ⇌ NH3(g) + HCl(l)
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