Doc Brown's Chemistry Advanced A Level Notes 
Theoretical–Physical Advanced Level Chemistry – Equilibria – Chemical
Equilibrium Revision Notes PART 2
2a. Chemical equilibrium expressions, equilibrium constant
and the effect of temperature on the equilibrium
constant K
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Introduction
How do we write out chemical equilibrium
expressions. What is the equilibrium constant? How do you do equilibrium
calculations?
All is explained with examples including the units for
concentrations (mol dm^{–3}) or partial pressures (e.g. atm, Pa or kPa) and
how to solve equilibrium problems using concentration or partial
pressure units.
The equilibrium constant K_{c} is deduced from the equation for
a reversible reaction, NOT experimental data as for rate expressions in
kinetics. The concentration, in mol dm^{3}, of a species X
involved in the expression for K_{c} is represented by in square
brackets i.e. [X]
The value of the equilibrium constant is not affected
either by changes in concentration or addition of a catalyst.
You need
to be able to construct an expression for K_{c} for a homogeneous system in
equilibrium, calculate a value for K_{c} from the equilibrium
concentrations for a homogeneous system at constant temperature, perform
calculations involving K_{c} and predict the qualitative effects
of changes of temperature on the value of K_{c}.
2a. Equilibrium expressions and applying Le Chatelier's Principle
IT IS IMPORTANT and ESSENTIAL that
Equilibria Part 1 is studied before working through this page
2.a Molar concentration expressions

K_{c} concentration equilibrium
expression INTRODUCTION

It is found
experimentally that the concentrations at the equilibrium point are related by
a simple mathematical equation known as an equilibrium expression
which is governed by an equilibrium constant K, at constant
temperature.

K only varies with temperature, and nothing else!

These equilibrium
expressions (many on this page) were originally derived from
experimental analysis of mixtures at equilibrium.

Patterns in these
equilibrium concentrations were 'spotted' and the resulting
mathematical expression of these concentrations were considered to
conform to what was called the 'law of mass action' ( a term
not really used these days!).

A classic study of the
ester formation equilibrium is often described in textbooks.

ALCOHOL + ACID
ESTER + WATER

Knowing the initial
amounts of alcohol and acid, it was easy to titrate the remaining
free carboxylic acid and then logically work out the amounts of the
water, alcohol and ester left in the equilibrium mixture.

They would also have
found out that it took some time to reach equilibrium, but
eventually all the concentrations remained constant i.e. in the
mixture, the point of equilibrium was reached.

See
example 2.2a.1 ester equilibrium calculation
and 2.a.5 too.

The theoretical
justification for K expressions came later in chemical history and
this need not concern us at this level because it involves some
pretty advanced
thermodynamics theory!

From a student's point
of view, here at this level, you are using K in terms of
concentrations or partial pressures only and therefore all other
equilibrium terms, apart from K itself, should be quoted in either ...

For any reaction
in solution or a gaseous mixture:

By convention, the
arithmetical product of the product concentrations^{*} of the forward reaction (RHS) are on the
top line and the arithmetical product of the reactant
concentrations^{*}
from the backward reaction (LHS) are on the bottom line.

^{
*} In all cases the product concentrations are
raised to the appropriate power (a, b, c, .. t, u, w, ..) given by the
stoichiometric mole ratios of the balanced equation.

AND again note that
K_{c} (like K_{p}) is only constant for a
specific constant temperature at which the concentrations of the
equilibrium components might vary from one dynamic equilibrium
situation to another (e.g. in reacting liquid mixtures or in
solutions).

For heterogeneous
equilibria, K expressions do not normally include values for solid phases,
since their chemical potential cannot change since the concentration
of a solid cannot change.

The effect of temperature on the
equilibrium constant (Kc or Kp)

Please remember, only temperature
changes K, because only changing temperature can change the energy
of the molecules.

First consider the simple
equilibrium: aA + bB cC + dD {(i) ΔH ve, (ii) ΔH +ve}

Using the convention described
above, writing out the concentration equilibrium expression gives
...

K_{c} =

[C]^{c}
[D]^{d} 
––––––––– 
[A]^{a}
[B]^{b} 

The equilibrium
constant, K_{c} (or K_{p} later), is governed by temperature, which is the only
factor that can alter the internal potential energy of the
reactants or products. The 'rule' for the trend in K value change is
provided by Le Chatelier's Principle.

(i) If the forward
reaction is exothermic, K_{c} (or K_{p} later) will decrease in value
with increase in temperature.

From
Le Chatelier's Principle, the
equilibrium position will shift more to the left in the endothermic
direction to minimise the temperature increase due to the effect of
increased heat input.

So, mathematically, by convention, the top line
concentrations of the forward products, [C] & [D],
will numerically decrease and the bottom line concentrations
[A] & [B] must
therefore numerically increase, since some of the C &
D are converted to A & B.

Hence the equilibrium
constant K must decrease for the new equilibrium
position.

(ii) If the forward
reaction is endothermic, K_{c} (or K_{p}) will increase in value
with increase in temperature.

From
Le Chatelier's Principle, the
equilibrium position will shift more to the right in the endothermic
direction to minimise the temperature increase due to the effect of
increased heat input.

So, mathematically, by convention, the top line
concentrations of the forward products, [C] & [D],
must numerically increase and the bottom line concentrations of
[A] & [B] must therefore
numerically decrease, since some of A & B are converted to C &
D.

Hence the equilibrium
constant K must increase for the new equilibrium
position.

Changes in
pressure or concentration have no effect on a K value for ideal
mixtures of gases/liquids or solutions.

Application of
a catalyst to a reaction also has no effect on a K value.

Why are the values of
equilibrium constants affected by temperature?

As we have noted, it is
very important to quote the specific constant temperature that
applies to any K_{c} or K_{p} value BECAUSE
equilibrium constants vary with temperature AND ONLY temperature.

This is because changes
in concentration, partial pressure or employing a catalyst
do NOT affect the energy
content of the molecules themselves (referred to in
thermodynamics as the internal energy of the molecule).

However, if you
change the temperature, you also change the fundamental energy
content of a molecule, and we are now talking about the thermodynamic property values of the equilibrium components.

Electronic energy is
stored in the chemical bonds of the molecules (chemical potential energy)
plus their thermal energies of translation (kinetic energy of
movement), rotation (of the whole or parts of a molecule) and
vibration (of bonded atoms).

If you change the
temperature, all the internal energy contents of the molecules are
also changed, but they don't change to the same amount for each
molecule for the same rise in temperature.

If you think of the
internal energy as a sort of chemical potential to effect a chemical
change, the formation of 'reactants' or 'products' may be favoured
one way or the other (l to r or r to l as you write the equilibrium
equation).

Hence the equilibrium
constant not only changes, but may increase or decrease depending on
whether the reaction is endothermic or exothermic (as argued above).

Therefore the change in
the internal energy (caused by change in temperature), a fundamental
thermodynamic property of a molecule, explains why equilibrium
constants are ONLY affected by temperature and NOT by concentration,
pressure or indeed, the presence of a catalyst.

You can
calculate equilibrium constant from
thermodynamic Gibbs free energy change data for the reaction,
but this may not be part of your course and certainly not
appropriate to study here.

See later specific
examples for the units of K_{c} (or K_{p}
later) and if K has no
units you should state so.

Some 'VERY
rough rules of thumb' for an equilibrium K value
and 'position' of
the equilibrium in terms of LHS (e.g. original reactants of he
forward reaction and
the RHS (products of the forward reaction)

For:
LHS
RHS

(for
A + B
C + D the rules below work ok BUT once the ratios of reactants or
products are not 1:1, things are not so simple)

If K is >> 1 the equilibrium is
mainly on the RHS, maybe virtually 100% completion of the
forward reaction i.e. a very large RHS yield i.e. and likely to be very
thermodynamically feasible.

If K is approx. 1 the equilibrium
is more evenly distributed between the RHS and LHS.

If K_{c} (or
K_{p}) is << 1 the equilibrium is
mainly on the LHS, maybe virtually 0% of products of the forward
reaction i.e. a very low RHS yield i.e. likely to be less
thermodynamically feasible.

BUT remember K changes
with temperature considerably changing the position of an
equilibrium, AND, at constant temperature, and therefore
constant K, the position of an equilibrium can change
significantly depending on relative concentrations/pressures of
'reactants' and 'products'.

Finally a catalyst may
speed up getting to the equilibrium but a catalyst cannot
affect the position of the equilibrium constant or the value of
the equilibrium constant K (K_{c} or K_{p}).
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with advanced level chemistry practice questions for solving
equilibrium problems, how do you write Kc equilibrium
expressions? how do you write Kp equilibrium expressions?
what are the units for Kc equilibrium expressions? what are
the units for Kp equilibrium expressions? how to do Kc
equilibrium calculations using molarity concentrations, how
to do Kp equilibrium calculations using partial pressures,
how to use partial pressure and molarities in equilibrium
expressions, explaining the carboxylic acid alcohol ester
water equilibrium experimental procedure, explaining methods
of solving equilibrium problems, solving hydrogen iodide
hydrogen iodine equilibrium problems using the equilibrium
expression, how to solve PCl5 phosphorus(V) chloride PCl3
phosphorus(III) chloride Cl2 chlorine problems calculations
from the equilibrium expression, solving the ammonia
hydrogen nitrogen equilibrium expression, how to do
calculations from the formation of ammonia equilibrium
expression, solving the phosphorus fluorine phosporus(5)
fluoride equilibrium expression units calculations, how to
write equilibrium expressions for complex ion formation, how
to work out units for equilibrium expressions, solving the
nitrogen oxygen nitrogen(II) oxide equilibrium expression
calculations, solving the equilibrium expression for the
contact process, solving the equilibrium expression for the
synthesis of methanol CH3OH from hydrogen H2 and carbon
monoxide CO
explain the effect of temperature on equilibrium constants,
how do you write Kc equilibrium expression? how do you solve
numerical equilibrium problems? how do you write out Kp
equilibrium expression in partial pressures? how do you
solve equilibrium problems using partial pressures? how do
you calculate the Kc equilibrium constant from
concentrations in mol/dm3? how do you calculate Kp
equilibrium constants using partial pressures atm Pa?
WHAT NEXT?
Advanced Equilibrium Chemistry Notes Part 1. Equilibrium,
Le Chatelier's Principle–rules
* Part 2. K_{c} and K_{p} equilibrium expressions and
calculations * Part 3.
Equilibria and industrial processes * Part 4
Partition between two
phases, solubility product K_{sp}, common ion effect,
ion–exchange systems *
Part 5. pH, weak–strong acid–base theory and
calculations * Part 6. Salt hydrolysis,
acid–base titrations–indicators, pH curves and buffers * Part 7.
Redox equilibria, half–cell electrode potentials,
electrolysis and electrochemical series
*
Part 8.
Phase equilibria–vapour
pressure, boiling point and intermolecular forces watch out for subindexes
to multiple sections or pages
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