Download Rate and Equilibrium

Chong Yu Cheung 6B (6)
Chemistry Chapter Summery
15 Methods of Following a Reaction and Factors Affecting Its
Rate
15.1 Introduction
Chemical kinetics is the study of the rates of the reactions and the factors that influence
them.
15.2 Rates of Chemical Reactions: Meaning and Possible Expressions
The rate of a chemical reaction is usually expressed as a charge in concentration of a
reactant or a product in a given interval of time. The rate of reaction can be expressed in
an equation:
A+B=C
Rate = -d[A]/dt = -d[B]/dt = d[C]/dt
15.3 Following a Reaction by Chemical and Physical Methods
Rates are measured by following the time dependence of the concentration by titration,
pH, pressure or volume measurements etc. It can be further divided into physical and
chemical methods.
Chemical methods: following the change in amount of reaction or product by titration.
Physical methods: following the volume and the mass change of a reaction, or formation
of observable precipitates and colorimetric measurement of light intensity during a
reaction.
15.4 Molecular Basis of Chemical Reaction
The chemical reaction can only occur when the reactants collide together and have the
right amount of energy.
Activation energy is the minimum amount of energy that chemicals must have before
they can change to products.
15.5 Factors Influencing The Rates of Reactions
The rates of reactions are affected by many factors.
Concentration of reactant: An increase in concentration will give more particles per
unit volume and hence more collisions per unit time, thus increasing the chance of
reaction.
Temperature: An increasing in temperature increases the number of reactant of having
energy greater than the activation energy and the average velocity of particles, thus
increasing the rate of reaction.
Surface area: The larger the surface area, the more the number of particles can collide
with the reactant, and hence increasing the chance of reaction.
Catalyst: The present of catalyst will provide another pathway of the reaction that has
lower activation energy, thus increasing the chance of reaction.
Light: A suitable frequencies of electromagnetic radiation are provided by light, which
can affect the bonding or outer electrons of reactants, resulting a reaction to occur.
16 Rate Equations, Order of Reaction and Their Establishment
From Experiment
16.1 Rate equations and order of reactions
The rate of reaction equals to the concentration of the reactants time a rate constant.
aX+bYproducts
rate = k [X]^a[y]^b
where k is the rate conatant,
the total order = a+b
16.2 Simple rate equations determined from experimental results
The rate equation can be found out by experiment by plotting a graph.
Rate = k[A]^n
Log(rate) = nlog[a] +logk
Where slope = n =order of reaction
k = rate constant
If several reactants is involved in the reaction, the method of excess reactants can be use.
In the experiment, some the reactants are keeping in a high concentration. They have
relatively little change during the reaction. Therefore, the rate with respect to one reactant
can be determined.
Rate = k[A][B][C]
Rate = k’[A]
Where [B][C]are excess
16.3 First, second and zeroth order reaction
First order reaction:
Rate equation: rate = k[A]
Rate equation with respect to time: ln[A]t = ln[A]o – kt
Half life is the time required for a reactant to reach half of its original concentration.
Half life of first order reaction: t1/2 = ln(2)/k
The half life of first order reaction does not depend on the concentration of reactant.
Second order reactions:
Rate equation: rate = k[A]^2
Rate equation with respect to time: 1/[A]t = kt + 1/[A]o
Half life of second order reaction: t1/2 = 1/k[A]o
The half life of second order reaction depends on both k and the initial concentration.
Zeroth order reaction:
Zeroth order has a constant rate and is independent of the concentrations of reactants.
Rate = k [A]^0 = k
Integrated rate law : [A]t = -kt +[A]o
Half life of zeroth order: t1/2 = [A]o/2k
17 Collision Theory, Effects of Temperature and Catalyst on
Reaction Rate
17.1 Interpretation of rates of gaseous reactions at a molecular level:
Simple Collision Theory
Distribution of gas and the effect of temperature:
All gases are in random motion. This is caused by the collision of gaseous particles in air.
The collisions are occurs randomly. Collisions may result in a loss or gain of kinetic
energy and an uneven distribution of speed amount gaseous particles. The
Maxwell-Boltzmann distribution shows the speed of a gas simple. It shows that the
heaviest molecules travel with speeds close to their average value. A light molecule not
only has a higher average speed, but the speeds of many individual molecules are very
different from the average speed.
An increase in temperature increases the kinetic energy of particles. There is a general
shift to higher velocity and a considerable increase in the number molecules having
higher velocity in the curve. The flattening of the curve indicates wider distribution of
velocity at higher temperature.
Simple collision theory and effect of concentration and temperature:
The theory is based on three major postulates. (1) Chemical reactions in the gas phase are
due to the collision of reactant particles. Most of the articles merely bounce apart if they
collide at low speed and not at a proper orientation. (2) A collision only results in a
reaction if certain threshold energy is exceeded. (3) A collision only results in a reaction
if the colliding particles are correctly orientated to one another.
As the concentration increases, the probability of a collision having sufficient energy for
a reaction to occur must also increase. As the temperature increase, the number of
particles has energy greater than the activation energy increase and thus the probability of
molecules with successive collision increase.
17.2 Effect of temperature on reaction rate: the Arrhenius equation
Arrhenius equation:
k = Ae^(Eact/RT)
lnk = lnA – Eact/RT
where k: rate constant
A: Arrhenius factor
Eact: activation energy
R: universal gas constant
T: absolute temperature of the reaction mixture
17.3 Energy profile
An energy profile is a graph showing the potential energy change during a chemical
reaction. The maximum point of the potential energy is known as activated-complex or
transition state. Transition State is the time during old bonds is breaking and new bonds
are forming.
For multi-stage reaction, it may have several transition states. The highest Transition
State shows the activation energy and the rate is also the slowest. It is called
rate-determining step.
17.4 Catalyst
A chemical reaction can be speeded up by not only increasing the concentration of
molecules or the temperature, but also a new reaction pathway leading to the same
products with a lower activation energy. The alternate pathway is achieved by the present
of catalyst.
A positive catalyst sped up the rate of reaction while a negative catalyst slow down the
rate of reaction. All the catalyst will not chemically change after the reaction. But
sometime change its physical form.
Heterogeneous catalyst:
It is catalyst process that occurs in more than one phase, with the catalyst in a phase
different form both the reactants and the products. Heterogeneous catalyst provides a
active reaction surface for the reactants. Once the reactants are adsorbing on the reaction
surface, they can react via a new reaction pathway with lower activation energy.
Homogeneous catalyst:
In homogeneous catalysis, the whole reaction usually occurs in a single phase only. A
homogeneous catalysis occurs by the catalyst forming some unstable intermediates with
the reagents to allow ready reaction and then followed by regeneration of catalyst.
An auto catalyst reaction is one in which one of the products acts as a catalyst for the
reaction itself. In an auto catalysis reaction, the rate of change of concentration of a
reactant will start low, increase to a maximum and them decrease to zero. This contrasts
with other reactions in which the rate of the reaction will start high and decrease to zero.
Application of catalyst:
Catalysts are used in many chemical industries in order to increase the number of product
and lower the investment.
Catalytic converters in car exhaust systems are used to reduce air pollution from motor
vehicles exhaust.
Enzyme is catalyst for biochemical reaction. Not only can small quantities of enzymes
convert large quantities of chemicals, but also they can do so at relatively low
temperature normal pressure.
18 Chemical Equilibrium: Dynamic Nature and Factors
Affecting It
18.1 Dynamic equilibrium
A dynamic equilibrium exists when two reversible or opposing is continually taking place
on the molecular level but that are balanced. It can further divide into physical equilibria
and chemical equilbria
The most important types of physical equilibria are phase equilibria. The equilibria
existing between the phases of a system.
A system is in chemical equilibrium when the rate of the forward reaction is equal to the
rate of the reverse reaction.
A reversible reaction is a chemical change that may take place in either direction and
may reach a position of dynamic equilibrium in which the rate of the forward reaction
equals the rate of the reverse reaction.
Characteristics of the dynamic equilibrium: (1) a stable state of dynamic equilibrium
can only be achieved in a close system. (2) it must in a reversible reaction. (3) at a given
temperature the overall properties does not change with time. (4) the equilibrium is not a
stationary but dynamic condition in which forward and backward reactions are occurring
at a rate which balance.
18.2 Relative concentration at equilibrium: The equilibrium law
If the concentration of one or more of the reacting substances in a reversible of
equilibrium is changed, then the equilibrium will shift in such a way as to preserve the
constancy of the relative concentrations of the products and reactants. Although
microscopically the two opposing reactions are still taking place at the rate, this has no
effect on the macroscopic concentration terms, so that the constancy of the relative
concentrations among products and reactants is also preserved. If a reversible reaction is
allowed to reach equilibrium, then the product of the concentrations of the products
divided by the product of the concentrations of the reactants has a constant value at a
particular temperature.
18.3 Equilibrium constants
If the reaction for the equilibrium is represented by the equation:
A+ B  X +Y
The equilibrium equation of Kc:
concentration of product/concentration of reactant = Kc
[X]epm [Y] epm / [A] epm [B] epm = Kc
Kc is a constant at a particular temperature
The equilibrium equation of Kp:
It can be expressed in terms of partial pressure
Kp = Px Py / Pa Pb
The equilibrium constant ofr a reversible reaction involving gases
General Significance of the equilibrium constant:
With very large equilibrium constants the reaction has gone essentially to completion. It
does not give any information about the rate of a reaction.
There is only one equilibrium constant for a given system at a particular temperature, but
there are an infinite number of equilibrium positions.
The position of a heterogeneous does not depend on the amounts of pure solids or liquids
present, as the concentrations of pure solids and liquids cannot change. If pure solids or
pure liquids are involved in a chemical reaction, their concentrations are not included in
the equilibrium.
18.4 Determination of equilibrium constants
Three things must be ensured in a laboratory measurement of equilibrium constants:
(1) The reactions and products of the reaction must have actually come to equilibrium.
(2) The temperature at which measurements are undertaken must be known and kept
constant
(3) The concentrations, or pressures for gases, must be found.
18.5 Simple calculations of Kc and Kp
The following approach is suggested for analyzing a chemical equilibrium problem:
(1) Write the balances equation for the reaction
(2) Write the equilibrium constant expression for equation.
(3) List the initial concentrations or number of moles
(4)Define the change needed to reach equilibrium and define the equilibrium
concentration by applying this change to the initial concentrations
(5)Substitute the equilibrium concentrations into the equilibrium constant expression,
and solve for the unknown.
18.6 Effect of concentration, pressure and temperature changes on
equilibria.
Le Chatelier’s principle states that if a change is imposed on a system at equilibrium,
the position of the equilibrium will shift in a direction that tends to reduce that change.
Effect of concentration change on equilibrium:
If the concentration of a substance involved in equilibrium is artificially increased, the
reaction tends to adjust the composition so as to minimize the increase. Kc remains
unchanged. Under constant temperature, any concentration changes on a system at
equilibrium will result in adjustment of the system to preserve the constancy of the value
of K at that temperature.
Effect of pressure change on equilibrium:
When the volume of the container holding a gaseous system is reduced, the
concentrations of reactants and products by are increased. By Le Chatelier’s principle, the
system responds by reducing its own volume. This is carried out by shifting the
equilibrium in such a direction that the total number of gaseous molecules in the system
is decreased.
Effect of temperature change on equilibrium:
The value of K, the equilibrium constant, changes with temperature. If energy is added to
the system at equilibrium by heating it, Le Chatelier’s principle predicts that the shift will
be in the direction that consumes energy.
Van’t Hoff’s equation relates K to the value of 1/T:
ln K = (-H1-H2/R)1/T + C
Where C= constant
19 Acid base equilibria I: Some basic Concepts
19.2 Concept of acid/base: Bronsted-Lowry theory
Arrhenius postulated that acids produce H+ ions in solutions and bases produce OHions.
A more general theory of acids and bases was suggested by Bronsted and Lowry which
says that acid is a proton donor, and base is a proton acceptor.
A conjugate base is everything that remains of the acid molecule after the proton is lost. A
conjugate acid is formed when a proton is transferred to the base. Two substances related
in this way are called a conjugate acid-base pair.
Under the Bronsted-Lowry concept, water can be both as an acid and base, depend on the
other substances present.
19.3 Dissociation of water and Kw
Water can partly be dissociated into H+ and OH- ions.
H2O  OH- + H+
The equilibrium constant of water:
K = [H+][OH-]/[H2O]
K[H2O] = Kw = [H+] [OH-]
This Kw is known as the ionic product of water. It has unit of mol^2dm^6, and its exact
value depends on temperature. At 25 degree Clesuis, its value is 1.0 * 10^-14. The value
become greater when the temperature increase. It is because the process is endithermic.
An increase in temperature will increase the rate of endithermic reaction by Le
Chatelier’s principle. Therefore, more ions are produced.
19.4 pH and its measurement
The pH of a solution is the logarithm, to the base 10, of the reciprocal or hydrogen ion
concentration of the solution.
pH = log1/[H3O+] or = -log[H3O+]
The pH changes by 1 for every power of 10 change in [H3O+]. Also the pH decreases as
[H3O+] increases.
Range of pH:
Theoretically there are no upper or lower limits to the values of pH. It can be larger than
14 or smaller than 1. The range of pH values actually encountered in aqueous solution
varies between just less than zero and a little over 14.An acid have a pH of less than 7,
while an alkali is larger than 7.
Measurement of pH:
The pH of a solution can be measured quickily and accurately with a pH meter. It is a
devices consists of a pairs of electrodes connected to a capable of measuring small
voltage. A voltage is generated when the electrode are placed in a solution.. Different pH
value will produced different voltage. However, it is quite difficult for a pH mater to
measure pH accuurately. One reason for this is that the glass electorde tends to change ots
voltage. Also the voltage will be affected by the temperature.
The electrode assembly connected to the pH meter is a very delicate and sensitive
insturment. So, always keep this glass bulb immersed in solutions. Never touch the glass
membrance with your fingers. Always remember to rinse the electorde assembly
thoroughly by distilled water from a squeeze bottle when transferring it from one solution
to another solution of a different pH.
The pH can also be measured by the universial indicater. To find the pH of a soltuion,
just add a few drops of this solution and then taken out to match the colour of the paper
with the standard colour chat.
19.5 Strong and weak acids
A strong acid is one for which the equilibrium lies far to the side of dissociation. The
conjugate base is therefore much more stable than undissociated acid. Also, the conjugate
base is less reactive. Conversely, a weak acid is one for which the equilibrium lies far to
the undissociated side.
For each concentration the hydrochloric acid solution has a higher concentration if
hydrogen ions then the ethanoic acid solution of the same concentration. As the ethanoic
acid is diluted, its pH becomes closer and closer to the pH of the strong acid at the same
concentration. This shows that dilution increases the extent of dissociation of ethanoic
acid. The same is true of other weak acid. The more dilute the weak acid solution, the
greater the percent dissociation.
Acid dissociated constant:
HA  H+ + AThe equilibrium constant Ka for this reaction is called the acid dissociation constant of
acid HA.
Ka = [H+][A-]/[HA]
Degree of dissociated = amount dissociated/initial concentration
The larger the value of Ka, the strong is the acid.
The stronger the acid, the weaker its conjugate base, or the weaker the acid, the stronger
its conjugate base.
19.6 Strong and weak bases
Strong bases are hydroxide salts, such as NaOH or KOH, which dissociated completely
in water to give hydroxide ions. All hydroxides of the group I elements are strong bases.
The alkaline earth metal hydroxides are also strong base. The hydroxyl ion they produce
serves as a good proton acceptor, according the Bronsted Lowry theory.
Weak base does not have to contain the hydroxide ion. They can be species that remove a
proton from water, producing a hydroxide ion.
The equilibrium constant Kb of the general reaction:
Kb = [BH+][OH-]/[B]
Where Kb always refer to the reaction of a base with water to form the conjugate acid and
the hydroxide ion.
Kw = KaKb
This is very important result for any weak acid and its conjugate base, and this reaction
will be applied frequently in subsequent calculation.
19.7 Acid or base
To describe a chemical species as an acid or a base, it is necessary to state its conjugate
counterpart simultaneously, in order to avoid confusions.
19.8 Lewis acids and bases: An introduction
The Lewis acid is an electron pair acceptor. A Lewis base is an electron pair donor. The
Lewis model encompasses the Bronsted model, but the reverse is not ture. The Lewis
theory is essentially qualitative, whereas the Bronsted-Lowry theory can be discussed
quantitatively in term of pH and pKa
20 Acid base Equilibria II: Buffers and indicators for titrations
20.1 Buffers
A buffer solution is one that resists the change of pH on a addition of a small amount of
strong acid or alkali, or upon dilution.
Buffer system can be made:
(1) At the acid pH by dissolving approximately equal concentrations of a weak acid and
its salts with a strong base in the same aqueous solution.
(2) At the alkaline pH by dissolving approximately equal concentrations of a weak base
and its salts with a strong acid in the same aqueous solution.
In the buffer system made up of a weak acid and its with strong base, the large amount of
ethanoic ions contributed by the fully dissociated salt tends to repress the dissociation of
the weak acid, according to Le Chatelier’s principle. Since the dissociation constant of
weak acid is very small, this result in a CH3COOH/CH3COONa system consisting of an
abundant applies of the undissociated acid and its conjugate base.
20.2 Calculations involving composition and pH of buffer solution
pH calculation on buffered solutions require exactly the same considerations as
introduced in the previous chapter.
20.3 Acid-base titrations and pH titration curves
The progress of an acid-base titration is often monitored by plotting the pH if the solution
against the volume of added titrant to give a pH curve, or titrations curve. On the titration
curve, there is a point called equivalence point, which is the point at which the original
acid or base in the solution has been exactly consumed by the titrant base or acid. The
shapes of the curves depend on the strength of acid and alkali being titrated together.
Strong base – strong acid titration:
Initially the curve falls slowly, because excess OH- ions control the pH in this region. At
the equivalence point of the titration of weak acid with a strong base, the pH is greater
than 7 because of the basicity of the conjugate base of the weak acid. The pH then
decreases slowly and levels off, because of the buffering effects of the weak acid and salt
mixture.
Strong acid – weak base titration
For a titration of a weak base, the pH at the equivalence point is always less than 7
because of the acidity of the conjugate acid of the weak base. Before the equivalence
point is the buffering range of the system. Beyond the equivalence point the pH is
determined simply by the excess H+ ions.
Weak acid – weak base titration
The titration of a weak acid with weak base id more complicated to deal with as there are
now three equilibria involved at the equivalence point, and the sluggish variation of the
pH makes the equivalence point difficult to detect.
20.4 Acid base indicators
An acid-base indicator is a substance which changes colour with the pH of its
environment. It is useful for detecting acidity and alkalinity and especially for
determining when reactions between acids and bases are complete. The most common
acid-base indicators are complex molecules that are themselves weak acids and are
representes by Hln. The useful pH range for colour change of an indicators is pKa + or –
1.
When chossing an indicators of titration, we want the end point and the titration
equivalence point to be as close as possible.
For a titration of strong acid by weak acid, the range where the pH changes sharply about
the equivalence point is much narrower. Thus there is less flexibility in choosing an
indicator.
Double indicator method has applications in the estimation of the amount sodium
carbonate in a mixture of sodium carbonate and sodium hydrigencarbonate, or the
amount of sodium carbonate and sodium hydroxide. It is also applicable when a diprotic
acid is titrated with a base.
In the titration of weak acid and weak base, the choice of indicators for detection of
equivalence point is difficult. The method of conductivity measeuremnet is therefore used
to detect the end point in this situation.
Conductivity of the weak base solution changes as the weak acid is added. Initially there
is only weakly dissociated base and conductivity of the solution is low. As weak acid is
added, the small amount of OH- ion replaced, and the conductivity rises as salt is formed.
After the end point the conductivity barely changes because the addition of weakly
dissociated acid does not result in a significant increase in the number of conducting ions
present.
The advantages of conductometric titration over volumetic titration are:
(1) No indicator required
(2) No problem with determining the end point, which can be found easily by
extrapolating the two linear portions of the conductometic curve before and after the
end point.
(3) It is more accurate.
The disadvantages are:
(1) It requires more sophisticated instruments
(2) It requires brief data treatment before the end point is found.