Chpt. 15 : p.1
L.S.T. Leung Chik Wai Memorial School
F.6 Chemistry
Chapter 15
THE EFFECT OF TEMPERATURE CHANGE ON REACTION RATE
REVIEW
As the temperature of a reaction mixture increases, the reaction rate increases, it is generally found that a temperature rise of
about 100C approximately doubles the rate of reaction. This can be explained in terms of
1. activation energy and
2. the collision theory.
II. EFFECT OF TEMPERATURE CHANGE ON REACTION RATE IN TERMS OF ACTIVATION ENERGY
(A) Activation Energy
<1> During a reaction, bonds are first broken and others are then formed. Energy is required to break certain bonds and start the process, whether the overall reaction is exothermic or endothermic.
<2> Particles will not always react when they collide because they may not have sufficient energy for appropriate bonds to break.
If a reaction is to occur, the colliding reactant particles must process more than a certain minimum amount of energy to overcome an energy barrier. This “minimum” amount of energy is known as activation energy, Ea.
Conversely, if the reactant particles do not possess the activation energy required for a reaction, this reaction will not occur.
If reactant particles possess energy equal to or greater than the activation energy,
they can cross the ‘energy barrier’. Reaction occur.
(B) Effect of Temperature change on Reaction Rate
<1> When temperature increases, the reactant particles will possess more energy.
<2> More reactant particles possess energy equal to or greater than the activation energy. as a result, reaction rate increases.
III. APPLICATION OF THE ARPHENIUS EQUATION TO DETERMINE THE ACTIVATION ENERGY OF A REACTION
(A) Arrhenius equation
The relationship between the rate constant and the temperature for a given reaction is given by the Arrhenius equation, which is expressed as
where
k = rate constant of the reaction
A = Arrhenius factor (of constant or coefficient)
exp = exponential constant = 2.718
Ea = activation energy of the reaction
T = temperature of the reaction mixture in the absolute scale (in K) i.e. ( 0C +273)
R = universal gas constant = 8.314 JK1molt
Note
<1> The exponential factor, suggest that
increasing the temperature increases greatly the proportion of high kinetic energy molecules.
<2> It is obvious that
Raising T makes Ea / RT smaller, k will increase and the reaction is faster.
Lowering T makes Ea / RT larger, k will decrease and the reaction is slower.
<3> Similarly,
If Ea is low, Ea / RT will be small. K will be large and the reaction will be fast.
If Ea is high, Ea / RT will be large. K will be small and the reaction will be slow.
(B) Natural Log of The Arrhenius Equation
Taking natural log of the Arrhenius equation gives
or
Measuring the rate constant at two different temperature provides enough information to evaluate the activation energy.
The Activation energy and the rates or rate constants (k1 and k2) at two temperatures (T1 and T2) can be related by the equation:
Exercise 1
If the rate constant of a reaction at 310K is double that a 298K, calculate the activation energy of the reaction.
(Gas constant = 8.314 JK-1mol-1)
ANSWER
Exercise 2
In the gas reaction
2NO(g) + 2H2(g) à N2(g) + 2H2O(g)
doubling the initial concentration of NO made the initial rate four times as fast, doubling the initial concentration of H2 made the reaction twice as rapid.
(a) deduce the rate law.
(b) what are the units of rate constant.
(c) Calculate the activation energy of the reaction if the rate constant at 1115K is double the value at 1093K.
( Gas constant ,R = 8.314 JK-1mol-1)
ANSWER
Exercise 3
At 300°C, the rate constant for the reaction
is 2.41x10-10 s-1. At 400°C. k equals to 1. 16x106s-1.
Determine the value of
(a) the activation energy (in kJ mol-1) and
(b) the Arrhenius factor A for this reaction.
(Gas constant, R = 8.314 J K-1 mol-1 )
ANSWER
Exercise 4
For the hypothetical reaction A à B + C,
the rate constant is 3.91x104 mol1dm3s-1 at 370°C and 4.05x102 mol-1dm3s-1 at 470°C.
calculate
(a) the activation energy, and
(b) the rate constant of the reaction at 450°C.
( Gas constant = 8.314 J K-1 mol-1 ) I
ANSWER
(C) Arrhenius Plot
The activation energy is determined from the dependence of the natural logarithm of rate constant on the reciprocal of temperature.
When the rate constant is known at more than two temperatures, the precision of the determination of the activation energy is increased by the Arrhenius plot, in k against 1/T.
The equation
can be rewritten as
to show the temperature dependence.
This expression is of the type y = mx + c, a plot of the values of ln k at different temperatures against l/T will give a
Straight-line graph with a slope (Ea/RT) and an intercept of ln A. Hence the activation energy and the Arrhenius Factor can be determined.
Example
This experiment is about the determination of the activation energy of the reaction between bromide ion and bromate(V) ion in acid solution:
5Br(aq) + BrO3(aq) + 6H+(aq) à 3Br2 (aq) + 3H2O(l)
The progress of the reaction is followed by adding a fixed amount of phenol together with some methyl red indicator. The bromine produced during the reaction reacts very quickly with phenol.
Once all the phenol is consumed, any further bromine produced bleaches the indicator immediately.
(a) Investigation of the activation energy of the reaction
Experimental procedure
<1> Place phenol solution, bromide solution and bromate solution and methyl red indicator into a boiling tube.
<2> place sulphuric acid into another boiling tube.
<3> Place both boiling tubes into a beaker of water (water bath)
which is maintained at 30°C. Allow the contents of both tubes
reach the temperature of the water bath.
<4> Mix the contents of the two tubes. Start the stop watch and swirl the tube gently. Keep the tube in the water bath throughout the experiment.
<5> Record the time (t) taken for the complete disappearance of the red colour.
<6> Repeat the above steps, maintaining the reaction temperature
at different temperatures, e.g. 35°C, 40°C. 45°C, 50°C.
( Temperature must be made the only variable in this experiment. )
Principle of determination
The time for the reaction to proceed to a certain extent is determined. (t denotes the time a definite quantity of bromine is produced at different temperatures.)
Reaction rate = (concentration change/time)
In general, the rate constant is related to the time of reaction by k a 1/t
where t = the time for methyl red to be bleached
For the Arrhenius equation k = exp(-Ea/RT), the following expression is obtained.
Putting k = concentration change (c)/t, plot the graph
using t at different temperatures
ln c and ln A are constants. The slope of the graph in t against 1/T is (Ea/R)
Knowing the value of the gas constant R, Ea can be determined.
(B) Necessary apparatus required for the determination
Thermometer, stop watch, water bath, volume measuring device (e.g. dropper, burette, measuring cylinder)
Exercise 5
The table below gives the rate constants obtained at different temperatures for the reaction
2N2O5(g) à 2N2O4(g) + O2(g)
Temperature/ °C / Rate constant / s-110 / 3.83 x 10-6
20 / 1.71 x 10-5
30 / 6.94 x 10-5
40 / 2.57 x 10-4
50 / 8.78 x 10-4
Determine
(a) the activation energy and
(b) the Arrhenius factor
for this reaction by plotting the graph for
[Gas constant, R = 8.314 J K1 mol1]
THE INTERPRETATION OF RATES OF GASEOUS RACTIONS AT MOLECULAR LEVEL
I. DISTRIBUTION OF MOLECULAR SPEEDS IN A GAS
• At any given temperature, all gases have the same average kinetic energy.
• However, the motion of gas molecules is random. It follows that the collisions between molecules also occur randomly and involve a transfer of energy.
• some collisions result in a gain of kinetic energy for one molecule and a loss of kinetic energy for the other.
• If a molecule undergoes a series of collisions such that each collision adds to its kinetic energy, it will end up with a kinetic energy higher than the average. Conversely, if a molecule undergoes a series of collisions such that each collision results in a loss of kinetic energy, it will end up with a kinetic energy lower than the average.
It can be concluded that
Since molecules undergo continual random collisions, the molecules of a gas at constant temperature do not travel with the same speed. This results in a distribution of molecular speeds in a gas.
II. GRAPHICAL REPRESENTATION OF THE MAXWELL-BOLTZMANN DISTRIBUTION AND ITS VARIATION WITH TEMPERATURE
Maxwell—Boltzmann distribution curve is a plot of distribution of molecular kinetic energies (or speeds) different temperatures.
Interpretation
<1> The total area under the curve is proportional to the total number of molecules, the area under any potion of the curve is proportional to the number of molecules with the energies in that range.
<2> The curve shows that some molecules have very low or very high speeds. However, most molecules have intermediate speeds. This results a normal distribution curve.
(A) Variation of Maxwell—Boltzmann curve with temperature
The effect on the Maxwell—Boltzmann distribution curve of increasing the temperature is shown below:
The spread of the Maxwell-Boltzmann distribution increases with increasing temperature
It can be seen that at a higher temperature, the following changes occur:
<1> The peak of the curve moves to the right, so that the mean energy of the molecules increases and the proportion of molecules having higher energy increases.
<2> The curve flattens so that there is a wider distribution of energies and the proportion of molecules with the most probable speed decreases.
<3> The area under the curve is still the same as that of the one at lower temperature, as the total number of molecules in the sample remains the same.
III. SIMPLE COLLISION THEORY
The collision theory explains chemical reactions at the molecular level. It is developed from the kinetic theory of gases to account for the effects of concentration and temperature on reaction rate. According to the collision theory
<1> Chemical reactions in the gas phase are due to collision of reactant particles.
<2> Not all collisions results in a reaction. For a collision to be effective such that a reaction can occur, the following conditions must be necessary
(i) The reactant particles must collide with kinetic energy greater than the activation energy Ea (a certain threshold) to break the bonds that need to be broken, and
(ii) The reactant particles must collide in the right direction (i.e. correct orientation or collision geometry) so that new bonds can form.
As the number of effective collisions increases, the rate constant and the reaction rate increase.
collision theory
In general, no of effective collisions =
collision frequency x fraction of collision x fraction of gas molecules with K.E.
with correct orientations greater than the Ea
where fraction of gas molecules with kinetic energy greater than the activation energy is given by the Maxwell—Boltzmann energy distribution curve
Since rate constant is proportional to the neither of effective collisions, the Arrhenius equation can be derived
Rate constant
(A) Temperature and the collision theory
When the temperature is raised, there is a greater proportion of molecules with kinetic energy more than the activation energy than there is at the lower temperature.
Interpretation
<1> Ea represent the minimum collision energy necessary for the reaction to occur.
<2> The area under the curve to the right of the activation energy represents the proportion of particles that collide with kinetic energies greater than the activation energy, Ea.
<3> The increase in the reaction rate with temperature corresponds closely to the ratio of the corresponding shaded areas.
<4> Therefore, as temperature changes, the area under the distribution curve for E > Ea changes. This means that
At higher temperatures, more molecules collide with energy greater than the activation energy and so the rate of reaction increase.
<5> The fraction of effective collisions increases exponentially with temperature. Approximately. 10°C rise in temperature doubles the number of molecules enough to cross the activation energy barrier.
Exercise 1
Discuss the effect of temperature on the rate of a reaction in terms of the Arrhenius equation.
ANSWER
(B) Concentration and the Collision Theory
The increase in the rate of a reaction with the increase of concentration of one or more reactant particles can be explained by the Collision Theory.
• As the concentration of the reactant increases, the frequency of collisions increases.
• The probability of effective collisions (collisions with correct orientations and sufficient energy for the reaction to occur) also increases.
• Reaction rate therefore increases.
ENERGY PROFILE
I. ENERGY PROFILE
Most reaction occur in more than one step. Each intermediate product has its specific potential energy.
Energy profile is a representation of the changes in potential energy (against time) during a reaction.
In an energy profile, the potential energies of the followings are shown:
1. reactants
2. products
3. intermediates
4. transition states.
II TRANSITION STATE THEORY
The transition state theory is developed to explain the rate of the reaction. It is mainly concerned with the events during collision.
In the transition state theory,
<1> As reactant particles collide and reaction takes place, they are temporarily in a less stable than the reactants or products. The atoms are rearranging themselves.
<2> As the atoms are separated, the potential energy of the system increases. This results in an energy barrier between the reactants and products.
<3> An activated complex in the transition state is formed.
Note
<1> The activated complex only exists for a fraction of a second.
It is in equilibrium with the reactants and the products:
( Product )
activated complex
in transition state
<2> The activated complex in the transition state possesses the maximum potential energy in the energy profile. It may decompose to the product or reactant.