# Topic 5 Reaction Kinetics

1. If the units for concentration and time are mol dm-3 and minute respectively, what is the possible unit of the reaction rate of a second-order reaction? q1

Rate = change in concentration / time = mol dm-3 min-1

2. In the following reaction:

PQ2 -> products

The concentrations of PQ2 at t = 16.8 min and t = 30.5 min are 3.06 mol dm-3 and 2.44 mol dm-3 respectively. During this time interval, what is the average rate of the reaction in mol dm-3 min-1 ? q4

Average rate of the reaction = change in concentration / time

= (3.06 – 2.44) / (30.5 – 16.8) = 0.045 mol dm-3 min-1

3. Consider this reaction:

2SO2 (g) + O2 (g) -> 2S03 (g)

The rate of disappearance of SO2 is 1.6 g dm-3 min-1. What is the rate of formation of SO3 in mol dm-3 min-1? q7

Rate of disappearance of SO2 = 1.6 g dm-3 min-1 / 64 = 0.025 mol dm-3 min-1

Rate of formation of SO3 = rate of disappearance of SO2 = 0.025 mol dm-3 min-1

4. Which of the following best explains the increase in the rate of reaction between hydrochloric acid and marble when the temperature increases? q10

A The activation energy of the reaction decreases.

B The solubility of marble increases when temperature increases.

C The number of effective collisions increases when temperature increases.

D The kinetic energy of the marble particles increases when temperature increases.

When temperature increases, the kinetic energy of the acid molecules increases and hence the number of effective collisions between the acid molecules and marble increases.

5. For the reaction, W + Y -> Z, a series of experiments were carried out using different amounts of W and Y in vessels of different volumes at the same temperature, T.

Mixture  /  Composition

i. 0.20 mol W and 0.20 mol Y in a 0.1 dm3 vessel

ii. 1.0 mol W and 1.0 mol Y in a 2.0 dm3 vessel

iii. 0.50 mol W and 0.50 mol Y in a 0.5 dm3 vessel

(a) Calculate the concentrations of W and Y in each reaction mixture.

(b) Which of the above mixtures will react at the highest rate?

(c) Which of the above mixtures will produce the most Z in a given time? q13

(a) In Mixture I, concentration of W = concentration of Y = = 0.20 / 0.1 = 2.0 mol dm-3 In Mixture II, concentration of W = concentration of Y = 1.0/2.0 = 0.5 mol dm-3. In Mixture III, concentration of W = concentration of Y = 0.50/ 0.5 = 1.0 mol dm-3

(b) Mixture I, because the concentration of the reactants is the highest.

(c) Mixture II, because it has the most amount of reactants.

6. The initial concentration of a reactant Q is 3.40 mol dm-3. After the reaction has started for 10.0 minutes, the concentration of Q is 2.85 mol dm-3.

(a) Calculate the average rate of dissociation of Q at this point.

(b) If the rate remains constant, what is the concentration of Q after the reaction has started for 30.0 minutes? (c) At what time after the reaction has started will the concentration of Q be 1.00 mol dm-3? q14

(a) Average rate = (3.40 – 2.85)/10.0 = 0.055 mol dm-3 min-1.

(b) After 30.0 minutes, the concentration of Q = 3.40 – (30 x 0.055) = 1.75 mol dm-3

(c) Time = (3.40 – 1.00)/0.055 = 43.6 minutes

7. Ammonia decomposes into its elements when heated at temperature T K.

(a) Write an equation for the decomposition of ammonia.

(b) In a 1 dm3 vessel, the initial pressure of ammonia is 380 kPa.

(i) What will the total gas pressure be when the partial pressure of ammonia has fallen to 100 kPa?

(ii) What is the average rate of decomposition of ammonia if the time taken for the reaction to complete is 45 minutes? Q15

(a) 2NH3(g) -> N2(g) + 3H2(g)

(b) (i) From the ideal gas equation, PV = nRT, the number of moles of gases that have reacted is proportional to its decrease in partial pressure. The partial pressure of ammonia has decreased by (380 – 100) = 280 kPa.

Partial pressure of nitrogen = 280/2 = 140 kPa.

Partial pressure of hydrogen = (280 X 3) / 2 = 420 kPa.

Total pressure = 100 + 140 + 420 = 660 kPa

(ii) Average rate = 380/45 = 8.44 kPa min-1.

8. (a) Define the following terms:

(i) rate of reaction

(ii) rate equation

(b) Explain in terms of collision theory, why

(i) the time taken for acidified potassium manganate (VII) to be decolourised is shorter when 35-volume hydrogen peroxide is used instead of 20-volume hydrogen peroxide.

(ii) the reaction rate between zinc and dilute hydrochloric acid is higher when the temperature of the acid is increased. q16

(a) (i) For a reaction, A + B → products. The rate of reaction is defined as ‘the decrease in the concentration of a reactant per unit time’ or ‘the increase in the concentration of a product per unit time’.

(ii) The rate equation is an equation relating the rate of a reaction to the rate constant and the concentrations of the reactants. For example, P + Q -> products Rate of reaction = [P]^a[Q]^b Rate = k[P]^a[Q]^b where k is the rate constant while a and b are the orders of the reaction.

(b) (i) The rate of reaction between acidified potassium manganate(VII) and 35-volume hydrogen peroxide is higher because the concentration of 35-volume hydrogen peroxide is higher than the concentration of 20-volume hydrogen peroxide. The number of collisions between the reactant molecules increases and hence, the frequency of effective collisions increases.

(ii) Generally, reaction rates increase as the temperature of the reactants increases. At lower temperatures, the kinetic energy of the reactant particles is lower. The number of molecules having sufficient energy to collide effectively is less. Thus, the rate of reaction is lower when the temperature of hydrochloric acid is lower.

### 5.1 Rate of reaction

Candidates should be able to:

(a) define rate of reaction, rate equation, order of reaction, rate constant, half-life of a first-order reaction, rate determining step, activation energy and catalyst;
(b) explain qualitatively, in terms of collision theory, the effects of concentration and temperature on the rate of a reaction.

5.2 Rate law

Candidates should be able to:

(a) calculate the rate constant from initial rates;
(b) predict an initial rate from rate equations and experimental data;
(c) use titrimetric method to study the rate of a given reaction.

5.3 The effect of temperature on reaction kinetics

Candidates should be able to:

(a) explain the relationship between the rate constants with the activation energy and temperature using Arrhenius equation k = Ae ^[-(Ea/RT)]
(b) use the Boltzmann distribution curve to explain the distribution of molecular energy.

5.4 The role of catalysts in reactions

Candidates should be able to:

(a) explain the effect of catalysts on the rate of a reaction;
(b) explain how a reaction, in the presence of a catalyst, follows an alternative path with a lower activation energy;
(c) explain the role of atmospheric oxides of nitrogen as catalysts in the oxidation of atmospheric sulphur dioxide;

(d) explain the role of vanadium (V) oxide as a catalyst in the Contact process;
(e) describe enzymes as biological catalysts.

5.5 Order of reactions and rate constants

Candidates should be able to:

(a) deduce the order of a reaction (zero-, first- and second-) and the rate constant by the initial rates method and graphical methods;
(b) verify that a suggested reaction mechanism is consistent with the observed kinetics;
(c) use the half-life (t½) of a first-order reaction in calculations.

## 5 Reaction Kinetics

5.1 Rate of reaction

(a) define rate of reaction, rate equation, order of reaction, rate constant, half-life of a first-order reaction, rate determining step, activation energy and catalyst;

rate of reaction

rate equation

order of reaction

rate constant

Rate constant gives the relation between the rate of the reaction and the concentration of the reactant in the reaction.

Unit of rate constant k for different reaction orders.

half-life of a first-order reaction

rate determining step

activation energy

The relationship between activation energy ( Ea ) and enthalpy of formation (ΔH) with and without a catalyst, plotted against the reaction coordinate. The highest energy position (peak position) represents the transition state. With the catalyst, the energy required to enter transition state decreases, thereby decreasing the energy required to initiate the reaction.

Catalyst: a material that enhances the rate and selectivity of a chemical reaction without itself being consumed in the reaction. Rates (kinetics): Rate = rate constant x [reactant]n. Rate constant (k or k’) = A exp (-EAct/RT) Consider, All catalysts work by providing alternative pathways: different, lower EAct. accelerates both forward AND reverse reactions. (increase kf and kb) catalysts do not influence how MUCH product forms. Reactants Products. kforward. kback.

(b) explain qualitatively, in terms of collision theory, the effects of concentration and temperature on the rate of a reaction.

The reaction rate (rate of reaction) or speed of reaction for a reactant or product in a particular reaction is intuitively defined as how quickly or slowly a reaction takes place.

Candidates should be able to:

(a) define rate of reaction,

rate equation,
The rate law or rate equation for a chemical reaction is an equation that links the reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders).
order of reaction,
The rate equation shows the effect of changing the concentrations of the reactants on the rate of the reaction. What about all the other things (like temperature and catalysts, for example) which also change rates of reaction? Where do these fit into this equation? These are all included in the so-called rate constant – which is only actually constant if all you are changing is the concentration of the reactants. If you change the temperature or the catalyst, for example, the rate constant changes. This is shown mathematically in the Arrhenius equation.
order of reaction,
rate constant,
half-life of a first-order reaction,
rate determining step,
The rate determining step is the slowest step of a chemical reaction that determines the speed (rate) at which the overall reaction proceeds. The rate determining step can be compared to the neck of a funnel.
activation energy
the minimum quantity of energy that the reacting species must possess in order to undergo a specified reaction.

and catalyst;
a substance that increases the rate of a chemical reaction without itself undergoing any permanent chemical change.

Catalysts increase the rate of reaction without being used up. They do this by lowering the activation energy needed. With a catalyst, more collisions result in a reaction, so the rate of reaction increases. Different reactions need different catalysts.

(b) explain qualitatively, in terms of

collision theory,

the effects of concentration and temperature on the rate of a reaction.

If the temperature is increased: the reactant particles move more quickly. … the particles collide more often, and more of the collisions result in a reaction. the rate of reaction increases.

Effect of temperature and concentration

The rate of a chemical reaction can be increased by raising the temperature. It can also be increased by increasing the concentration of a reactant in solution, or the pressure of a reactant gas.

Changing the temperature
If the temperature is increased:
– the reactant particles move more quickly
– they have more energy
– the particles collide more often, and more of the collisions result in a reaction
– the rate of reaction increases

Changing the concentration or pressure
If the concentration of a dissolved reactant is increased, or the pressure of a reacting gas is increased:
– the reactant particles become more crowded
– there is a greater chance of the particles colliding
– the rate of reaction increases

Factors Affecting Reaction Rates
i. Physical state of reactants
1. The more the reactants collide with each other, the faster the reaction rate.
2. If reactants are in different phases, the reaction is limited to the area of
contact.
3. Increasing surface area of a solid increases reaction rate.
ii. Concentration of reactants
1. If the concentration of one or more reactants is increased, most reactions will
go faster, due to an increased frequency of collisions.
iii. Temperature
1. Reactions go faster as temperature is increased.
• Increasing temperatures increases the kinetic energy of particles.
• Particles at higher temperatures collide more frequently and with
higher energy.
iv. Catalysts
1. Catalysts increase reaction rates without being used up.
2. Catalysts affect the kinds of collisions that lead to reaction.
5.2 Rate law

Candidates should be able to:

(a) calculate the rate constant from initial rates;
(b) predict an initial rate from rate equations and experimental data;
(c) use titrimetric method to study the rate of a given reaction.

Candidates should be able to:

(a) calculate the rate constant from initial rates;

(b) predict an initial rate from rate equations and experimental data;

(c) use titrimetric method to study the rate of a given reaction.
5.3 The effect of temperature on reaction kinetics

Candidates should be able to:

(a) explain the relationship between the rate constants with the activation energy and temperature using Arrhenius equation k = Ae ^[-(Ea/RT)]
(b) use the Boltzmann distribution curve to explain the distribution of molecular energy.

Candidates should be able to:

(a) explain the relationship between the rate constants with the activation energy and temperature using Arrhenius equation k = Ae ^[-(Ea/RT)]

(b) use the Boltzmann distribution curve to explain the distribution of molecular energy.
5.4 The role of catalysts in reactions

Candidates should be able to:

(a) explain the effect of catalysts on the rate of a reaction;
(b) explain how a reaction, in the presence of a catalyst, follows an alternative path with a lower activation energy;
(c) explain the role of atmospheric oxides of nitrogen as catalysts in the oxidation of atmospheric sulphur dioxide;

(d) explain the role of vanadium (V) oxide as a catalyst in the Contact process;
(e) describe enzymes as biological catalysts.

Candidates should be able to:

(a) explain the effect of catalysts on the rate of a reaction;

speeds up the rate of a chemical reaction
not consumed
appear in the steps of a reaction mechanism
but it will not appear in the overall chemical reaction (as it is not a reactant or product)
alter the mechanism of the reaction in a substantial way
new barriers along the reaction coordinate are significantly lower
By lowering the activation energy
rate constant is greatly increased (at the same temperature)
types of catalysts

Many reactions are catalyzed at the surface of metals
biochemistry, enormous numbers of reactions are catalyzed by enzymes

same phase as the chemical reactants or in a distinct phase.
same phase are called homogeneous catalysts
different phases are called heterogeneous catalysts
enzyme in solution catalyzing a solution phase biochemical reaction is a homogeneous catalyst
catalysts is that they are selective
catalyst doesn’t just speed up all reactions, but only a very particular reaction
Living biological systems require a myriad of specific chemical transformations
there is a unique enzyme to catalyze each of them.

Effect of catalysts

The effect of a catalyst is that it lowers the activation energy for a reaction.
catalyst changes the way the reaction happens (the mechanism).
We can visualize this for a simple reaction coordinate in the following way.
catalyzed reaction may have a number of new barriers and intermediates
the highest barrier will now be significantly lower than the previous largest barrier.
path with the catalyst now has two steps along with an intermediate species
the barriers for both steps are much much lower than in the uncatalyzed reaction.
How do catalysts work?
Many work same way.
provide a means for the reactant molecules to break bonds
form temporary bonds with the catalyst
catalyst must be somewhat reactive
but not too reactive (since we don’t want these bonds to be permanent)

Pt metal serves as a catalyst for many reactions involving hydrogen gas or oxygen gas
Pt metal as a catalyst for the reaction of hydrogen gas and ethene gas
Pt is a heterogeneous catalyst
This is because the Pt surface allows the H2 or O2 to break their bonds then form atomic species that are “bonded” to the Pt
new bonds can be weak enough that the atomic species can then react with other molecules and leave the surface
Pt metal returns to its pristine state after the reaction.
reaction of ethene and hydrogen gas
(1). The hydrogen lands on the surface and breaks its bond to form H atoms bonded to the surface
(2). The double bond of the ethene is also broken and the two carbon atoms also bond to the surface
(3).  Then the H atoms can migrate until they collide with the bound carbon species and react
(4) to form ethane which can then leave the surface
(5).

Is this how all catalysts work?  No.
The possibilities for how a catalysts actually works are endless.
Some catalysts actually change during the course of the chemical reaction, but then are returned to their original state at the end of the reaction.  For example, MnO2 catalyzes the decomposition of H2O2 to water and oxygen gas by the following mechanism. net reaction there is no change in MnO2.
during the reaction it is converted into Mn2+ as well as Mn(OH)2.
A catalyst can be identified this way in a reaction mechanism as it appears in the “reactants” initially but then is reformed later in the reaction.
function by “holding” molecules in particular configurations while simultaneously weakening some particular bonds.  This allows the catalyst to essentially “help” the chemistry by arranging the reacts in favorable geoemetries as well as by weakening bonds that need to break along the reaction coordinate.

(b) explain how a reaction, in the presence of a catalyst, follows an alternative path with a lower activation energy;

(c) explain the role of atmospheric oxides of nitrogen as catalysts in the oxidation of atmospheric sulphur dioxide;

(d) explain the role of vanadium (V) oxide as a catalyst in the Contact process;

The contact process is the current method of producing sulfuric acid in the high concentrations needed for industrial processes. Platinum used to be the catalyst for this reaction; however, as it is susceptible to reacting with arsenic impurities in the sulfur feedstock, vanadium(V) oxide (V2O5) is now preferred.

(e) describe enzymes as biological catalysts.

Enzymes
Enzymes are biological catalysts.
They are proteins that fold into particular conformations such that they can help speed up very particular chemical reactions
For biochemical reactions, the reactant is typically called the substrate.
The substrate is converted into the product.
The mechanisms for many enzymes are very similar.
The substrate(s) and the enzyme bind into a complex.
The physical location on the enzyme in which the substrate binds is called the “active site”.
Once bound this complex can then weaken particular bonds in the substrate such that chemistry occurs to form the product.
The product is weakly bound to the substrate such that it now dissociates and the enzyme is free to bind another substrate molecule.
The active sites in enzymes can be very specific such that the enzyme will only catalyze a very specific reaction for a very specific molecule.

Typically there is an equilibrium between the bound complex and the free substrate and enzyme such that the binding could be reversible.
In contrast, once the product is formed the backward reaction typically will never happen.

Substrate + Enzyme  ↔  Complex → Product.

The activity of many enzymes can be blocked by molecules which mimic the substrate but don’t do any chemistry.  These molecules then effectively “turn off” the enzyme by blocking the active site and preventing binding of the substrate.  Many pharmaceutical drugs operate in this way.  Such molecules are typically called inhibitors as they inhibit the activity of the enzyme.

5.5 Order of reactions and rate constants

Candidates should be able to:

(a) deduce the order of a reaction (zero-, first- and second-) and the rate constant by the initial rates method and graphical methods;
(b) verify that a suggested reaction mechanism is consistent with the observed kinetics;
(c) use the half-life (t½) of a first-order reaction in calculations.

Candidates should be able to:

(a) deduce the order of a reaction (zero-, first- and second-)

and the rate constant by the initial rates method and graphical methods;

(b) verify that a suggested reaction mechanism is consistent with the observed kinetics;

(c) use the half-life (t½) of a first-order reaction in calculations.