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Chemical Kinetics (Part I): Overview of Reaction Rates

Chemical kinetics deals with two main aspects of a chemical reaction: the rate of reaction (i.e, the speed at which the reaction occurs), and the reaction mechanism (i.e, the details of all the steps involved in the reaction). In this post, our focus shall be on the rates of chemical reactions.
Rates of Reactions
Rate is the degree of change of the property of a substance with respect to time. A chemical reaction is a change which involves the conversion of reactants to products, as stated below:
                   A ----> B
where A is the reactant and B is the product. In the above hypothetical equation, it can be said that at the beginning of the reaction at time, t = 0, the amount of A present will be 100%, while the amount of B will be 0%. After, a given time, say t1, the concentration of A will decrease, while that of B will be seen to increase. The speed at which these changes occur is said to be the rate of reaction.
Therefore, the rate of a chemical reaction is defined as the amount (concentration, mass or volume) of products formed per unit time. Also, in terms of the reactants, it is the amount (concentration, mass or volume) of reactants converted to products per unit time.
Mathematically, it can be expressed as:
rate of reaction = change in concentration of products formed/time taken, i.e,
rate = D[products]/Dt ………(i)
        = D[B]/Dt
(where D = delta (change), [ ] = concentration) or
rate of reaction = change in concentration of reactants converted/time taken, i.e,
rate = -D[reactants]/Dt………(ii)
        = -D[A]/Dt
The negative sign in equation (ii) indicates that the rate of reaction of the reactants decreases with respect to time, i.e,
rate of reaction & 1/time (where & is a sign of proportionality)
The concentration of the products or reactants is measured in mol dm^-3, while the time of reaction is measured in seconds. Therefore, the standard unit of rate of reaction is mol dm^-3 s^-1. However, if the mass or volume of the products or reactants is used, the unit will be expressed in g s^-1 or cm^3 s^-1. The rate of reaction can also be expressed in mol s^-1, if the mass of the product or reactant is converted to amount in moles.
As an illustration, let us consider the thermal decomposition of calcium trioxocarbonate (IV) to produce calcium oxide and carbon (IV) oxide according to the equation:
CaCO3(s) + heat ----> CaO(s) + CO2(g)
If, at the beginning of the reaction, the mass of the marble [CaCO3] was 100g, and after 100seconds, its mass was found to be 90g. Then, the rate of the reaction can be calculated thus:
rate of reaction = change in mass of CaCO3/time taken
                            = (final mass - initial mass)/time taken
                            = (90 - 100)/100
                            = -10/100
                            = -0.1 g s^-1
Similarly, the rate of reaction in mol s^-1 can be calculated by simply dividing the above result by 100 g mol^-1, the molar mass of CaCO3. Thus,
rate of reaction (mol s^-1) = rate of reaction (g s^-1)/molar mass
                                                = -0.1/100
                                                = -0.001 mol s^-1
Alternatively, the rate of reaction can be calculated in terms of the products. Let us assume that the 10g of CaCO3 were converted to CaO and CO2, then:
rate of reaction = change in mass of CaO + CO2 produced/time taken
                            = (final mass - initial mass)/time taken
                            = (10 - 0)/100
                            = 10/100
                            = 0.1 g s^-1
Since chemical reactions involve changes, there are certain properties of matter, which can indicate the possible occurrence of a reaction, and from which the rate of reaction can be determined. They include, but are not limited to:
a) change in mass
b) change in volume
c) change in concentration
d) change in colour intensity
e) degree of effervescence
Rate Curve
A plot of the concentration, mass or volume of the products against time gives a curve which starts from the origin with a steep slope and later flattens out. This curve is known as the rate curve and is used to describe the rate of a given reaction. The point at which the curve becomes parallel to the horizontal axis is the end-point of the reaction or the point at which the reaction is said to be complete. Click here to see the diagram of a rate curve.
Alternatively, the rate curve can be drawn by plotting the concentration, mass or volume of the reactants against time. This will give us a curve, with a negative gradient, that slopes from left to right. The negative gradient shows the inverse relationship between the concentration (mass or volume) of the reactants and time.
Click here to see an illustration, where the concentrations of the products and reactants are plotted on the same axis against time.
Instantaneous Rate: This is the rate of reaction at a given time, ti. It can be determined from the rate curve by calculating the gradient to the curve at a point on it, directly above ti. Click here to see the illustration. That is,
instantaneous rate = amount of product at time, ti /time, ti
Average Rate of Reaction: The rate curve can also be used to determine the average rate of a reaction by dividing the total amount of the products formed by the total time of reaction, bearing in mind, the end-point, i.e,
avg rate of reaction = total amount of products formed/total time of reaction
Collision Theory
Recall that a chemical reaction is the combination of the molecules or particles of the reactants to form products, as it involves bonds breaking and bonds formation. This implies that without the formation of products, a chemical reaction cannot occur. Therefore, to achieve this, there are two conditions that must be satisfied as explained by the collision theory. These are:
a) effective collisions (b) activation energy
Effective Collisions: During a reaction, millions of particles of the reactants undergo millions of collisions with one another to bring about the breaking of existing and subsequent formation of new intramolecular bonds. However, only a fraction of these collisions will actually result in the formation of products. This fraction is called effective collision, as illustrated in this chart.
Activation Energy: During a reaction, as the molecules of the reactants collide with one another, their potential energies are converted to kinetic energies. Hence, an increase in the frequency of collision leads to an increase in the average kinetic energy of the reactants. However, there is a minimum amount of energy, which the reactants must possess, without which no reaction can occur. This energy barrier is known as the activation energy, Ea.
The relationship between the rate of reaction, temperature and activation energy is given by the Arrhenius equation:
             Rate = Ae^(-Ea/RT) ...…(iii)
where,
A = a constant called the collision factor
Ea = activation energy (kJ mol^-1)
R = gas constant (8.314 J mol^-1 K^-1)
T = absolute temperature
The above equation is useful for determining the Ea of a reaction, through a graphical method or by studying the reaction at two different temperatures (T1 and T2), and evaluating the two equations simultaneously to obtain equation (vi) as shown:
Taking the natural log of both sides of equation (iii) under both conditions gives us,
                    ln Rate1 = ln A - Ea/RT1 ……………(iv)
                    ln Rate2 = ln A - Ea/RT2 ……………(v)
Subtract equation (iv) from (v)
  ln Rate2 - ln Rate1 = -Ea/RT2 - (-Ea/RT1)
  ln Rate2 - ln Rate1 = Ea/RT1 - Ea/RT2
      ln [Rate2/Rate1] = (Ea/R)[1/T1 - 1/T2] ………(vi)
Factors Affecting the Rates of Chemical Reactions
From the collision theory, it can be deduced that any factor that directly affects the frequency of collisions and the activation energy can influence the reaction rate. Such factors include:
a) effect of temperature
b) effect of concentration/pressure of the  reactants
c) effect of nature of the reactants
d) effect of surface area of contact of reactants
e) effect of a catalyst
Temperature: According to the kinetic theory of matter, the average kinetic energy of a body is directly proportional to its absolute temperature. This implies that if the temperature of a reaction is increased, it will lead to a corresponding increase in the frequency of collisions of the particles of the reactants, which has a direct implication on the average kinetic energy. The increased collisions or kinetic energy causes more molecules to acquire enough energy to overcome the energy barrier and form products, as illustrated in these charts showing the relationship between temperature and activation energy.
This explains why a cube of sugar dissolves faster in hot water than cold water. This is also why the liberation of carbon (IV) oxide will be seen to be greater when marble is heated at a higher temperature (say 30°C), than when it is heated at a lower temperature (say 20°C). If the graphs of the mass of CO2 produced under the two conditions are plotted against time on the same axes, two rate curves A (high temp) and B (low temp) will be obtained.
Reaction A is seen to come to completion first before reaction B. Also, the slope of reaction A is steeper at the beginning than that of reaction B, which indicates that the rate of reaction A is higher or faster than that of reaction B. Generally, increasing the temperature of the reaction increases the rate of a chemical reaction.
Concentration/Pressure of Reactants: Concentration is a term used to describe the amount of molecules or particles of a substance present in a given volume, space or region. Pressure, on the other hand, is the force exerted per unit area by gaseous molecules. So, while concentration has an effect on the reaction rate of solid and aqueous systems, pressure affects the rate of reaction of gaseous systems.
The number of molecules available in a particular space will determine the frequency of collisions in the reaction vessel. If there are say, 10 molecules of a substance in about 1,000cm^3 of its solution, it will take a longer time for the molecules to collide with one another because the average distance between them is wide. This translates to a slow rate of reaction.
However, if the amount of molecules in the 1,000cm^3 is increased to about 1,000; then, the reacting molecules will take a shorter time to collide with one another, because the average distance between them has been reduced due to overcrowding (higher concentration). Since the frequency of collisions of the molecules per unit time is increased, the rate of reaction will also increase.
This also holds true for gaseous systems. A gaseous system is one, by which at least one of the reactants is in the gaseous phase. So, increasing the pressure of the system is tantamount to decreasing the volume and the available area for collisions. Hence, the frequency of collisions will be higher, because the gas molecules will collide more with one another within a short time than when the pressure is decreased (i.e, increased volume).
Generally, the higher the concentration or pressure of the reactants, the higher the rate of reaction.
Nature of Reactants: The ability of a substance to react with other substances can also determine how fast or far, a reaction can go. For instance, let us consider the reaction of sodium, iron and gold with water. If a pellet of sodium metal is dropped into a beaker of cold water, the reaction proceeds vigorously with the liberation of heat and hydrogen gas, according to the equation:
            2Na(s) + 2H2O(l) ----> 2NaOH(aq) + H2(g)
The iron, on the other hand, does not react with the cold water, but reacts moderately with steam at red heat to produce hydrogen gas.
           3Fe(s) + 4H2O(g) ----> Fe3O4(s) + 4H2(g)
The gold will not react with the water, irrespective of the conditions. This is because, it is relatively unreactive by nature.
So, based on their chemical reactivity, if the three metals are involved in the same type of reaction under the same conditions, the reaction of sodium will be expected to end first (fastest reaction rate), followed by iron, while that of gold will come last (slowest reaction rate).
Therefore, the more reactive the reactants are, the faster the rate of reaction will be.
Surface Area of Contact: This is the portion of the reactants exposed at a given time, for a reaction. Usually, it is analysed based on the fineness of the reactant particles, with the finest forms (powder, dust etc) having the largest surface area, and the coarsest forms (lumps, rods, pellets etc) having the smallest surface area. This is because in the powdery form, there are more molecules available for collision at a given time, than in the lumpy form.
Let us consider the dissolution of two forms of sugar of equal mass in the same volume of water. The granulated sugar will be seen to dissolve faster than the sugar cubes. This is because, all the particles of the granulated sugar are exposed to hydration by the water molecules at the same time; whereas, in the sugar cubes, only the particles at the surfaces are available for hydration at a given time, and until they are completely hydrated and the surface layers broken down, the inner particles cannot be hydrated. This delays the dissolution of the sugar.
Hence, the larger the surface area of contact of the reactants, the faster the rate of reaction.
Catalyst: A catalyst is a substance that alters the rate of a reaction. It can be positive or negative.
A positive catalyst increases the rate of a chemical reaction by lowering the energy barrier of the reaction, e.g, manganese (IV) oxide [MnO2] in the thermal decomposition of potassium trioxochlorate (V) [KClO3] to produce potassium chloride [KCl] and oxygen gas.
  2KClO3(s) + MnO2 + heat ---->   2KCl(s) + 3O2(g)
                    
It achieves this by creating a new reaction pathway with a lower activation energy, by which the reactants can pass through to form the products. By reducing the energy barrier, more reacting molecules will possess the minimum energy required to form the products, as illustrated in this energy profile diagram.
A negative catalyst, on the other hand, decreases the rate of a chemical reaction by increasing the activation energy of the reaction.
There are certain reactions, which are catalysed by light. These reactions are known as photocatalytic reactions and examples include:
i) photosynthesis
ii) the chlorination of alkanes
iii) the reduction of silver ions to silver atoms in photography
iv) the reaction between hydrogen and halogens etc.
These reactions occur in the presence of sunlight or a source of UV light. The molecules of the reactants absorb the light energy and convert it to kinetic energy, which results in their excitement and increased frequency of collisions. This results in a higher percentage of effective collisions, and subsequent formation of products. The rates of the reactions vary depending on the intensity of the light and the nature of the reacting species. For instance, in the presence of sunlight, hydrogen reacts explosively with fluorine, vigorously with chlorine, moderately with bromine, and slowly with iodine. However, the reaction between hydrogen and chlorine will occur very slowly (almost negligibly) in the dark.
Collision Theory & Heat of Reaction
Recall that a chemical reaction involves bonds breaking and bonds formation. During this process, energy is evolved and absorbed in the form of bond energies, which are converted to heat energy of the system. Bond breaking occurs within the reactants, while bond formation occurs in products. It is important to note that when a bond is broken, heat is evolved, and when a bond is formed, heat is absorbed.
The heat content of a substance is also known as its enthalpy, and is represented by H. In a reaction, the enthalpy of reactants, Hr, is the total amount of heat energy evolved when the intramolecular and intermolecular bonds within the reactants are broken, while the enthalpy of products, Hp, is the total amount of heat energy absorbed when these bonds are formed within the products. The difference between Hp and Hr, is the enthalpy of reaction, also known as change in enthalpy, DH.
Hreaction = Hproducts - Hreactants
           DH = Hp - Hr
Exothermic and Endothermic Reactions
Depending on the nature of reaction, the heat content of the products can either be greater or less than the heat content of the reactants. If the heat content of the products is less than that of the reactants, the reaction is said to be exothermic, and DH will be negative. On the other hand, if the heat content of the products is greater than that of the reactants, the reaction is said to be endothermic, and DH will be positive, i.e:
Exothermic:  Hp < Hr;  DH < 0 (-ve)
Endothermic:  Hp > Hr;  DH > 0 (+ve)
Click here for the energy profile diagrams of exothermic and endothermic reactions.
In an exothermic reaction, the excess heat of the reactants is given off to the surrounding, and the reaction vessel is always hot to touch. Examples of exothermic reactions are the dissolution of sodium hydroxide pellets, dissolution of concentrated tetraoxosulphate (VI) acid. However, in an endothermic reaction, the inadequate heat energy which the reactants could not provide is absorbed from the surrounding, and this explains why the reaction vessel is always cold when touched. Example of an endothermic reaction is the dissolution of ammonium chloride [NH4Cl]. Click here to see the illustrations.
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Comments

  1. CORRECTION!

    COLLISION THEORY & HEAT OF REACTION
    Please note that when a bond is broken, energy is absorbed (endothermic), and energy is released when a bond is formed is formed (exothermic). It was an oversight and will be corrected from the back-end. Thank you

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