# Reaction Rate Process and Catalyst

## Catalyst

Those substances which change the rate as well as mechanism of the reaction are called catalyst. Most of the time a catalyst is used to increase the rate of the reaction. Although it participates in the reaction but it gets regenerated at the end of the reaction. A catalyst can be either solid, liquid or gasses.

## Positive Catalysts

Catalysts which increase the rate of a chemical reaction are positive catalysts. It increases the rate of reaction by lowering the activation energy barriers such that a large number of reactant molecules are converted into products.Examples:

Manganese dioxide as a catalyst accelerates the decomposition of potassium chlorate to liberate oxygen.

2 KClO_{3} ---MnO_{2}---> 2 KCl +3 O_{2}

Platinum as a catalyst accelerates the decomposition of hydrogen peroxide.

2 H_{2}O_{2} ---Pt---> 2 H_{2}O + O_{2}

## Negative Catalysts

Catalysts which decrease the rate of reaction are negative catalyst.
It decreases the rate of reaction by increasing the activation energy barrier which decreases the number of reactant molecules to converted into products.

Example:

The decomposition of hydrogen peroxide is suppressed by adding glycerol or Acetanilide to the solution of hydrogen peroxide. Here glycerol or Acetanilide acts as negative catalyst.

2 H_{2}O_{2} ---glycerol or Acetanilide---> 2 H_{2}O + O_{2}

## Promoter or Accelerators

A substance which increases the activity of catalyst are known as Promoters or accelerators.

Example: In Haber’s process (manufacture of ammonia) molybdenum act as Promoters.

## Catalyst Poisons or Inhibitors

Substances which decrease the activity of catalyst are known as catalyst poisons or inhibitors.

Example: In the hydrogenation of alkyne to an alkene, catalyst Pd is poisoned with BaSO_{4} in quinolone solution and the reaction is stopped at alkene level.

## Autocatalysis:

The phenonenon in which one of the products of reaction itself acts as a catalyst is called autocatalysis.

Example: The hydrolysis of ester is catalysed by H^{+} ions which is one of the products of the reaction.

CH_{3}COOC_{2}H_{5} + H_{2}O ⇌ CH_{3}COO^{−} + H^{+} + C_{2}H_{5}OH

Autocatalysed reactions proceed slowly at the start because there is little catalyst present, the rate of reaction increases progressively as the reaction proceeds as the amount of catalyst increases and then it again slows down as the reactant concentration decreases.

The graph for autocatalytic reactions is a sigmoid curve.

## First Order Kinetics

The reaction in which rate is determined by the variation of only one concentration term is called first order reaction.

Let us consider the following first order reaction-

This is the First order kinetics or rate constant for first order reaction.

1. A first order reaction is 20% complete in 10 minutes. Calculate the rate constant of the reaction.

2. Shows that for a first order reaction the time required for 99.9% completion is three times required for the completion of 90% reaction.

## Half life period (t_{1/2}) for First Order Reaction:

The time during which initial concentration of reactant is reduced to half is called half life period. It is denoted as t_{1/2}

We know that, for first order reaction, the rate constant (k) is-

k = (2.303/t) log(a/a-x) -------1

where a is initial concentration of reactant and (a-x) is concentration after time t.

From equation 1-

t = (2.303/k) log(a/a-x) -------2

Now, when, t = t_{1/2} then, x = a/2

Now putting the value of t and x in equation 2 we get-

t_{1/2} = (2.303/k) log2

or, t_{1/2} = 0.693/k --------3

From the equation 3 we see that half life period is inversely proportional to k and independent of initial concentration of the reactant.

## Second Order Kinetics

The reaction in which the rate is determined by the variation of two concentration terms of the reactant.

## Third Order Kinetics

The reaction in which the rate is determined by the variation of three concentration terms of the reactant.

## Methods for Determination of Order of a Reaction

Following methods can be use to detrmine the order of reaction-

1. Differential Method or Initial Rate Method

2. Graphical Method

3. Half Life Method

4. Van't Hoff Differential Method

## Differential Method

It is also called initial rates method. In this method concentration of one reactant varies while others are kept constant concentration and initial rate of reaction is determined. Suppose if three reactants A, B and C are taking part in the reaction then in this method we keep vary concentration of one reactant (for example reactant A) while concentration of other reactants such B and C constant.

## Graphical Method

This method can be used when there is only one reactant.

a. If the plot of log [A] vs time 't' is a straight line, the reaction follows first-order.

b. If the plot of 1/[A] vs time 't' is a straight line, the reaction follows second order.

c. If the plot of 1/[A]^{2} is a straight line , the reaction follows third order.

d. Generally, for a reaction of nth order, a graph of 1/[A]^{n-1} vs time 't' must be a straight line.

## Half Life Method

This method is used only when the rate law involved by only one concentration term.

t_{1/2} ∝ a^{1 − n}

or, t_{1/2} = K. 1/a^{n − 1}

or, log t_{1/2} = logK + (1 − n)a

Graph of *log t _{1/2} vs log a*, gives a straight line with slope (1-n) , where 'n' is the order of the reaction.Determining the slope we can find the order 'n' of reaction.

## Van't Hoff Differential Method

The differential rate equations for different order of reactions are-

1. dx/dt = k(a-x)^{0} for zero order reactions.

2. dx/dt = k(a-x)^{1} for first order reactions.

3. dx/dt = k(a-x)^{2} for second order reactions.

4. dx/dt = k(a-x)^{3} for third order reactions.

So for nth order reaction, the rate equation is-

dx/dt = k(a-x)^{n}

Let (a-x) = 'c' at any instant

− dx/dt = kc^{n}

For two different concentrations c_{1} and c_{2} of the reactants, we have-

− dc_{1}/dt = kc_{1}^{n} -----equation-1

− dc_{2}/dt = kc_{2}^{n} -----equation-2

taking log on both sides we get-

log(− dc_{1}/dt) = logk + nlog c_{1} -----equation-3

log(− dc_{2}/dt) = logk + nlog c_{2} -----equation-4

subtracting equation-4 from equation-3 we get-

nlog c_{1} − nlog c_{2} = log(− dc_{1}/dt) − log(− dc_{2}/dt)

n(log c_{1} − log c_{2}) = log(− dc_{1}/dt) − (− dc_{2}/dt)

n = [log(− dc_{1}/dt) − (− dc_{2}/dt)]/(log c_{1} − log c_{2})

The rates of reactions at two different concentrations can be calculated from the slopes of 'c' vs 't' plots. Substituting these values in the above equation, the order of the reaction can be determined.

## Effect of Catalyst on Rate of Reaction

Catalysts are chemical substance which change the rate of a chemical reaction without itself undergoing any permanent chemical change. They may participate in the reaction, but again regenerated and the end of the reaction. So it is of two types. One is Positive catalyst which increases the rate of reaction by decreasing the activation energy and Other is Negative catalyst which decreases the rate of reaction by increasing the activation energy. Catalyst does not change the quantity of products formed.

Example- Decomposition of potassium chlorate is increased by addition of MnO_{2}

2KClO_{3} ---MnO_{2}→ 2KCl + 3O_{2}

Decomposition of hydrogen peroxide solution is decreased in presence of glycerine.

2H_{2}O_{2}(aq) ---glycerine→ 2H_{2}O(l) + O_{2}(g)

## Activation Energy

Activation energy is defined as the minimum amount of extra energy required by a reacting molecule to get converted into product. It can also be described as the minimum amount of energy needed to activate molecules or atoms so that they can undergo a chemical reaction.

In case of ionic reactant, the activation energy will be low because there is an attraction between reacting species While in case of covalent reactant the activation energy will be high because energy is required to break the older bonds.

Positive catalyst also decrases the activation energy while negative catalyst increases the activation energy.

Smaller the activation energy, faster the rate of reaction.

Activation energy is denoted by Ea and is usually measured in joules (J) and or kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).

## Potential Energy Diagrams and Activated Complex

The energy changes that occur during a chemical reaction can be shown in a diagram called a potential energy diagram. A potential energy diagram shows the change in potential energy of a reactants are converted into products.

The enthalpy change (ΔH) is positive for an endothermic reaction and negative for an exothermic reaction.

The total potential energy of the system increases for the endothermic reaction as the system absorbs energy from the surroundings while the total potential energy of the system decreases for the exothermic reaction as the system releases energy to the surroundings. The first one graph is of endothermic while the second one is of exothermic reaction.

**Activated Complex** is a transitional state between the reactants and products. The transitional complex is a short-lived, very unstable species that is the intermediate between the reactants and products. So, It is the 'energy barrier' that must be overcome when changing reactants into products. The activated complex contains the highest amount of energy (where bonds are breaking and forming) of all of the species in the reaction. Its position is therefore at the top of the activation energy barrier.

## Arrhenius Equation

Arrhenius proposed an equation to calculate the activation energy of a chemical equation having rate constant 'K' and temperature 'T' in 1889.

By knowing the value of K_{1}, K_{2}, T_{1} and T_{2}, we can easily calculte the value of Activation Energy.

Straigh line equation for Arrhenius equation-