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# Reaction Rates

A chemical reaction involves the conversion of reactants to form new substances. These newly formed substances are called as products. The chemical equation can be used to represent the chemical reaction. The arrow between reactants and products is always headed towards products which indicate that reactants convert into products. The two sided arrow indicates a reversible reaction whereas single headed arrow indicates the irreversible reactions.

In a chemical reaction, reactant molecules are colliding with each other to form products. The collision between reactant molecules must be effective to form the products. All reactants molecules must have a minimum amount of energy to convert into product molecules. Similarly for effective collisions another essential condition is the correct orientation of molecules towards each other. The proper orientation of reactant molecules can only form product molecules. As the reaction moves in the forward direction, the concentration of reactant molecules decreases whereas the concentration of products increases.
In other words, with time the concentration of reactants and product change in the chemical reaction. It is just like with time, the distance cover by the rider changes and we can calculate the velocity with the covered distance and time. Similarly the speed of reaction can also be determined with the determination of change in concentration of involved molecules.

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## Activation Energy

Molecules require some minimum energy to react. Chemists visualize this as an energy barrier that must be surmounted by the reactants for a reaction to occur. The energy required to surmount the barrier is called the activation energy (Ea).

If the barrier is low the energy required is low, and a high proportion of the molecules in a sample may have sufficient energy to react. In such a case, the reaction will be fast. If the barrier is high the activation energy is high, and only a few reactant molecules in a sample may have sufficient energy.

In this case the reaction will be slow.

If the system of the reactant atoms is to proceed from the reactant to the product state it must somehow be excited at least to the energy corresponding to the activation energy.
In chemical kinetics the activation energy (abbreviated as Ea) is the energy barrier, which must be overcome for a sufficient number of molecules to acquire enough kinetic energy for a reaction to occur appreciably. The activation energy can generally be achieved by supplying external energy.

For most solid state reactions at low pressure, the volume change is small and hence the change in enthalpy $\Delta$H is approximated to the internal energy of the activated state.

The term "activation energy" is commonly used synonymously with activation enthalpy in such cases, although it is very important to note that this is not the same as free energy. Activation energy is expressed by the following expression.
K = A e-Ea/RT
Where 'K' is the rate constant, 'A' is the frequency factor, 'Ea' is the activation energy, 'R' is the gas constant and 'T' is the temperature given.

## Activation Energy and Catalysis

### Activation Energy

All chemical reactions that release free energy tend to occur spontaneously. Most of the reactions require an input of energy to get started. Before it is possible to form new chemical bonds, even bonds which have less energy, it is necessary to break the existing bonds, and that requires energy. The extra energy required to destabilize existing chemical bonds and initiate a chemical reaction is called activation energy.

The rate of an exergonic reaction depends on the activation energy required for the reaction to begin. Reactions with larger activation energies in overcoming the initial energy hurdle. Activation energies are not constant however; stressing particular chemical bonds can make them easier to break. The process of influencing chemical bonds in a way that lowers the activation energy needed to initiate a reaction is called catalysis, and substances that accomplish this are known as catalysts.

Catalysts cannot violate the basic laws of thermodynamics. They cannot for example make an endergonic reaction proceed spontaneously. By reducing the activation energy, a catalyst accelerates both the forward and the reverse reactions by exactly the same amount. Hence it does not alter the proportion of reactant ultimately converted into product.
The rate of a reaction depends on the activation energy necessary to initiate it. Catalysts reduce the activation energy and increase the rate of reaction although they do not change the final proportion of reactants and products.
The direction of a chemical reaction proceeds solely by the difference in free energy between reactants and products. Catalysts reduce the energy barrier that is preventing the reaction from proceeding. Catalysts don't favor endergonic reactions any more. Only exergonic reactions can proceed spontaneously and catalysts cannot change that.

1. The positive catalyst increases the rate of reaction by lowering the activation energy.
2. Catalyst does not change the heat of reaction. It makes a reaction faster by enhancing the rate of both backward and forward reactions thereby early establishing the equilibrium.
3. Catalyst do not change the yield of products.
4. The negative catalyst retards the rate of chemical reaction by deactivating the reactant molecules.

## Factors Affecting the Rate of Reaction

The rate of reaction for a given chemical change is the speed with which the reactants disappear and the products form. It is measured by the amount of products produced or reactants consumed per unit time. Usually this is done by monitoring the concentration of the reactants or products over time as the reaction runs.

The factors that affect the rate of the reaction are -
1. Nature of the reactants and products
2. Concentration of the reactants
3. Temperature of the system
4. Pressure of the reacting system
5. Nature of the catalyst if present
6. Surface area of reactants
7. Rate of heat and mass transfer
Chemists have identified many factors that affect the rate of a reaction. Some of these factors can be altered or controlled by chemists and some cannot.

### Nature of the Reactants

The nature of reactants includes not only the physical state of each reactant but also the particle size. The reaction rate is generally faster between liquid-state reactants than between solid-state reactants and is fastest between gaseous state reactants. Of the three states of matter the gaseous state is the one where there is the most freedom of movement and hence, collision between reactants are the most frequent in this state.

In the solid state, reactions occur at the boundary surface between reactants. The reaction rate increases as the amount of boundary surface area increases; subdividing a solid into smaller particles increases surface area and thus increases reaction rate.

When the particle size of a solid is extremely small, reaction rates can be so fast that an explosion results. Although a lump of coal is difficult to ignite, the spontaneous ignition of coal dust is a real threat to underground coal-mining operations.

### Change in Concentration of Reactants

According to law of mass action, the rate of a chemical reaction is directly proportional to the product of molar concentration of reactants. In a chemical reaction, the concentration of reactants decreases with time and simultaneously the concentration of products increases with time. Hence higher the initial concentration of reactants, higher will be the initial rate of reaction and the rate of the reaction decreases with time with decrease in concentration of reactants.

### Surface Area of the Reactants

The surface area of reactants influences the rate of heterogeneous chemical reactions. As particle size decreases, the total surface area for a given mass of reactants increases. Since such reactions occur by adsorption phenomenon the smaller molecules react faster than the larger particles.

Generally speaking, the greater the exposed surface area of the reactant, the greater the reaction rate. Foe example, a large piece of coal burns very slowly but coal dust burns rapidly, a consequence of which can lead to a disastrous coal mine explosion; solid potassium iodide reacts very slowly with solid lead nitrate, but when both are dissolved in solution the formation of lead iodide is instantaneous.

### Effect of Temperature

Since the number of activated molecules increases with the increase in temperature the number of effective collisions also increases with the rise in temperature and this increases the rate of reaction.

It is observed that the rate of majority of chemical reactions generally increases with rise in temperature. A rise of 10oC in temperature doubles and in some cases, even triples the rate of reaction and the rate constants. That is
$\frac{K35oC}{ K25oC}$≅ 2 - 3
This is called temperature coefficient of the reaction.

### Presence of a Catalyst

A catalyst increases the rate of a chemical reaction without undergoing any net chemical change. Some catalysts increase the rate of only one specific chemical reaction without affecting similar reactions. Other catalysts are more general and affect an entire set of similar reactions. Catalysts generally reroute the pathway of a chemical reaction so that this "alternate" path although perhaps more circuitous, has a lower activation energy for reaction than the uncatalyzed reaction.

A catalyst is generally specific in its action. It may affect a particular reaction only and becomes ineffective for some other reaction. A chemical reaction taking place with the help of a catalyst is called catalytic or catalyzed reaction. A catalyst does not alter the state of equilibrium and helps to attain the equilibrium faster. Overall, a catalyst is a substance which increases the rate of a chemical reaction and itself is not consumed in the overall reaction.

## Reaction Rate Problems

Below you could see problems

### Solved Examples

Question 1: For a reaction
2I → I2
in carbon tetrachloride, the value of the rate constant at 23oC is 7.0 x 106 m3 mol-1 S-1. At 30oC the value is 7.7 x 106 m3 mol-1 S-1. Find the activation energy.
Given data

R = 8.314 J /mol
T1 = 23oC = 23oC + 273 = 296K
T2 = 30oC = 30oC + 273K = 303K
K1 = 7.0 x 106 m3 mol-1 S-1
K2 = 7.7 x 106 m3 mol-1 S-1
Solution:
Ea = RT ln (K2 / K1) / (1/T1) - (1/T2)
Substitute all the values in the above equation
Ea = (8.314) ln {( 7.7 x 106 m3 mol-1 S-1) / (7.0 x 106 m3 mol-1 S-1)} / (1 / 296K) - (1 / 303K)

Ea = 10200 J mol-1

Question 2: The rate constant for the decomposition of NO2 is 0.516 L mol-1 S-1 at 592K and is 1.70 L mol-1 S-1 at 627K. Calculate the activation energy for the reaction.Given data

R = 8.314 J /mol
T1 = 592K
T2 = 627K
K1 = 0.516 L mol-1 S-1
K2 = 1.70 L mol-1 S-1
Solution:
Ea = RT ln (K2 / K1) / (1/T1) - (1/T2)
Substitute all the values in the above equation
Ea = (8.314) ln {( 1.70 L mol-1 S-1) / ( 0.516 L mol-1 S-1)} / (1 / 592K) - (1 / 627K)

Ea = 1.05 x 105 J / mol

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