Chemical Kinetics Of 1st And 2nd Order Rxn Biology Essay

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Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction. In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.

Rate of reaction

Chemical kinetics deals with the experimental determination of reaction rates from which rate laws and rate constants are derived. Relatively simple rate laws exist for zero-order reactions (for which reaction rates are independent of concentration), first-order reactions, and second-order reactions, and can be derived for others. In consecutive reactions the rate-determining step often determines the kinetics. In consecutive first-order reactions, a steady state approximation can simplify the rate law. The activation energy for a reaction is experimentally determined through the Arrhenius equation and the Eyring equation. The main factors that influence the reaction rate include: the physical state of the reactants, the concentrations of the reactants, the temperature at which the reaction occurs, and whether or not any catalysts are present in the reaction.

Factors affecting reaction rate

Nature of the reactants

Depending upon what substances are reacting, the time varies. Acid reactions, the formation of salts, and ion exchange are fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be very slow. Nature and strength of bonds in reactant molecules greatly influences the rate of its transformation into products. The reactions which involve lesser bond rearrangement proceed faster than the reactions which involve larger bond rearrangement.

Physical state

The physical state (solid, liquid, or gas) of a reactant is also an important factor of the rate of change. When reactants are in the same phase, as in aqueous solution, thermal motion brings them into contact. However, when they are in different phases, the reaction is limited to the interface between the reactants. Reaction can only occur at their area of contact, in the case of a liquid and a gas, at the surface of the liquid. Vigorous shaking and stirring may be needed to bring the reaction to completion. This means that the more finely divided a solid or liquid reactant, the greater its surface area per unit volume, and the more contact it makes with the other reactant, thus the faster the reaction. To make an analogy, for example, when one starts a fire, one uses wood chips and small branches-one doesn't start with large logs right away. In organic chemistry, On water reactions are the exception to the rule that homogeneous reactions take place faster than heterogeneous reactions.


Concentration plays a very important role in reactions according to the collision theory of chemical reactions, because molecules must collide in order to react together. As the concentration of the reactants increases, the frequency of the molecules colliding increases, striking each other more frequently by being in closer contact at any given point in time. Think of two reactants being in a closed container. All the molecules contained within are colliding constantly. By increasing the amount of one or more of the reactants it causes these collisions to happen more often, increasing the reaction rate.


Temperature usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have more thermal energy. Although collision frequency is greater at higher temperatures, this alone contributes only a very small proportion to the increase in rate of reaction.

A reaction's kinetics can also be studied with a temperature jump approach. This involves using a sharp rise in temperature and observing the relaxation rate of an equilibrium process.


The presence of the catalyst opens a different reaction pathway with a lower activation energy. The final result and the overall thermodynamics are the same. A catalyst is a substance that accelerates the rate of a chemical reaction but remains chemically unchanged afterwards. The catalyst increases rate reaction by providing a different reaction mechanism to occur with a lower activation energy. A catalyst does not affect the position of the equilibria, as the catalyst speeds up the backward and forward reactions equally.

Agitating or mixing a solution will also accelerate the rate of a chemical reaction, as this gives the particles greater kinetic energy, increasing the number of collisions between reactants and therefore the possibility of successful collisions

General form of reaction

A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, often coming about only after the input of some type of energy, viz. heat, light or electricity. Classically, chemical reactions encompass changes that strictly involve the motion of electrons in the forming and breaking of chemical bonds, although the general concept of a chemical reaction, in particular the notion of a chemical equation, is applicable to transformations of elementary particles, as well as nuclear reactions.

The substance/substances initially involved in a chemical reaction are called reactants. Chemical reactions are usually characterized by a chemical change, and they yield one or more products, which usually have properties different from the reactants.


(reactnt) (product)

The Rate Law

The rate law expresses the relationship of the rate of reaction to the rate constant and the concentrations of the reactants raised to some powers.

For general reaction-:

aA + Bb Cc + Dd

the rate law takes the form-:

rate = k[A]˟[B]ʸ

where 'x' and 'y' are no. that can be determined experimentally.

Half Life

Half-life is the period of time it takes for a substance undergoing decay to decrease by half. The name originally was used to describe a characteristic of unstable atoms (radioactive decay), but may apply to any quantity which follows a set-rate decay.

The original term, dating to 1907, was "half-life period", which was later shortened to "half-life" sometime in the early 1950s.[1]

Half-lives are very often used to describe quantities undergoing exponential decay-for example radioactive decay-where the half-life is constant over the whole life of the decay, and is a characteristic unit (a natural unit of scale) for the exponential decay equation. However, a half-life can also be defined for non-exponential decay processes, although in these cases the half-life varies throughout the decay process. For a general introduction and description of exponential decay, see the article exponential decay.

Probabilistic nature of half-life

Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note the law of large numbers: With more atoms, the overall decay is less random.A half-life often describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition "half-life is the time required for exactly half of

Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note the law of large numbers: With more atoms, the overall decay is less random.A half-life often describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition "half-life is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom with a half-life of 1 second, there will not be "half of an atom" left after 1 second. There will be either zero atoms left or one atom left, depending on whether or not the atom happens to decay.

Instead, the half-life is defined in terms of probability. It is the time when the expected value of the number of entities that have decayed is equal to half the original number. For example, one can start with a single radioactive atom, wait its half-life, and measure whether or not it decays in that period of time. Perhaps it will and perhaps it will not. But if this experiment is repeated again and again, it will be seen that it decays within the half life 50% of the time.

Order Of Reaction

In chemical kinetics, the order of reaction with respect to a certain reactant, is defined as the power to which its concentration term in the rate equation is raised.

For example, given a chemical reaction 2A + B → C with a rate equation

r = k[A]2[B]1

the reaction order with respect to A would be 2 and with respect to B would be 1, the total reaction order would be 2 + 1 = 3. It is not necessary that the order of a reaction be a whole number - zero and fractional values of order are possible - but they tend to be integers. Reaction orders can be determined only by experiment. Their knowledge allows conclusions about the reaction mechanism.

Zero Order Reaction

For a reaction maximum order is three and minimum is zero.

Zero-order reactions

A 0-order reaction has a rate which is independent of the concentration of the reactant(s). Increasing the concentration of the reacting species will not speed up the rate of the reaction. Zero-order reactions are typically found when a material that is required for the reaction to proceed, such as a surface or a catalyst, is saturated by the reactants. The rate law for a zero-order reaction is

r = k

where 'r' is the reaction rate, and k is the reaction rate coefficient with units of concentration/time. If, and only if, this zero-order reaction 1) occurs in a closed system, 2) there is no net build-up of intermediates, and 3) there are no other reactions occurring, it can be shown by solving a mass balance for the system that:

r = -d[A] = k


If this differential equation is integrated it gives an equation which is often called the integrated zero-order rate law.

[A]t = -kt + [A]0

Where [A]t represents the concentration of the chemical of interest at a particular time, and represents the initial concentration.

A reaction is zero order if concentration data are plotted versus time and the result is a straight line. The slope of this resulting line is the negative of the zero order rate constant k.

The half-life of a reaction describes the time needed for half of the reactant to be depleted (same as the half-life involved in nuclear decay, which is a first-order reaction). For a zero-order reaction the half-life is given by

T1/2 = [A]0


Example of a zero-order reaction

Reversed Haber process: 2NH3 (g) 3H2 + N2

It should be noted that the order of a reaction cannot be deduced from the chemical equation of the reaction.

First Order Reaction

A first-order reaction depends on the concentration of only one reactant (a unimolecular reaction). Other reactants can be present, but each will be zero-order. The rate law for an elementary reaction that is first order with respect to a reactant A is

r = - d[A]/dt = k[A]

k is the first order rate constant, which has units of 1/time.

The integrated first-order rate law is

ln[A] = -kt + ln[A]0

A plot of ln[A] vs. time t gives a straight line with a slope of − k.

The half life of a first-order reaction is independent of the starting concentration and is given by

t ½ = ln[2]/ k.

Examples of reactions that are first-order with respect to the reactant:

1. H2O2(L) H2O(L) + ½ O2

2. SO2Cl2(l) SO2 (l) + Cl2 (g)

Second Order Reaction

A second-order reaction depends on the concentrations of one second-order reactant, or two first-order reactants.

For a second order reaction, its reaction rate is given by:

r = k[A]²


r = k[A][B]


r = k[B]²

The integrated second-order rate laws are respectively

(The stoichiometric factor of 2 should not be included as a part of the rate constant for an elementary reaction of the type 2A → B. Unlike it is presented in several popular kinetics books, the proper definition of the rate law for second-order reactions is . This proper definition is used in most peer-reviewed literature, tables of rate constants, and simulation software[4].)


[A]0 and [B]0 must be different to obtain that integrated equation.

The half-life equation for a second-order reaction dependent on one second-order reactant is . For a second-order reaction half-lives progressively double.

Another way to present the above rate laws is to take the log of both sides:

Examples of a Second-order reaction





Rate Law

Integrated Rate Law

[Except first order]

Units of Rate Constant (k)

Linear Plot to determine k

[Except first order]



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Zumdahl, Steven S. Chemical Principles Fifth Edition. Boston: Houghton Mifflin Company, 2005. 550-551,957-964.

3) Silberberg, Martin S. Chemistry: The Molecular Nature of Matter and Change, Fourth Edition. New York: McGraw Hill Company, 2006. 1028 -1034.

4 )D. F. Shriver and P. W. Atkins Inorganic Chemistry 3rd edition, Oxford University Press, 2001. Pages: 227-236.


Murrel, J. N.; S. F. Tedder (1985). The Chemical Bond. John Wiley & Sons. ISBN 0-471-90759-6

6) I. Hargittai, When Resonance Made Waves, The Chemical Intelligencer 1, 34 (1995))

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8)text book of cordination chemistry by dr.R.K. sharma pg 61,62

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