Mahatma Gandhi P.G. College, Chemical kinetics BY Dr. N. K. shukla Associate Professor Mahatma Gandhi P.G. College, Gorakhpur-273001

CONTENTS Rate of a reaction and Factors influencing it Mathematical characteristics of simple chemical reactions Determination of the order of reaction

Rate of a reaction The rate of a reaction is the speed at which chemical reactions proceed. It is often expressed im terms of either the concentration (amount per unit volume) of a product that is formed in a unit of time or the concentration of a reactant that is consumed in a unit of time. The rate of reaction depends in several factors like concentration, temperature, pressure, solvent, light.

Factors influencing the rate of reaction CONCENTRATION: According to the law of mass action, the rate of reaction depends on the molar concentration of the reactants. Since the concentration of the reactants keep on falling with time, the rate of reaction keeps on decreasing with time. TEMPERATURE: Temperature (in Kelvin) is proportional to the kinetic energy of the particles in a substance. At higher temperatures, particles collide more frequently and with greater intensity an this increases the rate of reaction.

Factors influencing the rate of reaction PRESSURE : Under high pressure, gas molecules collide more frequently and at a faster rate. SOLVENT: The solvents are used to dissolve the reactants while doing so they help in providing more interactive surface between reactant molecules which may be otherwise in different phases or strongly bonded in solid phase. LIGHT: Light contains photons which provide energy to break chemical bonds and therefore overcome activation energy. The greater the intensity of light (visible or ultra violet) the more reactant molecules are likely to gain the required energy (activation energy) and react, so the reaction speed increases.

Factors influencing the rate of reaction CATALYST: A catalyst is a substance that can increase the velocity of a reaction but which itself remains unchanged in amount and chemical composition at the end of the reaction. When a catalyst is added, a new reaction path with a lower energy barrier is provided. Since the energy barrier is reduced in magnitude, a large number of molecules of the reactants can get over it.

Mathematical characteristics of simple chemical reactions FIRST ORDER REACTION: The rate law for first order reaction is given by: We can rearrange this equation to combine our variables and integrate both sides to get the integrated rate law: Finally putting this equation in terms of , we have:

Mathematical characteristics of simple chemical reactions FIRST ORDER REACTIONS: A B A: The plot of concentration vs time for first order reaction B: The plot of ln concentration vs time for first order reaction

Mathematical characteristics of simple chemical reactions SECOND ORDER REACTIONS: (When both the reactants are the same) The rate law for a second order reaction is given by: Rearranging our variables and integrating, we get the following: The final version of this integrated rate law is given by:

Mathematical characteristics of simple chemical reactions SECOND ORDER REACTIONS: (When both the reactants are different) The rate law is given by: Now, if , then the rate law simplifies to: However, if , the integrated rate law will take the form:

Mathematical characteristics of simple chemical reactions ZERO ORDER REACTIONS: The rate law for zero order is given by: Rearranging and integrating , we have:

Mathematical characteristics of simple chemical reactions

DETERMINATION OF ORDER OF REACTION DIFFERENTIAL METHOD This method was given by Van’t Hoff. Accordind to this method the rate ofan nth order reaction is given by: Taking logs, we have: Thus, if the double logarithmic plot of rate vs concentration gives a straight line then the slope gives the value of n and the intercept gives ln k. ln r vs ln c for an nth order reaction

DETERMINATION OF ORDER OF REACTION METHOD OF INTEGRATION: This method can either be used analytically or graphically. In the analytical method, we assume a certain order for the reaction and calculate the rate constants for the given data. The constancy of the k-values obtained suggests that the assumed order is correct. If the k-values obtained are not constant, we assume a different order for the reaction and again calculate the k- values using the new rate expression and see if k is constant. In the graphical method, if the plot of ln c vs t is a straight line, the reaction is first order. Similarly, the integrated expression for the second-order reaction can be utilized graphically to ascertain if the reaction is second order.

DETERMINATION OF ORDER OF REACTION HALF LIFE METHOD This method was suggested byOstwald. If two experiments are carried out at different initial molar concentrations then, Taking logs, The determination of half lives of a reaction at two different initial concentrations may lead to the determination of n.

DETERMINATION OF ORDER OF REACTION ISOLATION METHOD Sometimes the kinetics of a reaction are studied in successive experiments by keeping the concentrations of all but one reactant in large excess so that the result gives the order with respect to the reactant whose order is changing significantly. Thus the synthesis of HI from H2 and I2 is pseudo first order reaction with respect to H2 in the presence of large excess of I2 and also pseudo first order with respect to I2 in the large excess of H2. Hence, overall it is a second order reaction.

references Physical Chemistry – P.W. Atkins Advance Physical Chemistry- Gurtu & Snehi Advance Physical Chemistry- D.N. Bajpai Modern Physical Chemistry- R.P. Rastogi, K. Singh, K. Kishore, V.K. Srivastava & M.L. Srivastava Essentials of Physical Chemistry- Arun Bahl, B.S. Bahl & G.D. Tuli