Chapter II Chemical Kinetics

Lecture Outlines Introduction Factors affect reaction rate Experimental determination of reaction rate Computational determination of reaction rate (Mass Action Law) Arrhenius Law Orders of Reactions

Chemical Kinetics Studies the rate at which a chemical process occurs Besides information about the speed at which reactions occur, kinetics also sheds light on the reaction mechanism (exactly how the reaction occurs).

Factors That Affect Reaction Rates Physical State of the Reactants In order to react, molecules must come in contact with each other. The more homogeneous the mixture of reactants, the faster the molecules can react.

Factors That Affect Reaction Rates Concentration of Reactants As the concentration of reactants increases, so does the likelihood that reactant molecules will collide.

Factors That Affect Reaction Rates Temperature At higher temperatures, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy.

Factors That Affect Reaction Rates Pressure As the pressure of reactants increases, so does the likelihood that reactant molecules will collide.

Factors That Affect Reaction Rates Presence of a Catalyst Catalysts speed up reactions by changing the mechanism of the reaction.

Classification of chemical reactions according to type of chemical substance Gas phase reaction : Reactants of gaseous phases Liquid phase reaction: Reactants of liquid phases Solid phase reaction : Reactants of solid phases Heterogeneous reaction : Reactants of different phases

Classification of chemical reactions according to speed of reaction Explosive: dealing with determination of conditions under which chemical system undergoes very fast reaction and examination of the reaction mechanism Non-explosive: steady reaction; like many pollutants are formed in reacting zones of rather reaction in various combustion system

Reaction Rates Rate of reactions can be expressed in terms of the concentration ( rate of decrease of concentrations of reactants or the rate of increase of concentrations of products). Reaction rate units are moles/cm3.sec Note : Concentration units are moles/cm3 and it is denoted by [ ]. Concentration of A = [ A ]

Reaction Rates Rates of reactions can be determined by monitoring the change in concentration of either reactants or products as a function of time.

Reaction Rates C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) mole/cm3 In this reaction, the concentration of butyl chloride, C4H9Cl, was measured at various times.

Reaction Rates C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) mole/cm3 mole/cm3.sec The average rate of C4H9Cl over each interval is the change in concentration divided by the change in time: Average rate = [C4H9Cl] t

Reaction Rates C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) mole/cm3 mole/cm3.sec Note that the average rate decreases as the reaction proceeds. This is because as the reaction goes forward, there are fewer collisions between reactant molecules.

Reaction Rates C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) A plot of concentration vs. time for this reaction yields a curve like this. The slope of a line tangent to the curve at any point is the instantaneous rate at that time.

Reaction Rates C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) All reactions slow down over time. Therefore, the best indicator of the rate of a reaction is the instantaneous rate near the beginning.

Reaction Rates and Stoichiometry C4H9Cl(aq) + H2O(l)  C4H9OH(aq) + HCl(aq) In this reaction, the ratio of C4H9Cl to C4H9OH is 1:1. Thus, the rate of disappearance of C4H9Cl is the same as the rate of appearance of C4H9OH. Rate = -[C4H9Cl] t = [C4H9OH]

Mass Action Law A stoichiometric relation describing a one-step chemical reaction     Example

Mass Action Law The law of mass action, which is confirmed experimentally, states that the rate of disappearance of a chemical species i , defined as RRi , is proportional to the product of the concentrations of the reacting chemical species, where each concentration is raised to a power equal to the corresponding stoichiometric coefficient; that is,     k is the proportionality constant called the specific reaction rate coefficient.

Mass Action Law    

Rate Equation      

Arrhenius Equation k = A e−Ea/RT where It is a well-known fact that raising the temperature increases the reaction rate. Quantitatively this relationship between the rate a reaction proceeds and its temperature is determined by the Arrhenius Equation: k = A e−Ea/RT where A : is the frequency factor, a number that represents the likelihood that collisions would occur with the proper orientation for reaction. Ea: is the activation energy, the minimum energy required to start a chemical reaction (J/mole) R: universal gas constant (8.314 J/mole.K) T: Temperature (K)

Arrhenius Equation The Arrhenius equation is often written in the logarithmic form: y = ln k m = - Ea / R b = ln A The activation energy Ea can be determined from the slope m of this line: Ea = - m · R . The value of the y-intercept corresponds to ln A. Hint An accurate determination of the activation energy requires at least three runs completed at different reaction temperatures. The temperature intervals should be at least 5 °C.

Arrhenius Equation Eq.(1) Eq.(2) Subtracting two equations The activation energy can also be found algebraically by substituting two rate constants (k1, k2) and the two corresponding \temperatures (T1, T2) into the Arrhenius Equation Eq.(1) Eq.(2) Subtracting two equations Rearrangement

Zero Order of reaction rate [A] A reaction is of zero order when the rate of reaction is independent of the concentration of materials. The rate of reaction is a constant. k = rate, 0th order [A] rate Rearranging Integrating

First Order of reaction For a general unimolecular reaction where A is a reactant and P is a product, the reaction rate expression for a first order reaction is Separation of the variables Integrating

First Order of reaction [A] = [A]o e – k t t½ This means that the concentration of A decreases exponentially as a function of time. [A]=1/2[A]o The rate constant k can also be determined from the half-life t1/2. Half-life time is the time it takes for the concentration to fall from [ A ]o to [ A ]o / 2 ==> [ A ] = 1 / 2 [ A ]o.

Second Order of reaction For the general case of a reaction between A and B, such that the rate of reaction will be given by : Case 1 Initial concentrations of the two reactants are equal Separating the variables and integrating 2nd order 1st order

Second Order of reaction Case 2 Starting concentrations of the two reactants are different If [ A ]o and [ B ]o are different the variable, x is used which represent the reacted part of A or B. [ A ] = [ A ]o - x [ B ] = [ B ]o - x To integrate, perform a partial fraction expansion d [ A ] = -dx