Reaction Mechanisms Arrhenius Equation Reaction Mechanisms Some reactions

Reaction Mechanisms & Arrhenius Equation

Reaction Mechanisms Ø Some reactions are not represented in the reaction equation; such as, - Absorbing light energy - Colliding to the walls of the container Many reactions proceed through a sequence of steps to arrive at the products Ø Each step is called an elementary reaction and occurs through collision of atoms, ions and molecules. Ø

Reaction Mechanisms Ø The slowest step in a reaction mechanism is called the Rate-determining Step Ø In multistep reactions, increasing the concentration of reactants at any steps other than the rate-determining step will not increase the rate of reaction Ø A chemical species that form and then are consumed in the reaction is called Reaction Intermediates

Rate Equation Ø Ø m. X + n. Y -----> products of reaction or intermediates then r α [X]m [Y]n r = k[X]m [Y]n When writing the reaction mechanism, there are three rules: - each step must be elementary, with no more than three reactants - The rate-determining step must be consistent with the rate equation - The elementary steps must all add up to be the overall equation

� Elementary reactions (Molecularity) � Unimolecular; Decomposition (ex. N 2 O 5(g) NO 2(g) + NO 3(g)) rate = k[N 2 O 5] � Bimolecular; Collision of 2 atoms, ions or molecules (ex. NO(g) + O 3(g) NO 2(g) + O 2(g)) rate = k[No][O 3] � Termolecular; Simultaneous collision of 3 molecules (ex. 2 I(g) + Ar(g) I 2(g) + Ar(g) ) rate = k[I][I][Ar] = k[I]2[Ar]

� Reaction mechanism is a detailed sequence of elementary reactions, with their rate, that are combined to yield the overall reaction. � Consider the mechanism: 1) Cl 2(g) 2 Cl(g) 2) Cl(g) + CHCl 3(g) HCl(g) + CCl 3 (g) 3) CCl 3 (g) + Cl (g) CCl 4(g) � Some of the possible questions are…

a) What's the molecularity of each step? 1) Unimolecular 2) Bimolecular 3) Bimolecular b) Write the overall equation for the reaction Cl 2(g) + CHCl 3(g) HCl(g) + CCl 4(g) c) Identify the reaction intermediate(s) Cl(g) & CCl 3

The Arrhenius Equation To explain the large effect of temperature and catalysis, the Arrhenius Equation is used to account for their effects k = Ae-Ea/RT Ea is the activation energy (J) A is constant related to the geometry of molecule R is the gas constant (8. 314 J/(mol • K)) T is the temperature (K) Ø the answer k is the rate constant for the rate law equation r = k[A]n[B]m Ø

� By taking ln (natural log) to each side, ln k = -Ea/RT + ln A � Arrhenius equation is written for the rate constant determined at each temperature giving, ln k 1 = -Ea/RT 1 + ln A ln k 2 = -Ea/RT 2 + ln A � Subtracting second equation from the first, ln(k 1/k 2) = -Ea/R(1/T 1 – 1/T 2) � The rate and the rate constant are directly proportional to each other as long as the concentrations are held constant.

Examples � At 200 K the rate constant for a reaction is 3. 5 X 10 -3 s-1 , and at 250 K the rate constant is 4. 0 X 10 -3 s-1. What is the activation energy? Ea = 1. 11 KJ/mol � What is the rate of reaction at 450 o. C if the reaction rate is 6. 75 X 10 -6 mol/(L*s) at 25 o. C? The activation energy was previously determined to be 35. 5 k. J/mol. The rate of reaction at 450 o. C is 3. 05 X 10 -2 mol/(L*s)

The Arrhenius Equation Ø To test the answer for reasonableness, two principles must be remembered: 1) The larger rate constant (or rate) will always be associated with the higher temperature 2) The activation energy always has a positive sign.

Summary Reactions that contain more than 3 molecules colliding occurs in multi-steps Ø Each elementary step should only have 3 or less reactants Ø r = k[A]n[B]m Ø k = Ae-Ea/RT Ø Temperature and activation energy affects the value of k exponentially Ø